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At least 19 records
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DOE OSTI2022

Entropic order parameters in weakly coupled gauge theories

The entropic order parameters measure in a universal geometric way the statistics of non-local operators responsible for generalized symmetries. In this article, we compute entropic order parameters in weakly coupled gauge theories. To perform this computation, the natural route of evaluating expectation values of physical (smeared) non-local operators is prevented by known difficulties in constructing suitable smeared Wilson loops. We circumvent this problem by studying the smeared non-local class operators in the enlarged non-gauge invariant Hilbert space. This provides a generic approach for smeared operators in gauge theories and explicit formulas at weak coupling. In this approach, the Wilson and ’t Hooft loops are labeled by the full weight and co-weight lattices respectively. We study generic Lie groups and discuss couplings with matter fields. Smeared magnetic operators, as opposed to the usual infinitely thin ones, have expectation values that approach one at weak coupling. The corresponding entropic order parameter saturates to its maximum topological value, except for an exponentially small correction, which we compute. On the other hand, smeared ’t Hooft loops and their entropic disorder parameter are exponentially small. We verify that both behaviors match the certainty relation for the relative entropies. In particular, we find upper and lower bounds (that differ by a factor of 2) for the exact coefficient of the linear perimeter law for thin loops at weak coupling. This coefficient is unphysical/non-universal for line operators. We end with some comments regarding the RG flows of entropic parameters through perturbative beta functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Bootstrapping a stress-tensor form factor through eight loops

We bootstrap the three-point form factor of the chiral stress-tensor multiplet in planar $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory at six, seven, and eight loops, using boundary data from the form factor operator product expansion. This may represent the highest perturbative order to which multi-variate quantities in a unitary four-dimensional quantum field theory have been computed. In computing this form factor, we observe and employ new restrictions on pairs and triples of adjacent letters in the symbol. We provide details about the function space required to describe the form factor through eight loops. Plotting the results on various lines provides striking numerical evidence for a finite radius of convergence of perturbation theory. By the principle of maximal transcendentality, our results are expected to give the highest weight part of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD through eight loops. These results were also recently used to discover a new antipodal duality between this form factor and a six-point amplitude in the same theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory

The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate L – 1 loop momenta of the L-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at L = 4 is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at L = 4. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like ζ 3 , ζ 5 to the cusp anomalous dimension.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A two-loop four-point form factor at function level

Recently, the maximally-helicity-violating four-point form factor for the chiral stress-energy tensor in planar $\mathcal{N}$ = 4 super Yang-Mills was computed to three loops at the level of the symbol associated with multiple polylogarithms. It exhibits antipodal self-duality, or invariance under the combined action of a kinematic map and reversing the ordering of letters in the symbol. Here we lift the two-loop form factor from symbol level to function level. We provide an iterated representation of the function’s derivatives (coproducts). In order to do so, we find a three-parameter limit of the five-parameter phase space where the symbol’s letters are all rational. We also use function-level information about dihedral symmetries and the soft, collinear, and factorization limits, as well as limits governed by the form-factor operator product expansion (FFOPE). We provide plots of the remainder function on several kinematic slices, and show that the result is compatible with the FFOPE data. We further verify that antipodal self-duality is valid at two loops beyond the level of the symbol.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Two-loop MHV form factors from the periodic Wilson loop

We discuss how to compute maximal-helicity-violating (MHV) form factors for the chiral part of the stress-tensor supermultiplet from periodic light-like polygon Wilson loops in planar $\mathcal{N}$ = 4 super Yang-Mills theory beyond the one-loop level. We show that the periodicity imposes path ordering on points on different edges, which explains the appearance of square roots coming from non-planar Feynman diagrams. Taking such diagrams into account, we provide the integrand of the two-loop n-particle MHV form factor, compute all diagrams, prove the cancellation of divergences and finally compute the two-loop 5-particle and 6-particle form factors as examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Study of gapped phases of 4d gauge theories using temporal gauging of the ℤN 1-form symmetry

To study gapped phases of 4d gauge theories, we introduce the temporal gauging of Z N 1-form symmetry in 4d quantum field theories (QFTs), thereby defining effective 3d QFTs with $\tilde{Z}_N$ × Z N 1-form symmetry. In this way, spatial fundamental Wilson and ’t Hooft loops are simultaneously genuine line operators. Assuming a mass gap and Lorentz invariant vacuum of the 4d QFT, the $\tilde{Z}_N$ × Z N symmetry must be spontaneously broken to an order-N subgroup H, and we can classify the 4d gapped phases by specifying H. This establishes the 1-to-1 correspondence between the two classification schemes for gapped phases of 4d gauge theories: one is the conventional Wilson-’t Hooft classification, and the other is the modern classification using the spontaneous breaking of 4d 1-form symmetry enriched with symmetry-protected topological states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Mapping out the internal space in AdS/BCFT with Wilson loops

We study Wilson loops in string theory realizations of AdS/BCFT and wedge holography. The field theories are based on 3d N = 4 long quiver gauge theories engineered by D3, D5 and NS5 branes, and on BCFTs involving 4d N = 4 SYM coupled to such 3d theories. The holographic duals have geometry AdS 4 × S 2 × S 2 warped over a strip. We identify the holographic representation of antisymmetric Wilson loops associated with individual 3d gauge nodes in terms of probe D5-branes. The expectation values obtained holographically are matched to supersymmetric localization computations. Our results yield an identification of regions in the internal space with individual 3d gauge nodes. Connecting to bottom-up braneworld models, this gives a concrete notion of which parts of the 10d solutions correspond to the end-of-the-world brane and which to the remaining bulk. We also construct supersymmetric Janus on the brane embeddings in AdS 5 ×S 5 , which describe surface defects with boundaries and interfaces in N = 4 SYM.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Beyond AdS 2 /dCFT 1 : insertions in two Wilson loops

We consider two-point correlators of local operator insertions in a system of two Wilson-Maldacena loops in $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory on both sides of the AdS/CFT correspondence. On the holographic side the correlator of two Wilson-Maldacena loops is given by a classical string world-sheet which in one phase connects two asymptotically AdS 2 regions and in the other phase is given by two disconnected AdS 2 caps; this configuration breaks supersymmetry as well as conformal invariance. We present a complete systematic account of the string world-sheet fluctuations, including the fermionic sector, and study the behavior of the holographic two-point correlators. On the field theory side we compute certain two-point correlators of local operator insertions by resumming sets of ladder diagrams. Our results demonstrate the efficacy of previously developed methods in tackling this non-conformal, non-susy regime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Generalized symmetry in dynamical gravity

We explore generalized symmetry in the context of nonlinear dynamical gravity. Our basic strategy is to transcribe known results from Yang-Mills theory directly to gravity via the tetrad formalism, which recasts general relativity as a gauge theory of the local Lorentz group. By analogy, we deduce that gravity exhibits a one-form symmetry implemented by an operator U α labeled by a center element α of the Lorentz group and associated with a certain area measured in Planck units. The corresponding charged line operator W ρ is the holonomy in a spin representation ρ, which is the gravitational analog of a Wilson loop. The topological linking of U α and W ρ has an elegant physical interpretation from classical gravitation: the former materializes an exotic chiral cosmic string defect whose quantized conical deficit angle is measured by the latter. We verify this claim explicitly in an AdS-Schwarzschild black hole background. Notably, our conclusions imply that the standard model exhibits a new symmetry of nature at scales below the lightest neutrino mass. More generally, the absence of global symmetries in quantum gravity suggests that the gravitational one-form symmetry is either gauged or explicitly broken. The latter mandates the existence of fermions. Finally, we comment on generalizations to magnetic higher-form or higher-group gravitational symmetries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Four-fermion deformations of the massless Schwinger model and confinement

We consider the massless charge-N Schwinger model and its deformation with two four-fermion operators. Without the deformations, this model exhibits chiral symmetry breaking without confinement. It is usually asserted that the massless Schwinger model is always deconfined and a string tension emerges only when a mass for the fermion field is turned on. We show that in the presence of these four-fermion operators, the massless theory can in fact confine. One of the four-fermion deformations is chirally neutral, and is a marginal deformation. The other operator can be relevant or irrelevant, and respects a Z 2 subgroup of chiral symmetry for even N, hence forbidding a mass term. When it is relevant, even the exactly massless theory exhibits both confinement and spontaneous chiral symmetry breaking. The construction is analogous to QCD(adj) in 2d. While the theory without four-fermion deformations is deconfined, the theory with these deformations is generically in a confining phase. We study the model on R 2 using bosonization, and also analyze the mechanism of confinement on R × S 1 , where we find that confinement is driven by fractional instantons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Dressed vs. pairwise states, and the geometric phase of monopoles and charges

We construct the Faddeev-Kulish dressed multiparticle states of electrically and magnetically charged particles, incorporating the effects of real and virtual soft photons. We calculate the properties of such dressed states under Lorentz transformations, and find that they can be identified with the pairwise multi-particle states that transform under the pairwise little group. The shifts in the dressing factors under Lorentz transformations are finite and have a simple geometric interpretation. Using the transformation properties of the dressed states we also present a novel, fully quantum field theoretic derivation of the geometric (Berry) phase obtained by an adiabatic rotation of the Dirac string, and also of the Dirac quantization condition. For half integer pairwise helicity, we show that these multiparticle states have flipped spin-statistics, reproducing the surprising fact that fermions can be made out of bosons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N -ality

We study a 3d lattice gauge theory with gauge group U(1) N– 1 ⋉ S N , which is obtained by gauging the S N global symmetry of a pure U(1) N– 1 gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU( N ) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤ N , we observe that the string tensions do not obey the N -ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1) N– 1 one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to W -bosons, such non-invertible symmetries are explicitly broken so that the N -ality rule should emerge in the deep infrared regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Exploring non-invertible symmetries in free theories

Symmetries corresponding to local transformations of the fundamental fields that leave the action invariant give rise to (invertible) topological defects, which obey group-like fusion rules. One can construct more general (codimension-one) topological defects by specifying a map between gauge-invariant operators from one side of the defect and such operators on the other side. In this work, we apply such construction to Maxwell theory in four dimensions and to the free compact scalar theory in two dimensions. In the case of Maxwell theory, we show that a topological defect that mixes the field strength F and its Hodge dual *F can be at most an SO(2) rotation. For rational values of the bulk coupling and the θ-angle we find an explicit defect Lagrangian that realizes values of the SO(2) angle φ such that cos φ is also rational. We further determine the action of such defects on Wilson and ’t Hooft lines and show that they are in general non-invertible. We repeat the analysis for the free compact scalar Φ in two dimensions. In this case we find only four discrete maps: the trivial one, a Z 2 map dΦ → –dΦ, a Τ-duality-like map dΦ → i • dΦ, and the product of the last two.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Polyakov’s confinement mechanism for generalized Maxwell theory

We study fractional-derivative Maxwell theory, as appears in effective descriptions of, for example, large N f QED 3 , graphene, and some types of surface defects. We argue that when the theory is realized on a lattice, monopole condensation leads to a confining phase via the Polyakov confinement mechanism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Generalized symmetries of the graviton

We find the set of generalized symmetries associated with the free graviton theory in four dimensions. These are generated by gauge invariant topological operators that violate Haag duality in ring-like regions. As expected from general QFT grounds, we find a set of “electric” and a dual set of “magnetic” topological operators and compute their algebra. To do so, we describe the theory using phase space gauge-invariant electric and magnetic dual variables constructed out of the curvature tensor. Electric and magnetic fields satisfy a set of constraints equivalent to the ones of a stress tensor of a 3d CFT. The constraints give place to a group $\mathbb{R}^{20}$ of topological operators that are charged under space-time symmetries. Finally, we discuss similarities and differences between linearized gravity and tensor gauge theories that have been introduced recently in the context of fractonic systems in condensed matter physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Charges in the UV completion of neutral electrodynamics

A theory with a non-compact form-symmetry is described by two closed form fields of degrees k and d – k. Effective theory examples are non-linear electrodynamics, a photon field coupled to a neutron field, and a low energy Goldstone boson. We show these models cannot be completed in the UV without breaking the non-compact form-symmetry down to a compact one. This amounts to the existence of electric or magnetic charges. A theory with an unbroken non-compact k-form symmetry is massless and free.

't Hooft and Polyakov loops↗
DOE OSTI2024

Line operators, vortex statistics, and Higgs versus confinement dynamics

We study a 2+1D lattice gauge theory with fundamental representation scalar fields which has both Higgs and confining regimes with a spontaneously-broken U(1) 0-form symmetry. We show that the Higgs and confining regimes may be distinguished by a natural gauge invariant observable: the phase Ω of a correlation function of a vortex line operator linking with an electric Wilson line. We employ dualities and strong coupling expansions to analytically explore parameter regimes which were inaccessible in previous continuum calculations, and discuss possible implications for the phase diagram.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Generalized symmetries and Noether’s theorem in $\mathrm{QFT}$

We show that generalized symmetries cannot be charged under a continuous global symmetry having a Noether current. Further, only non-compact generalized symmetries can be charged under a continuous global symmetry. These results follow from a finer classification of twist operators, which naturally extends to finite group global symmetries. They unravel topological obstructions to the strong version of Noether’s theorem in QFT, even if under general conditions a global symmetry can be implemented locally by twist operators (weak version). We use these results to rederive Weinberg-Witten’s theorem within local QFT, generalizing it to massless particles in arbitrary dimensions and representations of the Lorentz group. Several examples with local twists but without Noether currents are described. We end up discussing the conditions for the strong version to hold, dynamical aspects of QFT’s with non-compact generalized symmetries, scale vs conformal invariance in QFT, connections with the Coleman-Mandula theorem and aspects of global symmetries in quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗