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49 records · Page 3

Soft and collinear limits in $\mathcal{N}$ = 8 supergravity using double copy formalism

It is known that $\mathcal{N}$ = 8 supergravity is dual to $\mathcal{N}$ = 4 super Yang-Mills (SYM) via the double copy relation. Using the explicit relation between scattering amplitudes in the two theories, we calculate the soft and collinear limits in $\mathcal{N}$ = 8 supergravity from know results in $\mathcal{N}$ = 4 SYM. In our application of double copy, a particular self-duality condition is chosen for scalars that allows us to constrain and determine the R-symmetry indices of the supergravity states in the collinear limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Liouville theory, AdS 2 string, and three-point functions

This is a write-up of the lectures given in Young Researchers Integrability School 2017. The main goal is to explain the connection between the ODE/IM correspondence and the classical integrability of strings in AdS. As a warm up, we first discuss the classical three-point function of the Liouville theory. The starting point is the well-known fact that the classical solutions to the Liouville equation can be constructed by solving a Schrodinger-like differential equation. We then convert it into a set of functional equations using a method similar to the ODE/IM correspondence. The classical three-point functions can be computed directly from these functional equations, and the result matches with the classical limit of the celebrated DOZZ formula. We then discuss the semi-classical three-point function of strings in AdS 2 and show that one can apply a similar idea by making use of the classical integrability of the string sigma model on AdS 2 . Furthermore, the result is given in terms of the "massive" generalization of Gamma functions, which show up also in string theory on pp-wave backgrounds and the twistorial generalization of topological string.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Two-loop HTL-resummed thermodynamics for $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory

We compute the two-loop hard-thermal-loop (HTL) resummed thermodynamic potential for \( \mathcal{N} \) = 4 supersymmetric Yang-Mills (SYM). Our final result is manifestly gauge-invariant and was renormalized using only simple vacuum energy, gluon mass, scalar mass, and quark mass counter terms. The HTL mass parameters m D , M D , and m q are then determined self-consistently using a variational prescription which results in a set of coupled gap equations. Based on this, we obtain the two-loop HTL-resummed thermodynamic functions of \( \mathcal{N} \) = 4 SYM. We compare our final result with known results obtained in the weak- and strong-coupling limits. We also compare to previously obtained approximately self-consistent HTL resummations and Padé approximants. We find that the two-loop HTL resummed results for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2 and is in agreement with previous approximately self-consistent HTL resummation results for λ ≲ 6.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Holography from lattice $\mathcal{N}$ = 4 super Yang-Mills

In this paper we use lattice simulation to study four dimensional $\mathcal{N}$ = 4 super Yang-Mills (SYM) theory. We have focused on the three color theory on lattices of size 12 4 and for ’t Hooft couplings up to λ = 40.0. Our lattice action is based on a discretization of the Marcus or GL twist of $\mathcal{N}$ = 4 SYM and retains one exact supersymmetry for non-zero lattice spacing. We show that lattice theory exists in a single non-Abelian Coulomb phase for all ’t Hooft couplings. Furthermore the static potential we obtain from correlators of Polyakov lines is in good agreement with that obtained from holography — specifically the potential has a Coulombic form with a coefficent that varies as the square root of the ’t Hooft coupling.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

One-loop central-emission vertex for two gluons in $\mathcal{N}$ = 4 super Yang-Mills theory

A necessary ingredient for extending the BFKL equation to next-to-next-to-leading logarithmic (NNLL) accuracy is the one-loop central emission vertex (CEV) for two gluons which are not strongly ordered in rapidity. Here we consider the one-loop six-gluon amplitude in $\mathcal{N}$ = 4 super Yang-Mills (SYM) theory in a central next-to-multi-Regge kinematic (NMRK) limit, we show that its dispersive part factorises in terms of the two-gluon CEV, and we use it to extract the one-loop two-gluon CEV for any helicity configuration within this theory. This is a component of the two-gluon CEV in QCD. Although computed in the NMRK limit, both the colour structure and the kinematic dependence of the two-gluon CEV capture much of the complexity of the six-gluon amplitudes in general kinematics. In fact, the transcendental functions of the latter can be conveniently written in terms of impact factors, trajectories, single-emission CEVs and a remainder, which is a function of the conformally invariant cross ratios which characterise the six-gluon amplitudes in planar $\mathcal{N}$ = 4 SYM. Finally, as expected, in the MRK limit the two-gluon CEV neatly factorises in terms of two single-emission CEVs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Revisiting single inclusive jet production: timelike factorization and reciprocity

Factorization theorems for single inclusive jet production play a crucial role in the study of jets and their substructure. In the case of small radius jets, the dynamics of the jet clustering can be factorized from both the hard production dynamics, and the dynamics of the low scale jet substructure measurement, and is described by a matching coefficient that can be computed in perturbative Quantum Chromodynamics (QCD). A proposed factorization formula describing this process has been previously presented in the literature, and is referred to as the semi-inclusive, or fragmenting jets formalism. By performing an explicit two-loop calculation, we show the inconsistency of this factorization formula, in agreement with another recent result in the literature. Building on recent progress in the factorization of single logarithmic observables, and the understanding of reciprocity, we then derive a new all-order factorization theorem for inclusive jet production. The use of a jet algorithm, being only a modification of the infrared structure of the measurement, modifies the structure of convolutions in the factorization theorem, as compared to inclusive fragmentation, but maintains the universality of the inclusive hard function and its associated Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution, which are ultraviolet properties. However, the non-trivial structure of convolutions in the factorization theorem implies that the jet functions exhibit a modified evolution. We perform an explicit two-loop calculation of the jet function in both N = 4 super Yang-Mills (SYM), and for all color channels in QCD, finding exact agreement with the structure derived from our renormalization group equations. In addition, we derive several new results, including an extension of our factorization formula to jet substructure observables, a jet algorithm definition of a generating function for the energy correlators, and new results for exclusive jet functions. Our results are a key ingredient for achieving precision jet substructure at colliders.

Effective Field Theories↗

Does a Quark-Gluon Plasma Feature an Extended Hydrodynamic Regime?

Here we investigate the response of the near-equilibrium quark-gluon plasma (QGP) to perturbation at nonhydrodynamic gradients. We propose a conceivable scenario under which sound mode continues to dominate the medium response in this regime. Such a scenario has been observed experimentally for various liquids and liquid metals. We further show that this extended hydrodynamic regime (EHR) indeed exists for both the weakly coupled kinetic equation in the relaxation time approximation (RTA) and the strongly coupled $\mathcal{N}$ = 4 supersymmetric Yang-Mills (SYM) theory. We construct a simple but nontrivial extension of Müller-Israel-Stewart (MIS) theory—namely MIS*—and demonstrate that it describes the EHR response for both the RTA and SYM theory. This indicates that MIS* equations can potentially be employed to search for QGP EHR via heavy-ion collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

\( \mathcal{N} \) = 4 supersymmetric Yang-Mills thermodynamics to order λ 2

We calculate the resummed perturbative free energy of \( \mathcal{N} \) = 4 supersymmetric Yang-Mills in four spacetime dimensions (SYM 4 , 4 ) through second order in the ’t Hooft coupling λ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over SYM 4 , 4 ring diagrams. Non-analytic terms at \( \mathcal{O} \) ( λ 3 / 2 ) and \( \mathcal{O} \) ( λ 2 log λ ) are generated by dressing the A 0 and scalar propagators. The gauge-field Debye mass m D and the scalar thermal mass M D are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of SYM 4 , 4 to \( \mathcal{O} \) ( λ 2 ). We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large- N c strong-coupling result. Our results suggest that the \( \mathcal{O} \) ( λ 2 ) weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗

The lion, the witch, and the wormhole: ensemble averaging the symmetric product orbifold

Abstract We consider the ensemble average of two dimensional symmetric product orbifold CFTs Sym N (𝕋 D ) over the Narain moduli space. We argue for a bulk dual given byNcopies of an abelian Chern-Simons theory coupled to topological gravity, endowed with a discrete gauge symmetry exchanging theNcopies. As a check of this proposal, we calculate the ensemble average of various partition and correlation functions of the symmetric product orbifold theory and compare the resulting expressions to gauge theory quantities in the bulk. We comment on the ensemble average of the tensionless string partition function on AdS 3 × S 3 × 𝕋 4 by considering the specific case ofD= 4 with the addition of supersymmetry.

Physics↗

Radial Response of Outer Radiation Belt Relativistic Electrons During Enhancement Events at Geostationary Orbit

Forecasting relativistic electron fluxes at geostationary Earth orbit (GEO) has been a long‐term goal of the scientific community, and significant advances have been made in the past, but the relation to the interior of the radiation belts, that is, to lower L‐shells, is still not clear. In this work we have identified 60 relativistic electron enhancement events at GEO to study the radial response of outer belt fluxes and the correlation between the fluxes at GEO and those at lower L‐shells. The enhancement events occurred between 1 October 2012 and 31 December 2017 and were identified using Geostationary Operational Environmental Satellite (GOES) 15 >2 MeV fluxes at GEO, which we have used to characterize the radial response of the radiation belt, by comparing to fluxes measured by the Van Allen probes Energetic Particle, Composition and Thermal Plasma Suite Relativistic Electron‐Proton Telescope (ECT‐REPT) between 2.5 5.0 and generally similar for L>4.5. Post‐enhancement maximum fluxes show a remarkable correlation for all L>4.0 although the magnitude of the pre‐existing fluxes on the outer belt plays a significant role and makes the ratio of pre‐enhancement to post‐enhancement fluxes less predictable in the region 4.0<L<4.5. For L<4 the fluxes are poorly correlated with geostationary orbit, but they also tend to be less variable. We have also examined SYM‐H, Kp, and AE indices and found that depending on their magnitude, the response of different parts of the outer belt can be better quantified.

Victor A. Pinto↗

Perfecting one-loop BCJ numerators in SYM and supergravity

We take a major step towards computing D-dimensional one-loop amplitudes in general gauge theories, compatible with the principles of unitarity and the color-kinematics duality. For n-point amplitudes with either supersymmetry multiplets or generic non-supersymmetric matter in the loop, simple all-multiplicity expressions are obtained for the maximal cuts of kinematic numerators of n-gon diagrams. At n = 6, 7 points with maximal supersymmetry, we extend the cubic-diagram numerators to encode all contact terms, and thus solve the long-standing problem of simultaneously realizing the following properties: color-kinematics duality, manifest locality, optimal power counting of loop momenta, quadratic rather than linearized Feynman propagators, compatibility with double copy as well as all graph symmetries. Color-kinematics dual representations with similar properties are presented in the half-maximally supersymmetric case at n = 4, 5 points. The resulting gauge-theory integrands and their supergravity counterparts obtained from the double copy are checked to reproduce the expected ultraviolet divergences.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High-Efficiency Ka-Band Waveguide Two-Way Asymmetric Power Combiner

NASA is planning a number of Space Exploration, Earth Observation and Space Science missions where Ka-band solid-state power amplifiers (SSPAs) could have a role. Monolithic microwave integrated circuit (MMIC) based SSPAs with output powers on the order of 10 W at Ka-band frequencies would be adequate to satisfy the data transmission rate requirements at the distances involved. MMICs are a type of integrated circuit fabricated on a GaAs wafer, which operates at micro wave frequencies and performs the function of signal amplification. The highest power Ka-band (31.8 to 32.3 GHz) SSPA to have flown in space had an output power of 2.6 W with an overall efficiency of 14.3 percent. This SSPA was built around discrete GaAs pHEMT (high electron mobility transistor) devices and flew aboard the Deep Space One spacecraft. State-of-the-art GaAs pHEMT-based MMIC power amplifiers (PAs) can deliver RF power at Ka-band frequencies anywhere from 3 W with a power added efficiency (PAE) of 32 percent to 6 W with a PAE of 26 percent. However, to achieve power levels higher than 6 W, the output of several MMIC PAs would need to be combined using a high-efficiency power combiner. Conventional binary waveguide power combiners, based on short-slot and magic-T circuits, require MMIC PAs with identical amplitude and phase characteristics for high combining efficiency. However, due to manufacturing process variations, the output powers of the MMIC PAs tend to be unequal, and hence the need to develop unequal power combiners. A two-way asymmetric magic-T based power combiner for MMIC power amplifiers, which can take in unequal inputs, has been successfully designed, fabricated, and characterized over NASA s Deep Space Network (DSN) frequency range of 31.8 to 32.3 GHz. The figure is a transparent view of the a sym - metric combiner that shows the 4-port configuration and the internal structure. The rod, post, and iris are positioned by design to achieve the desired asymmetric power ratio, phase equality, and port isolation. Although the combiner was designed for an input power ratio of 2:1, it can be custom-designed for any arbitrary power ratio and frequency range. The manufactured prototype combiner was precision machined from aluminum and is less than 2 in.3 (32.8 cm3). Previously investigated rectangular waveguide unequal power combiners were based on shunt/series coupling slots, E-plane septums, or H-plane T-junctions. All the prior art unequal power combiners operated at or below X-band (10 GHz) frequencies and were primarily used in the feed network of antenna arrays. The only reported asymmetric magic-T was developed as a 2:1 power divider for operation at a much lower frequency, around 500 MHz. The measured power ratio when tested as a power divider was very close to 2 and the phase balance was within 2.6, resulting in near ideal performance. When tested as a combiner using two MMIC SSPAs with a 2:1 power output ratio, an efficiency greater than 90 percent was demonstrated over the 500 MHz DSN frequency range. The return loss at the combiner output port (1) was greater than 18 dB and the input port (2 and 3) isolation was greater than 22 dB. The results show the asymmetric combiner to be a good candidate for high-efficiency power combining of two or more SSPAs needed to achieve the 6 to 10 W required by space communications systems of future NASA missions.

Wintucky, E. G.↗