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DOE OSTI2024

Heavy states in 3d gravity and 2d CFT

We discuss correlators of light fields in heavy states in AdS 3 gravity and holographic 2d CFTs. In the bulk, the propagator of free fields in AdS backgrounds containing a conical defect or a BTZ black hole can be obtained by solving a wave equation, as well as by the method of images. On the boundary, these geometries are sourced by heavy operator insertions, and the propagator is dual to a heavy-light (HHLL) correlator. By matching its expansion in Virasoro blocks to our bulk results, we determine the OPE coefficients of all contributing states in both the s and t channels. In the s channel, these states are excitations of the light field on top of the heavy state, and their OPE coefficients are the amplitudes to create them. The t-channel OPE is dominated by the Virasoro vacuum block, but there is also an infinite family of light two-particle states that contribute to the correlator. The OPE coefficients that couple these states to heavy operators represent their expectation values in heavy backgrounds. We determine them exactly, derive their asymptotic form at large twist, and discuss their behavior near and above the BTZ threshold, where they become thermal one-point functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation

We derive a saturation theorem for general Effective Field Theories (EFTs) constructed using spurion analysis. Let S be a set of spurion fields introduced to organize the breaking of a global symmetry G f , and H S be the subgroup of G f that remains unbroken under a generic vacuum expectation value ⟨S⟩; we show that the EFT Lagrangian constructed from the spurion analysis saturates the EFT Lagrangian without the spurions but restricted to H S invariance, provided that arbitrary powers of the spurion fields are allowed. As examples, we study several implementations of the Minimal Lepton Flavor Violation (MLFV) principle, corresponding to various origins of the neutrino masses. In each scenario, we compute the Hilbert series to obtain the numbers of independent lepton flavor covariants that appear in the corresponding EFT at mass dimension 6. These numbers agree with the number of H S invariants in the EFT without the spurions, demonstrating the saturation theorem.

Effective Field Theories↗
DOE OSTI2021

Strong coupling expansion of free energy and BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal models with fundamental hypermultiplets

As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625 ) of strong-coupling expansion of non-planar corrections in \( \mathcal{N} \) = 2 4d superconformal models we consider two special theories with gauge groups SU( N ) and Sp(2 N ). They contain N -independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding \( \mathcal{N} \) = 4 SYM theories. These \( \mathcal{N} \) = 2 theories can be realised on a system of N D3-branes with a finite number of D7-branes and O7-plane; the dual string theories should be particular orientifolds of AdS 5 × S 5 superstring. Starting with the localization matrix model representation for the \( \mathcal{N} \) = 2 partition function on S 4 we find exact differential relations between the 1 /N terms in the corresponding free energy F and the \( \frac{1}{2} \) -BPS Wilson loop expectation value \( \left\langle \mathcal{W}\right\rangle \) and also compute their large ’t Hooft coupling ( λ » 1) expansions. The structure of these expansions is different from the previously studied models without fundamental hypermultiplets. In the more tractable Sp(2 N ) case we find an exact resummed expression for the leading strong coupling terms at each order in the 1 /N expansion. We also determine the exponentially suppressed at large λ contributions to the non-planar corrections to F and \( \left\langle \mathcal{W}\right\rangle \) and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.

1/N expansion↗
DOE OSTI2024

A supersymmetric SYK model with a curious low energy behavior

We consider N = 2,4 supersymmetric SYK models that have a peculiar low energy behavior, with the entropy going like S = S 0 + (constant)T a , where a ≠ 1. The large N equations for these models are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing the BFSS matrix quantum mechanics or other related matrix models. Here we reanalyze these equations in order to better understand the low energy physics of these models. We find that the scalar fields develop large expectation values which explore the low energy valleys in the potential. The low energy physics is dominated by quadratic fluctuations around these values. These models were previously conjectured to have a spin glass phase. We did not find any evidence for this phase by using the usual diagnostics, such as searching for replica symmetry breaking solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Entanglement maximization and mirror symmetry in two-Higgs-doublet models

We consider 2-to-2 scatterings of Higgs bosons in a CP-conserving two-Higgs-doublet model (2HDM) and study the implication of maximizing the entanglement in the flavor space, where the two doublets Φ a , a = 1, 2, can be viewed as a qubit: Φ 1 = |0⟩ and Φ 2 = |1⟩. More specifically, we compute the scattering amplitudes for Φ a Φ b → Φ c Φ d and require the outgoing flavor entanglement to be maximal for a full product basis such as the computational basis, which consists of {|00⟩, |01⟩, |10⟩, |11⟩}. In the unbroken phase and turning off the gauge interactions, entanglement maximization results in the appearance of an U(2) × U(2) global symmetry among the quartic couplings, which in general is broken softly by the mass terms. Interestingly, once the Higgs bosons acquire vacuum expectation values, maximal entanglement enforces an exact U(2) × U(2) symmetry, which is spontaneously broken to U(1) × U(1). As a byproduct, this gives rise to Higgs alignment as well as to the existence of 6 massless Nambu-Goldstone bosons. The U(2) × U(2) symmetry can be gauged to lift the massless Goldstones, while maintaining maximal entanglement demands the presence of a discrete Z 2 symmetry interchanging the two gauge sectors. The model is custodially invariant in the scalar sector, and the inclusion of fermions requires a mirror dark sector, related to the standard one by the Z 2 symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

A Goldstone boson equivalence for inflation

The effective field theory of single-field inflation characterizes the inflationary epoch in terms of a pattern of symmetry breaking. An operator acquires a time-dependent vacuum expectation value, defining a preferred spatial slicing. In the absence of dynamical gravity, the fluctuations around the time-dependent background are described by the Goldstone boson associated with this symmetry breaking process. With gravity, the Goldstone is eaten by the metric, becoming the scalar metric fluctuation. In this paper, we will show that in general single-field inflation, the statistics of scalar metric fluctuations are given by the statistics of this Goldstone boson decoupled from gravity up to corrections that are controlled as an expansion in slow-roll parameters. This even holds in the presence of additional parameters, like the speed of sound, that naively enhance the impact of the gravitational terms. In the process, we derive expressions for leading and sub-leading gravitational corrections to all-orders in the Goldstone boson.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Lorentzian dynamics and factorization beyond rationality

We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on analyticity and Lorentzian dynamics including aspects of chaos. We derive a formula relating the infinite boost limit, which holographically encodes the “opacity” of bulk scattering, to the action of topological defect lines on local operators. Leveraging the unitary bound on the opacity and the positivity of fusion coefficients, we show that the spectral radii of a large class of topological defect lines are given by their loop expectation values. Factorization also gives a formula relating the local and defect operator algebras and fusion categorical data. We then review factorization in rational conformal field theory from a defect perspective, and examine irrational theories. On the orbifold branch of the c = 1 free boson theory, we find a unified description for the topological defect lines through which the twist fields are factorized; at irrational points, the twist fields factorize through “non-compact” topological defect lines which exhibit continuous defect operator spectra. Along the way, we initiate the development of a formalism to characterize non-compact topological defect lines.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Recursion relations for 5-point conformal blocks

We consider 5-point functions in conformal field theories in d2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Froggatt-Nielsen meets the SMEFT

We study the matching of Froggatt-Nielsen theories of flavour onto the Standard Model Effective Field Theory (SMEFT), upon integrating out a heavy Beyond-the-Standard-Model (BSM) scalar ‘flavon’ whose vacuum expectation value breaks an Abelian flavour symmetry at energies Λ FN well above the electroweak scale, Λ FN > Λ SM . We include matching contributions to the infrared d SM = 6 (Warsaw basis) SMEFT sourced from ultraviolet contact terms suppressed up to order 1/${\Lambda}_{\textrm{UV}}^2$ in the Froggatt-Nielsen Lagrangian, where Λ UV > Λ FN is an arbitrary ultraviolet scale where further unspecified BSM particles are dynamical. This includes tree-level (one-loop) ultraviolet diagrams with d FN = 6 (5) effective vertices. We first do so with a toy model, but then generalize our findings to arbitrary Frogatt-Nielsen charges. Our results indicate a rich and non-trivial signature of Froggatt-Nielsen theories on the (otherwise) model-independent operators of the SMEFT, and we briefly speculate on extending our analysis to broader classes of BSM flavour models, e.g. non-Abelian and/or gauged theories. We thus take an important step towards determining how to use rapidly developing theoretical and experimental SMEFT technologies to gain unambiguous insight into the SM’s longstanding fermion flavour puzzle.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Spontaneous breaking of U(1) symmetry in coupled complex SYK models

As shown in [1], two copies of the large N Majorana SYK model can produce spontaneous breaking of a Z 2 symmetry when they are coupled by appropriate quartic terms. In this paper we similarly study two copies of the complex SYK model coupled by a quartic term preserving the U(1) x U(1) symmetry. We also present a tensor counterpart of this coupled model. When the coefficient α of the quartic term lies in a certain range, the coupled large N theory is nearly conformal. We calculate the scaling dimensions of fermion bilinear operators as functions of α. We show that the operator c$^†_{1i}$c 2i , which is charged under the axial U(1) symmetry, acquires a complex dimension outside of the line of fixed points. We derive the large N Dyson-Schwinger equations and show that, outside the fixed line, this U(1) symmetry is spontaneously broken at low temperatures because this operator acquires an expectation value. We support these findings by exact diagonalizations extrapolated to large N.

1/N expansion↗
DOE OSTI2021

Bootstrapping quantum extremal surfaces. Part I. The area operator

Quantum extremal surfaces are central to the connection between quantum information theory and quantum gravity and they have played a prominent role in the recent progress on the information paradox. We initiate a program to systematically link these surfaces to the microscopic data of the dual conformal field theory, namely the scaling dimensions of local operators and their OPE coefficients. We consider CFT states obtained by acting on the vacuum with single-trace operators, which are dual to one-particle states of the bulk theory. Focusing on AdS 3 /CFT 2 , we compute the CFT entanglement entropy to second order in the large c expansion where quantum extremality becomes important and match it to the expectation value of the bulk area operator. We show that to this order, the Virasoro identity block contributes solely to the area operator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Absolute entropy and the observer’s no-boundary state

We investigate the no-boundary proposal for closed universes with an observer. We argue that the observer’s no-boundary state is the identity operator on the physical Hilbert space, i.e., the maximum entropy state and show this explicitly in Jackiw-Teitelboim gravity. Geometrically, the no-boundary state is a bra-ket wormhole. Expectation values in the no-boundary state provide a trace for the observer’s algebra, which allows one to define von Neumann entropy for observers in different universes as the relative entropy with respect to the no-boundary state. This result is consistent with all previously discussed cases of traces for invariantly defined regions.

Cosmological models↗
DOE OSTI2020

Riemann-Hilbert correspondence and blown up surface defects

The relationship of two dimensional quantum field theory and isomonodromic deformations of Fuchsian systems has a long history. Recently four-dimensional N = 2 gauge theories joined the party in a multitude of roles. In this paper we study the vacuum expectation values of intersecting half-BPS surface defects in SU(2) theory with N f = 4 fundamental hypermultiplets. We show they form a horizontal section of a Fuchsian system on a sphere with 5 regular singularities, calculate the monodromy, and define the associated isomonodromic tau-function. Using the blowup formula in the presence of half-BPS surface defects, initiated in the companion paper, we obtain the GIL formula, establishing an unexpected relation of the topological string/free fermion regime of supersymmetric gauge theory to classical integrability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Jarzynski Equality for Conditional Stochastic Work

It has been established that the inclusive work for classical, Hamiltonian dynamics is equivalent to the two-time energy measurement paradigm in isolated quantum systems. However, a plethora of other notions of quantum work has emerged, and thus the natural question arises whether any other quantum notion can provide motivation for purely classical considerations. In the present analysis, we propose the conditional stochastic work for classical, Hamiltonian dynamics, which is inspired by the one-time measurement approach. This novel notion is built upon the change of expectation value of the energy conditioned on the initial energy surface. As main results, we obtain a generalized Jarzynski equality and a sharper maximum work theorem, which account for how non-adiabatic the process is. Our findings are illustrated with the parametric harmonic oscillator.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗
DOE OSTI2022

On the closedness and geometry of tensor network state sets

Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. Here we discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states, and the multiscale entanglement renormalization ansatz are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The carbon-concentrating mechanism of the extremophilic red microalga Cyanidioschyzon merolae

Abstract Cyanidioschyzon merolae is an extremophilic red microalga which grows in low-pH, high-temperature environments. The basis of C. merolae ’s environmental resilience is not fully characterized, including whether this alga uses a carbon-concentrating mechanism (CCM). To determine if C. merolae uses a CCM, we measured CO 2 uptake parameters using an open-path infra-red gas analyzer and compared them to values expected in the absence of a CCM. These measurements and analysis indicated that C. merolae had the gas-exchange characteristics of a CCM-operating organism: low CO 2 compensation point, high affinity for external CO 2 , and minimized rubisco oxygenation. The biomass δ 13 C of C. merolae was also consistent with a CCM. The apparent presence of a CCM in C. merolae suggests the use of an unusual mechanism for carbon concentration, as C. merolae is thought to lack a pyrenoid and gas-exchange measurements indicated that C. merolae primarily takes up inorganic carbon as carbon dioxide, rather than bicarbonate. We use homology to known CCM components to propose a model of a pH-gradient-based CCM, and we discuss how this CCM can be further investigated.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Finding Promising Candidates for Wet Growing Conditions: The Effect of Two Row Spacings on Biomass Production of Four Bioenergy Prairie Cordgrass Populations in a Wet Marginal Land

Demand for energy and the environmental consequences associated with fossil fuel emissions has created a need for alternative energy sources. To avoid conflict over the conversion of existing agricultural land from food production to fuel production, bioenergy crops could instead be cultivated on marginal land. Here, this study compared the performances, biomass yield, tiller density, and lignocellulosic bioenergy feedstock composition of four prairie cordgrass populations with two-row spacings cultivated on a waterlog-prone marginal land, as well as three other bioenergy candidate crops used as controls: big bluestem, M. × giganteus , and switchgrass. Across all populations and spacings, annual biomass yield of prairie cordgrass was 13 Mg ha −1 . Row spacing had significant impacts on prairie cordgrass productivity, with higher biomass yields observed in the 45 cm spacing than in the 90 cm spacing. Feedstock composition (cellulose, hemicellulose, ADL, and ash concentration) was not influenced by row spacing and did not deviate from expected values for growth on agricultural lands. However, biomass yields of the control species M . × giganteus and switchgrass planted in 45 cm spacing were higher than the prairie cordgrass. Our results provide evidence that prairie cordgrass could be a good energy crop with comparable biomass yield production to the energy crops M . × giganteus and switchgrass on waterlogged marginal land.

Bioenergy crops↗