We propose an integrability approach for planar three-point functions at finite coupling in $$ \mathcal{N} $$ = 2 superconformal field theories obtained as $\textit{ℤ}$ orbifolds of $$ \mathcal{N} $$ = 4 super Yang-Mills (SYM). Generalizing the hexagon formalism for $$ \mathcal{N} $$ = 4 SYM, we reproduce the structure constants of Coulomb branch operators, previously obtained by supersymmetric localization, as exact functions of the ’t Hooft coupling. Our analysis explains the common physical origin of Fredholm kernels in integrability and localization, and hints at structures after the resummation in the hexagon formalism. Notably, we conjecture an all-loop, all-magnon expression for the wrapping contribution, that we checked against the Fredholm determinant result. We were also able to check that the first few magnon contributions are consistent with the factorized form of the final result.

Germany

Gwenaël Ferrando

Switzerland

Shota Komatsu

Brazil

France

Gabriel Lefundes

Didina Serban

Exact three-point functions in $$ \mathcal{N} $$ = 2 superconformal field theories: integrability vs. localization

For correlators in $$ \mathcal{N} $$ = 4 Super Yang-Mills preserving half the supersymmetry, we manifestly recast the gauge theory Feynman diagram expansion as a sum over dual closed strings. Each individual Feynman diagram maps on to a Riemann surface with specific moduli. The Feynman diagrams thus correspond to discrete lattice points on string moduli space, rather than discretized worldsheets. This picture is valid to all orders in the 1/$\textit{N}$ expansion. Concretely, the mapping is carried out at the level of a two-matrix integral with its dual string description. It provides a microscopic picture of open/closed string duality for this topological subsector of the full AdS/CFT correspondence. At the same time, the concrete mechanism for how strings emerge from the matrix model Feynman diagrams predicts that multiple open string descriptions can exist for the same dual closed string theory. By considering the insertion of determinant operators in $$ \mathcal{N} $$ = 4 SYM, we indeed find six equivalent open-string descriptions. Each of them generates Feynman diagrams related to one another via (partial) graph duality, and hence encodes the same information. The embedding of these Kontsevich-like duals into the 1/2 SUSY sector of AdS/CFT is achieved by open strings on giant graviton branes.

India

Rajesh Gopakumar

Rishabh Kaushik

Edward Mazenc

United States

Debmalya Sarkar

Strings from Feynman diagrams

<p>We propose a bosonic string dual to large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi></mrow></math> chiral Yang-Mills theory in two dimensions at finite `t Hooft coupling. The worldsheet theory is a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>β</mi><mtext>−</mtext><mi>γ</mi></mrow></math> system deformed by a chiral Polchinski-Strominger term. We reproduce the partition function on a torus, cylinder three-point amplitudes, and the area law for Wilson loops. We also present candidate string duals to symmetric product orbifolds for general seed conformal field theories with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mo>&lt;</mo><mn>24</mn></math> and their <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi><mover accent="true"><mrow><mi>T</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mover accent="true"><mrow><mi>T</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> deformations. The results hint at interrelations among confining, nonrelativistic, and matrix strings and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>/</mo><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mrow></math>.</p>

CERN

Pronobesh Maity

String Duals of Two-Dimensional Yang-Mills Theory and Symmetric Product Orbifolds

Using supersymmetric localization, we compute the partition function and some protected correlators of the polarized IKKT matrix model. Surprisingly, we find that the original IKKT model is different from polarized IKKT in the limit of vanishing mass deformation. We study different regimes of the localization results and recover the electrostatic problem which defines the gravity dual.

Adrien Martina

Joao Penedones

Antoine Vuignier

Xiang Zhao

Einstein gravity from a matrix integral. Part II

We construct backreacted geometries dual to the supersymmetric mass deformation of the IKKT matrix model. They are Euclidean type IIB supergravity solutions given in terms of an electrostatic potential, having SO(7) × SO(3) isometry and 16 supersymmetries. Quantizing the fluxes, we find that the supergravity solutions are in one-to-one correspondence with fuzzy sphere vacua of the matrix model.

Einstein gravity from a matrix integral. Part I

We study one-point functions of non-BPS single-trace operators on the Coulomb branch of planar $$\mathcal{N}=4$$ supersymmetric Yang-Mills theory. Holography relates them to overlaps between on-shell closed string states and a boundary state describing a probe D3-brane in $\textit{AdS}$ × $\textit{S}$ . Assuming that the D-brane preserves integrability, we formulate and solve integrable bootstrap equations satisfied by the boundary state at finite ’t Hooft coupling. This leads to a closed-form determinant expression for one-point functions at finite coupling, valid for sufficiently long operators. We test the result against direct field theory computations at tree level and one loop, finding perfect agreement.

Frank Coronado

United Kingdom

Denmark

Sweden

Konstantin Zarembo

Coulomb branch and integrability

We revisit the Berenstein-Maldacena-Nastase (BMN) conjecture relating M-theory on a PP-wave background and Matrix Quantum Mechanics (MQM) of $\textit{N}$ × $\textit{N}$ matrices. In particular, we study the BMN MQM at strong coupling and finite $\textit{N}$ and derive an effective Hamiltonian that describes non-relativistic free particles in a harmonic trap. The energy spectrum predicted by this Hamiltonian matches the supergravity excitation spectrum around the PP-wave background, if we further assume the existence of bound states. Our derivation is based on the strong coupling expansion of the wavefunction and supersedes the naive path integral approach that can lead to incorrect results, as we demonstrate in a simple toy model. We conclude with open questions about various regimes of the theory when we vary the size of the matrices, the coupling and the temperature.

Noé Suchel

Gravity from quantum mechanics of finite matrices

We initiate the S-matrix bootstrap analysis of theories with non-invertible symmetries in (1+1) dimensions. Our previous work [1] showed that crossing symmetry of S-matrices in such theories is modified, with modification characterized by the fusion category data. By imposing unitarity, symmetry and the modified crossing, we constrain the space of consistent S-matrices, identifying integrable theories with non-invertible symmetries at the cusps of allowed regions. We also extend the modified crossing rules to cases where vacua transform in non-regular representations of fusion category, utilizing a connection to a dual category $$ {\mathcal{C}}_{\mathcal{M}}^{\ast } $$ and Symmetry Topological Field Theory (SymTFT). This highlights the utility of SymTFT in the analysis of scattering amplitudes.

Christian Copetti

Lucía Córdova

S-matrix bootstrap and non-invertible symmetries

We study analytic properties and integrable structures of the meson spectrum in large $\textit{N}$ QCD . We show that the integral equation that determines the masses of the mesons, often called the ’t Hooft equation, is equivalent to finding solutions to a TQ-Baxter equation. Our analysis extends some of previous results by Fateev et al. to general quark masses $\textit{m}$ = $\textit{m}$ = $\textit{m}$ , as a perturbative series of the mass parameter. This reformulation, together with its relation to an inhomogeneous Fredholm equation, makes accessible the analytic structure of the spectrum in the complex plane of the quark masses. We also comment on applications of our techniques to non-perturbative topological string partition functions.

Federico Ambrosino

2d QCD and integrability. Part I. ’t Hooft model

We show that crossing symmetry of <math><mrow><mi>S</mi></mrow></math> matrices is modified in certain theories with noninvertible symmetries or anomalies. Focusing on integrable flows to gapped phases in two dimensions, we find that <math><mrow><mi>S</mi></mrow></math> matrices derived previously from the bootstrap approach are incompatible with noninvertible symmetries along the flow. We present consistent alternatives, which, however, violate standard crossing symmetry and obey modified rules dictated by fusion categories. We extend these rules to theories with discrete anomalies.