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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Unexplained Fe, Ni and S anomalies in CV chondrite components

Large negative anomalies in Fe, Co, Ni, S and Se are present in Allende Type B Ca-Al-rich inclusions (CAI's). Based on compilations of all the known published analyses, Allende chondrules, aggregates and other types of CAI's also display anomalies. These observations show that: (1) since Fe, Co, Ni, S and Se are more depleted than elements bracketing them in volatility (such as Pt and Au, and Su and Cd), the anomalies were not produced during the volatility dependent, high temperature CAI forming processes; (2) since Pt, Au, Ge and other siderophiles are not as depleted as Fe, Co and Ni, the anomalies are not due to a metal/silicate fractionation; (3) the association of Fe, Co, and Ni anomalies with S and Se anomalies suggests that the anomalies are due to the removal of FeNi sulfide; and (4) since these anomalies occur in all types of Allende inclusions, aggregates and chondrules, the Allende parental material must have undergone sulfide loss before the formation of these components.

Wark, D. A.↗
NASA NTRS1985

Long-wavelength magnetic and gravity anomaly correlations on Africa and Europe

Preliminary MAGSAT scalar magnetic anomaly data were compiled for comparison with long-wavelength-pass filtered free-air gravity anomalies and regional heat-flow and tectonic data. To facilitate the correlation analysis at satellite elevations over a spherical-Earth, equivalent point source inversion was used to differentially reduce the magnetic satellite anomalies to the radial pole at 350 km elevation, and to upward continue the first radial derivative of the free-air gravity anomalies. Correlation patterns between these regional geopotential anomaly fields are quantitatively established by moving window linear regression based on Poisson's theorem. Prominent correlations include direct correspondences for the Baltic shield, where both anomalies are negative, and the central Mediterranean and Zaire Basin where both anomalies are positive. Inverse relationships are generally common over the Precambrian Shield in northwest Africa, the Basins and Shields in southern Africa, and the Alpine Orogenic Belt. Inverse correlations also presist over the North Sea Rifts, the Benue Rift, and more generally over the East African Rifts. The results of this quantitative correlation analysis support the general inverse relationships of gravity and magnetic anomalies observed for North American continental terrain which may be broadly related to magnetic crustal thickness variations.

Vonfrese, R. R. B.↗
NASA NTRS1985

The resolution of a magnetic anomaly map expected from GRM data

Data from the MAGSAT mission were used to derive a global scalar magnetic anomaly map at an average altitude of about 400 km. It was possible to work with 2 data sets corresponding to dawn and dusk. The anomalies which were repeatable at dawn and at dusk was identified and the error limits of these anomalies were estimated. The repeatable anomalies were downward continued to about 10 km altitude. The anomalies over Canada were correlated quantitatively with bandpass filtered magnetic anomalies derived from aeromagnetic surveys. The close correlation indicates that the repeatable anomalies detected from orbit are due to geological causes. This correlation supports the geological significance of the global anomaly map.

Strangway, D. W.↗
NASA NTRS1994

Simulated life cycles of persistent anticyclonic anomalies over the North Pacific: Role of synoptic-scale eddies

This study examines the role of synoptic-scale eddies during the development of persistent anticyclonic height anomalies over the central North Pacific in a general circulation model under perpetual January conditions. The General Circulation Model (GCM) replicates the basic characteristics of the evolution of the anomaly patterns found in observations. The life cycle is characterized by the rapid establishment of the major anomaly center and considerably longer maintenance and decay phases, which include the development of downstream anomaly centers. The simulation also shows a realistic evolution of synoptic-scale activity beginning with enhanced activity off the east coast of Asia prior to onset, followed by a northward shift of the Pacific storm track, which lasts throughout the maintenance phase. The initial enhancement of synoptic-scale eddy activity is associated with a large-scale cyclonic anomaly that developes over Siberia several days prior to the onset of the main anticyclonic anomaly over the central North Pacific. The observations, however, show considerable interdecadel variability in the details of the composite onset behavior; it is unclear whether this variability is real or whether it reflects differences in the data assimilation systems. The role of the time mean flow and synoptic-scale eddies in the development of the persistent Pacific anomalies is studied within the context of a kinetic energy budget in which the flow is decomposed into the time-mean, low-frequency (timescales longer than 10 days), and synoptic (timescales less than 6 days) components. The budget, which is carried out for the simulation at 500 mb, shows that the initial growth of the persistent anticyclonic anomalies is associated with barotropic conversions of energy, with approximately equal contributions coming from the mean flow and the synoptic-scale eddies. After onset the barotropic conversion from the mean flow dominates, whereas the decay phase is associated with baroclinic processes within the low-frequency flow.

Higgins, R. W.↗
NASA NTRS1994

Contributions of cretaceus quiet zone natural remanent magnetization to Magsat anomalies in the Southwest Indian Ocean

The Magsat magnetic anomalies over the Southwest Indian Ocean are modeled using a combination of induced plus viscous remanent magnetization (IM/VRM) and natural remanent magnetization (NRM). Two broad, roughly parallel, SW to NE trending triple-peaked positive anomalies dominate the region, one lying south of Africa and the other north of Antarctica. Although these anomaly peaks generally correspond with the Agulhas Plateau/Maud Rise, Mozambique Plateau/Astrid Ridge, and Madagascar Ridge/Conrad Rise conjugate pairs, the IM/VRM contribution from structural characteristics (i.e., crustal thickness) accounts for only about 20% of the anomaly amplitudes. A spatially variable but observationally constrained NRM contribution in Cretaceous Quiet Zone (KQZ) crust is required to account for the location, shape, and amplitude contrast of these anomalies. Many crustal features in the Southwest Indian Ocean near Antarctica have little geophysical data to constrain their structure but do hagve tectonic conjugates near Africa for which much more geophysical data are generally available. Using geophysical and geological constraints from one member to model the magnetization structure of its conjugate reproduces the observed Magsat reduced-to-pole anomalies over both structures very well. This suggests that no significant alteration in their magnetization structure has occurred since the features split. Models of these conjugate structures show that IM/VRM reproduces the Magsat anomalies associated with non-KQZ crust but that both IM/VRM and a dominant NRM component are required to explain the anomalies associated with KQZ crust.

Fullerton, Lawrence G.↗
NASA NTRS2001

Southern Ocean Climate and Sea Ice Anomalies Associated with the Southern Oscillation

The anomalies in the climate and sea ice cover of the Southern Ocean and their relationships with the Southern Oscillation (SO) are investigated using a 17-year of data set from 1982 through 1998. We correlate the polar climate anomalies with the Southern Oscillation index (SOI) and examine the composites of these anomalies under the positive (SOI > 0), neutral (0 > SOI > -1), and negative (SOI < -1) phases of SOL The climate data set consists of sea-level pressure, wind, surface air temperature, and sea surface temperature fields, while the sea ice data set describes its extent, concentration, motion, and surface temperature. The analysis depicts, for the first time, the spatial variability in the relationship of the above variables and the SOL The strongest correlation between the SOI and the polar climate anomalies are found in the Bellingshausen, Amundsen and Ross sea sectors. The composite fields reveal anomalies that are organized in distinct large-scale spatial patterns with opposing polarities at the two extremes of SOI, and suggest oscillating climate anomalies that are closely linked to the SO. Within these sectors, positive (negative) phases of the SOI are generally associated with lower (higher) sea-level pressure, cooler (warmer) surface air temperature, and cooler (warmer) sea surface temperature in these sectors. Associations between these climate anomalies and the behavior of the Antarctic sea ice cover are clearly evident. Recent anomalies in the sea ice cover that are apparently associated with the SOI include: the record decrease in the sea ice extent in the Bellingshausen Sea from mid- 1988 through early 199 1; the relationship between Ross Sea SST and ENSO signal, and reduced sea ice concentration in the Ross Sea; and, the shortening of the ice season in the eastern Ross Sea, Amundsen Sea, far western Weddell Sea, and the lengthening of the ice season in the western Ross Sea, Bellingshausen Sea and central Weddell Sea gyre over the period 1988-1994. Four ENSO episodes over the last 17 years contributed to a negative mean in the SOI (-0.5). In each of these episodes, significant retreats in the Bellingshausen/Amundsen Sea were observed providing direct confirmation of the impact of SO on the Antarctic sea ice cover.

Kwok, R.↗
NASA NTRS2004

Magsat to CHAMP: Magnetic Satellite Explorations of Lithospheric Anomalies over Kursk, Bangui and the Antarctic

We compare crustal magnetic anomaly maps over the Kursk (Russia) and Bangui (Central African Republic) isolated anomalies and the Antarctic derived from the Magsat, \Orsted and CHAMP satellite fields. We wish to demonstrate how progress in satellite magnetic missions has improved the recovery of the crustal magnetic field. The 6-month long Magsat mission of 25 years ago generated two major methods of processing satellite magnetic anomaly data for lithospheric studies. The first was a global perspective using spherical harmonics that emphasize the more regional and global lithospheric fields. However, these fields commonly do not resolve local anomaly features in any detail. Therefore a second procedure involved the use of the individual satellite orbit or track data to recover small-scale anomalies on a regional scale. We present results over prominent magnetic anomalies such as Kursk, Bangui and the large Antarctic continent that demonstrate how the various analysis methods affect the recovery of crustal anomalies. The more recent \Orsted and CHAMP missions are successfully recording data with an improved accuracy and with full spatial and temporal coverage. We show and interpret the total magnetic intensity anomaly maps over these areas from all three satellite magnetometer data sets.

Kim, H.↗
NASA NTRS2006

Spatial and Temporal Coherence of SeaWiFS Chlorophyll Concentration Anomalies in the North Atlantic Bloom (1998-2005) Examined with Giovanni

The availability of climatological chlorophyll-a concentration data products from the SeaWiFS mission spanning the eight-year mission period allowed the creation of a climatological anomaly analysis function in Giovanni, the GES DISC Interactive Online Visualization and ANalysis Infrastructure. This study utilizes the Giovanni anomaly analysis function to examine mesoscale anomalies in the North Atlantic Ocean during the springtime North Atlantic Bloom. This examination indicates that areas exhibiting positive anomalies and areas exhibiting negative anomalies are coherent over significant spatial scales, with relatively abrupt boundaries between areas with positive and negative anomalies. Year-to-year variability in anomaly "intensity" can be caused by either variability in the temporal occurrence of the bloom peak or by variability in the peak chlorophyll concentration in a particular area. The study will also discuss the feasibility of combining chlorophyll anomaly analysis with other data types.

Acker, James G.↗
NASA NTRS2021

Inversion of Magnetic Measurements of the Swarm A Satellite of the Bangui Magnetic Anomaly

We wanted to make a satellite altitude magnetic anomaly map of the large magnetic anomaly in the Central African Republic, the Bangui magnetic anomaly, with data from the Swarm satellites. In the first part of our study, we summarize the earlier investigations and their interpretation. In the second we discuss our data processing applied to produce a magnetic anomaly map. We used the IGRF 12th to remove the long-wavelength regional anomalies. We will use an inverse procedure, which always requires a solution of the direct problem, and a horizontal polygonal prism given in the Descartes coordinate system. For this, reason the total magnetic anomaly was transformed into the Descartes coordinate system. The magnetization and its direction were used from our previous paper. The inverse problem is solved by the Simplex procedure. Our selected polygon has 14 geometrical parameters however, the inverse problem that is the numerical determination of the minimum problem is solved in the 14 dimensions. The result of our inverse problem was the 12 horizontal coordinates and the two upper and lower data of the polygon. The origin of the Bangui anomaly has been discussed in several scientific reports, either as a deep crustal tectonic feature or the result of a large external impactor. However, according to our inversion computations we cannot make any unambiguous finding for the origin of this feature. The inaccuracy in our total anomaly map is given by the Gaussian error propagation.

KI Kis↗
NASA NTRS2022

The Cooling Loop A Anomaly of 2013: A Case Study in Human-Systems Resilience

Throughout the history of human spaceflight, NASA has employed an operational paradigm of 24/7 dependence on experts in Mission Control Center (MCC). In addition to nominal flight control and mission operations, these 85+ experts per shift manage anomaly detection, diagnosis, and response, and support the crew in real-time in performing maintenance and repair, procedure execution, and other complex mission operations. Future long-duration exploration missions (LDEMs) beyond low-Earth orbit (LEO) will not operate successfully using this same Human-Systems Integration Architecture (HSIA) where crew rely on ground controllers, have ready access to resupply, and have a fallback plan of evacuation. As distance from Earth increases and the communication delay grows, crews will need to respond independently and adequately to time-critical vehicle malfunctions. It will not always be sufficient or even possible to ‘safe the system’ and then wait upon ground intervention. A new and radically different HSIA is needed to accommodate the paradigm shift of deep-space travel. Historical International Space Station (ISS) data show that for a 30-day mission, the likelihood of a high-consequence vehicle anomaly of uncertain origin that requires rapid response is greater than 10%. The likelihood of such an event is 50% by the fourth month of the mission, and it grows exponentially with time. Our team has conducted in-depth investigations into these events and their corresponding anomaly resolution activities. Using MCC and Mission Evaluation Room (MER) anomaly resolution artifacts (including meeting summaries, caution and warning data, and ISS daily summaries), we created timelines detailing ground actions and in-orbit events for two significant anomalies. We then mapped these timelines onto Mars transit conditions, introducing a ground-crew communications time delay and shifting immediate response, time-critical task execution, and vehicle commanding to the crew. In detailing successful anomaly resolution in transit to Mars, the timelines highlight where effective resolution requires drastically evolved onboard capabilities. Though this research has yielded a rich data set based on ground response in past missions, there is still insufficient knowledge to assess the potential impact of inflight anomalies on a small autonomous crew on future LDEMs beyond LEO. To begin building an evidence base that will inform future HSIA standards and requirements, we are developing an approach to systematically capture crew anomaly response and procedure execution during early Artemis missions. Being the first human spaceflight beyond LEO since Apollo, early Artemis missions provide a rare and unique opportunity to serve as a testbed for Mars missions. Our work aims to capitalize on planned data collection to derive crew operational responses to anomalous events in real-time. Our team is also researching the level of simulation fidelity required for empirically validating proposed HSIA standards and evaluating HSIA implementations for LDEMs beyond LEO. This work will produce a trade space study of HSIA simulation objectives and fidelity requirements. Ultimately, these research efforts will assist in developing the standards and technologies needed to build a next-generation HSIA for LDEMs beyond LEO.

human-systems integration architecture↗
NASA NTRS2023

Using Orbiting Carbon Observatory-2 (OCO-2) column CO2 retrievals to rapidly detect and estimate biospheric surface carbon flux anomalies

The global carbon cycle is experiencing continued perturbations via increases in atmospheric carbon concentrations, which are partly reduced by terrestrial biosphere and ocean carbon uptake. Greenhouse gas satellites have been shown to be useful in retrieving atmospheric carbon concentrations and observing surface and atmospheric CO2 seasonal-to-interannual variations. However, limited attention has been placed on using satellite column CO2 retrievals to evaluate surface CO2 fluxes from the terrestrial biosphere without advanced inversion models at low latency. Such applications could be useful to monitor, in near real time, biosphere carbon fluxes during climatic anomalies like drought, heatwaves, and floods, before more complex terrestrial biosphere model outputs and/or advanced inversion modelling estimates become available. Here, we explore the ability of Orbiting Carbon Observatory-2 (OCO-2) column-averaged dry air CO2 (XCO2) retrievals to directly detect and estimate terrestrial biosphere CO2 flux anomalies using a simple mass-balance approach. An initial global analysis of surface–atmospheric CO2 coupling and transport conditions reveals that the western US, among a handful of other regions, is a feasible candidate for using XCO2 for detecting terrestrial biosphere CO2 flux anomalies. Using the CarbonTracker model reanalysis as a test bed, we first demonstrate that a well-established mass-balance approach can estimate monthly surface CO2 flux anomalies from XCO2 enhancements in the western United States. The method is optimal when the study domain is spatially extensive enough to account for atmospheric mixing and has favorable advection conditions with contributions primarily from one background region. We find that errors in individual soundings reduce the ability of OCO-2 XCO2 to estimate more frequent, smaller surface CO2 flux anomalies. However, we find that OCO-2 XCO2 can often detect and estimate large surface flux anomalies that leave an imprint on the atmospheric CO2 concentration anomalies beyond the retrieval error/uncertainty associated with the observations. OCO-2 can thus be useful for low-latency monitoring of the monthly timing and magnitude of extreme regional terrestrial biosphere carbon anomalies.

Andrew F. Feldman↗
NASA NTRSDate not supplied

Anomaly Detection for the Roman Space Telescope Wide Field Instrument’s Science Data Processing Pipeline

The Roman Space Telescope (RST) Wide Field Instrument (WFI) will be utilizing a preliminary Science Data Processing (SDP) pipeline during its Integration and Test, and to some extent during Operations, to track basic statistics and identify known features such as cosmic rays, snowballs as well as possible anomalies in raw detector data. In our detectors, these anomalies appear as jumps in the ramp of a readout and are classified as cosmic rays if they appear as a streak or snowballs if they’re more circular. The WFI employs an array of 18 H4RG-10 detectors that collect image samples. Each set of raw frames within a non-destructive exposure is packaged by the SDP pipeline into image cubes for each detector. Each cube is a time series of 4096 × 4096 accumulating pixel frames. The preliminary analysis pipeline is used to locate anomalies in these time-series accumulation frames and identify the type of anomaly, either natural phenomena or detector characteristic. To compare different methods, we’ve implemented both heuristic-based and data-driven methods to identify anomalies. For the heuristic-based approach, we identify snowballs and cosmic rays by the size and shape of outlier pixel clusters between consecutive frames. For data driven methods, we evaluated a Convolutional Neural Network (CNN) model, and more traditional methods like Principal Component Analysis (PCA). CNN is a supervised learning/classification method. Thus, we used a labeled dataset of anomalies to perform segmentation of the image and identify anomalies. We used previously identified cosmic rays and snowballs to measure the accuracy and efficiency of the mentioned approaches. In evaluating these methods, we aim to pick the best fit for the SDP pipeline’s anomaly detection in terms of both performance and runtime.

Paul Horton↗
NASA NTRS2008

Anomaly Trends for Missions to Mars: Mars Global Surveyor and Mars Odyssey

The long term flight operations of the Mars Global Surveyor and Mars Odyssey spacecraft give us an excellent chance to examine the operations of two long lived spacecraft in orbit around Mars during overlapping time periods. This study examined the anomalies for each mission maintained for NASA at the Jet Propulsion Laboratory. By examining the anomalies each mission encountered during their multiyear missions, trends were identified related to when anomalies occurred during each mission, the types of anomalies encountered, and corrective actions taken to mitigate the effects of the anomalies. As has been discovered in previous studies the numbers of anomalies directly correlate with mission activity and show a decreasing trend with elapsed mission time. Trend analysis also identified a heavy emphasis on software as the source or solution to anomalies for both missions.

Mars↗
NASA NTRSDate not supplied

Multiclass Flight Anomaly Detection Using Sensor Fusion Based on Dempster-Shafer Theory

As aviation systems in commercial operations continue to grow in complexity, the anomalies exhibited by these systems become more elaborate and difficult to detect. To address the challenge of detecting these complex anomalies, deep learning models have been used extensively in aviation anomaly detection studies, at the expense of end-user interpretability. Aiming to maintain the same level of interpretability as traditional threshold-exceedance methods, we continue our development of prediction models using ordinal patterns and their distributions throughout the flight. Specifically, this study extends our work into multiclass anomaly detection using sensor fusion based on Dempster-Shafer theory (DST), a second-order probability theory used to combine information from different sources of evidence. Our approach uses DST toreduce the uncertainty in the class predictions of an ensemble of classifiers. These classifiers rely on the similarity between flight data and class templates to make a prediction of the state of the aircraft. Our approach aims to take advantage of simple models trained on interpretable features (ordinal patterns) to correctly predict an anomaly and identify the flight dynamics linked to the anomaly. Our results show an improvement when using DST-based sensor fusion over simple majority voting. Additionally, our results provide insight into aircraft states linked to rare high-risk anomalies.

Risk detection↗
DOE OSTI2024

Coincident learning for unsupervised anomaly detection of scientific instruments

Abstract Anomaly detection is an important task for complex scientific experiments and other complex systems (e.g. industrial facilities, manufacturing), where failures in a sub-system can lead to lost data, poor performance, or even damage to components. While scientific facilities generate a wealth of data, labeled anomalies may be rare (or even nonexistent), and expensive to acquire. Unsupervised approaches are therefore common and typically search for anomalies either by distance or density of examples in the input feature space (or some associated low-dimensional representation). This paper presents a novel approach called coincident learning for anomaly detection (CoAD), which is specifically designed for multi-modal tasks and identifies anomalies based on coincident behavior across two different slices of the feature space. We define an unsupervised metric, F ^ β , out of analogy to the supervised classification F β statistic. CoAD uses F ^ β to train an anomaly detection algorithm on unlabeled data , based on the expectation that anomalous behavior in one feature slice is coincident with anomalous behavior in the other. The method is illustrated using a synthetic outlier data set and a MNIST-based image data set, and is compared to prior state-of-the-art on two real-world tasks: a metal milling data set and our motivating task of identifying RF station anomalies in a particle accelerator.

43 PARTICLE ACCELERATORS↗
NASA NTRSDate not supplied

Multiclass Flight Anomaly Detection Using Sensor Fusion Based on Dempster-Shafer Theory

As aviation systems in commercial operations continue to grow in complexity, the anomalies exhibited by these systems become more elaborate and difficult to detect. To address the challenge of detecting these complex anomalies, deep learning models have been used extensively in aviation anomaly detection studies, at the expense of end-user interpretability. Aiming to maintain the same level of interpretability as traditional threshold-exceedance methods, we continue our development of prediction models using ordinal patterns and their distributions throughout the flight. Specifically, this study extends our work into multiclass anomaly detection using sensor fusion based on Dempster-Shafer theory (DST), a second-order probability theory used to combine information from different sources of evidence. Our approach uses DST to reduce the uncertainty in the class predictions of an ensemble of classifiers. These classifiers rely on the similarity between flight data and class templates to make a prediction of the state of the aircraft. Our approach aims to take advantage of simple models trained on interpretable features (ordinal patterns) to correctly predict an anomaly and identify the flight dynamics linked to the anomaly. Our results show an improvement when using DST-based sensor fusion over simple majority voting. Additionally, our results provide insight into aircraft states linked to rare high-risk anomalies.

Risk detection↗
DOE OSTI2025

Robust Spectral Anomaly Detection in EELS Spectral Images via 3D Convolutional Variational Autoencoders

Abstract A 3D Convolutional Variational Autoencoder (3D‐CVAE) is introduced for automated anomaly detection in electron energy‐loss spectroscopy spectrum imaging (EELS‐SI) data. This approach leverages the full 3D structure of EELS‐SI data to detect subtle spectral anomalies while preserving both spatial and spectral correlations across the datacube. By employing cross‐entropy loss and training on bulk spectra, the model learns to reconstruct bulk features characteristic of the defect‐free material. In exploring methods for anomaly detection, both the 3D‐CVAE approach and principal component analysis (PCA) are evaluated, testing their performance using FeL‐edge ΔEpeak shifts designed to simulate material defects. These results show that 3D‐CVAE achieves superior anomaly detection and maintains consistent performance across various shift magnitudes. The method demonstrates clear bimodal separation between bulk and anomalous spectra, enabling reliable classification. Further analysis verifies that lower‐dimensional representations are robust to anomalies in the data. While performance advantages over PCA diminish with decreasing anomaly concentration, our method maintains high reconstruction quality even in challenging, noise‐dominated spectral regions. This approach provides a robust framework for unsupervised automated detection of spectral anomalies in EELS‐SI data, particularly valuable for analyzing complex material systems.

Chemistry↗
DOE OSTI2024

Anomalies of 4d SpinG theories

Abstract We consider ’t Hooft anomalies of four-dimensional gauge theories whose fermion matter content admits Spin G (4) generalized spin structure, withGeither gauged or a global symmetry. We discuss methods to directly computew 2 ∪w 3 ’t Hooft anomalies involving Stiefel-Whitney classes of gauge and flavor symmetry bundles that such theories can have on non-spin manifolds, e.g.M 4 = ℂℙ 2 . Such anomalies have been discussed for SU(2) gauge theory with adjoint fermions, where they were shown to give an effect that was originally found in the Donaldson-Witten topological twist of$$ \mathcal{N} $$ N = 2 SYM theory. We directly compute these anomalies for a variety of theories, including generalGgauge theories with adjoint fermions, SU(2) gauge theory with fermions in general representations, and Spin(N) gauge theories with fundamental matter. We discuss aspects of matching these and other ’t Hooft anomalies in the IR phase where global symmetries are spontaneously broken, in particular for generalG gauge theory withN f adjoint Weyl fermions. For example, in the case ofN f = 2 we discuss anomaly matching in the IR phase consisting of$$ {h}_{G_{\textrm{gauge}}}^{\vee } $$ h G gauge ∨ copies of a ℂℙ 1 non-linear sigma model, including for thew 2 w 3 anomalies when formulated with$$ {\textrm{Spin}}_{\textrm{SU}{(2)}_{\textrm{global}}}(4) $$ Spin SU 2 global 4 structure.

Physics↗