Publications

Order by: publication date number of citations

• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD

  Aleksey Cherman, Theodore Jacobson, Yuya Tanizaki, Mithat Ünsal

  SciPost Phys. 8, 072 (2020) · published 5 May 2020 | Toggle abstract · pdf

  We show that $2$d adjoint QCD, an $SU(N)$ gauge theory with one massless adjoint Majorana fermion, has a variety of mixed 't Hooft anomalies. The anomalies are derived using a recent mod $2$ index theorem and its generalization that incorporates 't Hooft flux. Anomaly matching and dynamical considerations are used to determine the ground-state structure of the theory. The anomalies, which are present for most values of $N$, are matched by spontaneous chiral symmetry breaking. We find that massless $2$d adjoint QCD confines for $N >2$, except for test charges of $N$-ality $N/2$, which are deconfined. In other words, $\mathbb Z_N$ center symmetry is unbroken for odd $N$ and spontaneously broken to $\mathbb Z_{N/2}$ for even $N$. All of these results are confirmed by explicit calculations on small $\mathbb{R}\times S^1$. We also show that this non-supersymmetric theory exhibits exact Bose-Fermi degeneracies for all states, including the vacua, when $N$ is even. Furthermore, for most values of $N$, $2$d massive adjoint QCD describes a non-trivial symmetry-protected topological (SPT) phase of matter, including certain cases where the number of interacting Majorana fermions is a multiple of $8$. As a result, it fits into the classification of $(1+1)$d SPT phases of interacting Majorana fermions in an interesting way.

  42 citations

• On anomalies and gauging of U(1) non-invertible symmetries in 4d QED

  Avner Karasik

  SciPost Phys. 15, 002 (2023) · published 6 July 2023 | Toggle abstract · pdf

  In this work we propose a way to promote the anomalous axial $U(1)$ transformations to exact non-invertible $U(1)$ symmetries. We discuss the procedure of coupling the non-invertible symmetry to a (dynamical or background) gauge field. We show that as part of the gauging procedure, certain constraints are imposed to make the gauging consistent. The constraints emerge naturally from the form of the non-invertible $U(1)$ conserved current. In the case of dynamical gauging, this results in new type of gauge theories we call non-invertible gauge theories: These are gauge theories with additional constraints that cancel the would-be gauge anomalies. By coupling to background gauge fields, we can discuss 't-Hooft anomalies of non-invertible symmetries. We show in an example that the matching conditions hold but they are realized in an unconventional way. Turning on non-trivial background for the non-invertible gauge field changes the vacuum even when the symmetry is not broken and the background is very weak. The anomalies are then matched by the appearance of solitons in the new vacuum.

  42 citations

• Anomalies and symmetry fractionalization

  Diego Delmastro, Jaume Gomis, Po-Shen Hsin, Zohar Komargodski

  SciPost Phys. 15, 079 (2023) · published 5 September 2023 | Toggle abstract · pdf

  We study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $\Gamma$. In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a fractionalization class, needs to be specified. Distinct choices of a fractionalization class can result in different values for the anomalies of $G$ if the theory has an anomaly involving $\Gamma$. Therefore, the computation of the 't Hooft anomaly for an ordinary symmetry $G$ generally requires first discovering the one-form symmetry $\Gamma$ of the physical system. We show that the multiple values of the anomaly for $G$ can be realized by twisted gauge transformations, since twisted gauge transformations shift fractionalization classes. We illustrate these ideas in QCD theories in diverse dimensions. We successfully match the anomalies of time-reversal symmetries in $2+1d$ gauge theories, across the different fractionalization classes, with previous conjectures for the infrared phases of such strongly coupled theories, and also provide new checks of these proposals. We perform consistency checks of recent proposals about two-dimensional adjoint QCD and present new results about the anomaly of the axial $\mathbb{Z}_{2N}$ symmetry in $3+1d$ ${\cal N}=1$ super-Yang-Mills. Finally, we study fractionalization classes that lead to 2-group symmetry, both in QCD-like theories, and in $2+1d$ $\mathbb{Z}_2$ gauge theory.

  41 citations

• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

  Cyril Closset, Horia Magureanu

  SciPost Phys. 12, 065 (2022) · published 17 February 2022 | Toggle abstract · pdf

  The simplest non-trivial 5d superconformal field theories (SCFT) are the famous rank-one theories with $E_n$ flavour symmetry. We study their $U$-plane, which is the one-dimensional Coulomb branch of the theory on $\mathbb{R}^4 \times S^1$. The total space of the Seiberg-Witten (SW) geometry -- the $E_n$ SW curve fibered over the $U$-plane -- is described as a rational elliptic surface with a singular fiber of type $I_{9-n}$ at infinity. A classification of all possible Coulomb branch configurations, for the $E_n$ theories and their 4d descendants, is given by Persson's classification of rational elliptic surfaces. We show that the global form of the flavour symmetry group is encoded in the Mordell-Weil group of the SW elliptic fibration. We study in detail many special points in parameters space, such as points where the flavour symmetry enhances, and/or where Argyres-Douglas and Minahan-Nemeschansky theories appear. In a number of important instances, including in the massless limit, the $U$-plane is a modular curve, and we use modularity to investigate aspects of the low-energy physics, such as the spectrum of light particles at strong coupling and the associated BPS quivers. We also study the gravitational couplings on the $U$-plane, matching the infrared expectation for the couplings $A(U)$ and $B(U)$ to the UV computation using the Nekrasov partition function.

  41 citations

• Relative entropy in scattering and the S-matrix bootstrap

  Anjishnu Bose, Parthiv Haldar, Aninda Sinha, Pritish Sinha, Shaswat S Tiwari

  SciPost Phys. 9, 081 (2020) · published 24 November 2020 | Toggle abstract · pdf

  We consider entanglement measures in 2-2 scattering in quantum field theories, focusing on relative entropy which distinguishes two different density matrices. Relative entropy is investigated in several cases which include $\phi^4$ theory, chiral perturbation theory ($\chi PT$) describing pion scattering and dilaton scattering in type II superstring theory. We derive a high energy bound on the relative entropy using known bounds on the elastic differential cross-sections in massive QFTs. In $\chi PT$, relative entropy close to threshold has simple expressions in terms of ratios of scattering lengths. Definite sign properties are found for the relative entropy which are over and above the usual positivity of relative entropy in certain cases. We then turn to the recent numerical investigations of the S-matrix bootstrap in the context of pion scattering. By imposing these sign constraints and the $\rho$ resonance, we find restrictions on the allowed S-matrices. By performing hypothesis testing using relative entropy, we isolate two sets of S-matrices living on the boundary which give scattering lengths comparable to experiments but one of which is far from the 1-loop $\chi PT$ Adler zeros. We perform a preliminary analysis to constrain the allowed space further, using ideas involving positivity inside the extended Mandelstam region, and elastic unitarity.

  41 citations

• Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions

  Sthitadhi Roy, David E. Logan

  SciPost Phys. 7, 042 (2019) · published 3 October 2019 | Toggle abstract · pdf

  Many-body localisation is studied in a disordered quantum spin-1/2 chain with long-ranged power-law interactions, and distinct power-law exponents for interactions between longitudinal and transverse spin components. Using a self-consistent mean-field theory centring on the local propagator in Fock space and its associated self-energy, a localisation phase diagram is obtained as a function of the power-law exponents and the disorder strength of the random fields acting on longitudinal spin-components. Analytical results are corroborated using the well-studied and complementary numerical diagnostics of level statistics, entanglement entropy, and participation entropy, obtained via exact diagonalisation. We find that increasing the range of interactions between transverse spin components hinders localisation and enhances the critical disorder strength. In marked contrast, increasing the interaction range between longitudinal spin components is found to enhance localisation and lower the critical disorder.

  40 citations

• Eikonal amplitudes from curved backgrounds

  Tim Adamo, Andrea Cristofoli, Piotr Tourkine

  SciPost Phys. 13, 032 (2022) · published 25 August 2022 | Toggle abstract · pdf

  Eikonal exponentiation in QFT describes the emergence of classical physics at long distances in terms of a non-trivial resummation of infinitely many diagrams. Long ago, 't Hooft proposed a beautiful correspondence between ultra-relativistic scalar eikonal scattering and one-to-one scattering in a background shockwave space-time, bypassing the need to resum. In this spirit, we propose here a covariant method for computing one-to-one amplitudes in curved background space-times which gives rise what we conjecture to be a general expression for the eikonal amplitude. We show how the one-to-one scattering amplitude for scalars on any stationary space-time reduces to a boundary term that captures the long-distance behavior of the background and has the structure of an exponentiated eikonal amplitude. In the case of scalar scattering on Schwarzschild, we recover the known results for gravitational scattering of massive scalars in the eikonal regime. For Kerr, we find a remarkable exponentiation of the tree-level amplitude for gravitational scattering between a massive scalar and a massive particle of infinite spin. This amplitude exhibits a Kawai-Lewellen-Tye-like factorization, which we use to evaluate the eikonal amplitude in momentum space, and study its analytic properties.

  40 citations

• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

  Nabil Iqbal, John McGreevy

  SciPost Phys. 13, 114 (2022) · published 22 November 2022 | Toggle abstract · pdf

  By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string field -- defined on the space of closed loops -- that can be used to describe the creation, annihilation, and condensation of effective strings. Like its zero-form cousin, the mean string field theory provides a useful picture of the phase diagram of broken and unbroken phases. We provide a transparent derivation of the area law for charged line operators in the unbroken phase and describe the dynamics of gapless Goldstone modes in the broken phase. The framework also provides a theory of topological defects of the broken phase and a description of the phase transition that should be valid above an upper critical dimension, which we discuss. We also discuss general consequences of emergent one-form symmetries at zero and finite temperature.

  39 citations

• Generalized dilaton gravity in 2d

  Daniel Grumiller, Romain Ruzziconi, Céline Zwikel

  SciPost Phys. 12, 032 (2022) · published 21 January 2022 | Toggle abstract · pdf

  Generalized dilaton gravity in 2d is the most general consistent deformation of the Jackiw-Teitelboim model that maintains local Lorentz invariance. The action is generically not power-counting renormalizable, thus going beyond the class of models typically studied. Nevertheless, all these models are exactly soluble. We focus on a subclass of dilaton scale invariant models. Within this subclass, we identify a 3-parameter family of models that describe black holes asymptoting to AdS2 in the UV and to dS2 in the IR. Since these models could be interesting for holography, we address thermodynamics and boundary issues, including boundary charges, asymptotic symmetries and holographic renormalization.

  39 citations

• Anomalies of non-invertible symmetries in (3+1)d

  Clay Córdova, Po-Shen Hsin, Carolyn Zhang

  SciPost Phys. 17, 131 (2024) · published 12 November 2024 | Toggle abstract · pdf

  Anomalies of global symmetries are important tools for understanding the dynamics of quantum systems. We investigate anomalies of non-invertible symmetries in 3+1d using 4+1d bulk topological quantum field theories given by Abelian two-form gauge theories, with a 0-form permutation symmetry. Gauging the 0-form symmetry gives the 4+1d "inflow" symmetry topological field theory for the non-invertible symmetry. We find a two levels of anomalies: (1) the bulk may fail to have an appropriate set of loop excitations which can condense to trivialize the boundary dynamics, and (2) the "Frobenius-Schur indicator" of the non-invertible symmetry (generalizing the Frobenius-Schur indicator of 1+1d fusion categories) may be incompatible with trivial boundary dynamics. As a consequence we derive conditions for non-invertible symmetries in 3+1d to be compatible with symmetric gapped phases, and invertible gapped phases. Along the way, we see that the defects characterizing $\mathbb{Z}_{4}$ ordinary symmetry host worldvolume theories with time-reversal symmetry $\mathsf{T}$ obeying the algebra $\mathsf{T}^{2}=C$ or $\mathsf{T}^{2}=(-1)^{F}C,$ with $C$ a unitary charge conjugation symmetry. We classify the anomalies of this symmetry algebra in 2+1d and further use these ideas to construct 2+1d topological orders with non-invertible time-reversal symmetry that permutes anyons. As a concrete realization of our general discussion, we construct new lattice Hamiltonian models in 3+1d with non-invertible symmetry, and constrain their dynamics.

  39 citations