<p>We study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></mrow></math> symmetric Gross-Neveu model at finite density in the presence of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> chemical potential <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi></math> for a generic number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>≤</mo><mi>N</mi><mo>−</mo><mn>2</mn></mrow></math> of fermion fields. By combining perturbative quantum field theory, semiclassical large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, and Bethe ansatz techniques, we show that at finite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> two new dynamically generated scales <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">c</mi></msub></math> appear in the theory, governing the mass gap of neutral and charged fermions, respectively. Above a certain threshold value for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi></math>-fermion bound states condense and form an inhomogeneous configuration, which at infinite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> is a crystal spontaneously breaking translations. At large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi></math>, this crystal has mean <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">n</mi></msub></math> and spatial oscillations of amplitude <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">c</mi></msub></math>. The two scales also control the nonperturbative corrections to the free energy, resolving a puzzle concerning fractional-power renormalons and predicting new ones.</p>

Italy

Francesco Benini

Ohad Mamroud

Tomás Reis

Marco Serone

Condensates, Crystals, and Renormalons in the Gross-Neveu Model at Finite Density

<p>We study a class of Sachdev, Ye, and Kitaev (SYK) models with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> supersymmetry, described by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> fermions in chiral Fermi multiplets, as well as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mi>N</mi></math> first-order bosons in chiral multiplets. The interactions are characterized by two integers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo stretchy="false">)</mo></math>. We focus on the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> and low energy limit of these models. Despite the presence of dynamical bosons, we find conformal behavior akin to the standard SYK model. We use <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">I</mi></math>-extremization of a Witten index to study the supersymmetric solutions. In particular, we find an exact expression for the entropy, which matches the numerical solutions to the Schwinger-Dyson equations. We further solve the model both in the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math> and large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>p</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>q</mi></mrow></math> limits. Numerically, we verify our analytical results and obtain estimates for the Schwarzian coupling in the near zero-temperature limit. We also study the low-lying spectrum of operators to determine the parameter ranges where the Schwarzian mode dominates the IR dynamics. Lastly, we study out-of-time-ordered correlators to show that the model is maximally chaotic.</p>

Saman Soltani

China

Ziruo Zhang

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> SYK models with dynamical bosons and fermions

Entanglement asymmetry is a measure of symmetry breaking in quantum subsystems, inspired by quantum information theory, particularly suited to study out-of-equilibrium states. We study the entanglement asymmetry of a class of excited “coherent states” in conformal quantum field theories with a <italic>U</italic>(1) symmetry, employing Euclidean path-integral methods with topological symmetry defects and the replica formalism. We compute, at leading order in perturbation theory, the asymmetry for a variety of subsystems, including finite spherical subregions in flat space, in finite volume, and at positive temperature. We also study its Lorentzian time evolution, showcasing the dynamical restoration of the symmetry due to thermalization, as well as the presence of a quantum Mpemba effect. Our results are universal, and apply in any number of dimensions. We also show that the perturbative entanglement asymmetry is related to the Fisher information metric, which has a known holographic dual called the Hollands&#8211;Wald canonical energy, and that it is captured by the anti-de-Sitter bulk charge contained in the entanglement wedge.

Victor Godet

Amartya Harsh Singh

Entanglement Asymmetry in Conformal Field Theory and Holography

We study how non-invertible self-duality defects arise in theories with a holographic dual. We focus on the paradigmatic example of $$ \mathfrak{su}(N) $$ $$ \mathcal{N} $$ = 4 SYM. The theory is known to have non-invertible duality and triality defects at = and = /3 , respectively. At these points in the gravitational moduli space, the gauged SL(2, ) duality symmetry of type IIB string theory is spontaneously broken to a finite subgroup , giving rise to a discrete emergent gauge field. After reduction on the internal manifold, the low-energy physics is dominated by an interesting 5d Chern-Simons theory, further gauged by , that we analyze and which gives rise to the self-duality defects in the boundary theory. Using the five-dimensional bulk theory, we compute the fusion rules of those defects in detail. The methods presented here are general and may be used to investigate such symmetries in other theories with a gravity dual.

Andrea Antinucci

Christian Copetti

Giovanni Galati

Giovanni Rizi

The holography of non-invertible self-duality symmetries

Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that its one-form symmetry defects have nontrivial braiding, namely they are charged under the same symmetry they generate, which is then anomalous. This poses a few puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk. First, the braiding between lines at the boundary seems to be ill-defined when such lines are pulled into the bulk. Second, the Symmetry TFT appears to be too trivial to allow for topological boundary conditions encoding all the different global variants. We show that both of these puzzles can be solved by including endable (tubular) surfaces in the class of bulk topological operators one has to consider. In this way, we are able to reproduce all global variants of the theory, with their symmetries and their anomalies. We check the validity of our proposal also against a top-down holographic realization of the same class of theories.

Belgium

Riccardo Argurio

Matteo Bertolini

United States

Pierluigi Niro

On the symmetry TFT of Yang-Mills-Chern-Simons theory

We explore novel examples of RG flows preserving a non-invertible self-duality symmetry. Our main focus is on   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 quadratic superpotential deformations of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super-Yang-Mills theory with gauge algebra   <math> <mi>su</mi> <mfenced> <mi>N</mi> </mfenced> </math>  $$ \mathfrak{su}(N) $$ . A theory that can be obtained in this way is the so-called   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1* SYM where all adjoint chiral multiplets have a mass. Such IR theory exhibits a rich structure of vacua which we thoroughly examine. Our analysis elucidates the physics of spontaneous breaking of self-duality symmetry occurring in the degenerate gapped vacua. The construction can be generalized, taking as UV starting point a theory of class   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$ , to demonstrate how non-invertible self-duality symmetries exist in a variety of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 SCFTs. We finally apply this understanding to prove that the conifold theory has a non-invertible self-duality symmetry.

Jeremias Damia

Sergio Benvenuti

Luigi Tizzano

Non-invertible symmetries along 4d RG flows

We construct an   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 supersymmetric gauged quantum mechanics, by starting from the 3d Chern-Simons-matter theory holographically dual to massive Type IIA string theory on AdS4 × S 6, and Kaluza-Klein reducing on S 2 with a background that is dual to the asymptotics of static dyonic BPS black holes in AdS4. The background involves a choice of gauge fluxes, that we fix via a saddle-point analysis of the 3d topologically twisted index at large N. The ground-state degeneracy of the effective quantum mechanics reproduces the entropy of BPS black holes, and we expect its low-lying spectrum to contain information about near-extremal horizons. Interestingly, the model has a large number of statistically-distributed couplings, reminiscent of SYK models.

A quantum mechanics for magnetic horizons

The superconformal index of the <math><mi>N</mi><mo>=</mo><mn>4</mn></math> <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> supersymmetric Yang-Mills theory counts the <math><mn>1</mn><mo>/</mo><mn>16</mn></math>-BPS (Bogomol’nyi-Prasad-Sommerfield) states in this theory, and has been used via the <math><mrow><mi>AdS</mi><mo>/</mo><mi>CFT</mi></mrow></math> correspondence to count black hole microstates of <math><mn>1</mn><mo>/</mo><mn>16</mn></math>-BPS black holes. On one hand, this index may be related to the Euclidean partition function of the theory on <math><msup><mi>S</mi><mn>3</mn></msup><mo>×</mo><msup><mi>S</mi><mn>1</mn></msup></math> with complex chemical potentials, which maps by the <math><mrow><mi>AdS</mi><mo>/</mo><mi>CFT</mi></mrow></math> correspondence to a sum over Euclidean gravity solutions. On the other hand, the index may be expressed as a sum over solutions to Bethe Ansatz (BA) equations. We show that the solutions to the BA equations that are known to have a good large <math><mi>N</mi></math> limit, for the case of equal chemical potentials for the two angular momenta, have a one-to-one mapping to (complex) Euclidean black hole solutions on the gravity side. This mapping captures both the leading contribution from the classical gravity action (of order <math><msup><mi>N</mi><mn>2</mn></msup></math>), as well as nonperturbative corrections in <math><mn>1</mn><mo>/</mo><mi>N</mi></math>, which on the gravity side are related to wrapped D3-branes. Some of the BA solutions map to orbifolds of the standard Euclidean black hole solutions (which obey exactly the same boundary conditions as the other solutions). A priori there are many more gravitational solutions than Bethe Ansatz solutions, but we show that, by considering the nonperturbative effects, the extra solutions are ruled out, leading to a precise match between the solutions on both sides.

Israel

Ofer Aharony

Paolo Milan

Gravity interpretation for the Bethe Ansatz expansion of the <math><mi>N</mi><mo>=</mo><mn>4</mn></math> SYM index

We consider three-dimensional sQED with 2 flavors and minimal supersymmetry. We discuss various models which are dual to Gross-Neveu-Yukawa theories. The U(2) ultraviolet global symmetry is often enhanced in the infrared, for instance to O(4) or SU(3). This is analogous to the conjectured behaviour of non-supersymmetric QED with 2 flavors. A perturbative analysis of the Gross-Neveu-Yukawa models in the D = 4 − ε expansion shows that the U(2) preserving superpotential deformations of the sQED (mod- ulo tuning mass terms to zero) are irrelevant, therefore the fixed points with enhanced symmetry are stable. We also construct an example of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 sQED with 4 flavors that exhibits enhanced SO(6) symmetry.

<math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 QED in 2 + 1 dimensions: dualities and enhanced symmetries

We study the Bethe Ansatz formula for the superconformal index, in the case of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super-Yang-Mills with gauge group SU(N). We observe that not all solutions to the Bethe Ansatz Equations (BAEs) contribute to the index, and thus formulate “reduced BAEs” such that all and only their solutions contribute. We then propose, sharpening a conjecture of Arabi Ardehali et al. [1], that there is a one-to-one correspondence between branches of solutions to the reduced BAEs and vacua of the 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1* theory. We test the proposal in the case of SU(2) and SU(3). In the case of SU(3), we confirm that there is a continuous family of solutions, whose contribution to the index is non-vanishing.