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.

Switzerland

Shota Komatsu

Adrien Martina

Joao Penedones

Antoine Vuignier

France

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

<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

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.

Germany

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.

Noninvertible Symmetries, Anomalies, and Scattering Amplitudes

We compute the tree-level connected six-point function of identical scalar fluctuations of the AdS2 string worldsheet dual to the half-BPS Wilson line in planar   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 Super Yang-Mills. The calculation can be carried out analytically in the conformal gauge approach, where the boundary reparametrization mode of the string plays a crucial role. We also study the analytic continuation of the six-point function to an out-of-time-order configuration, which is related to a 3-to-3 scattering amplitude in flat space. As a check of our results, we also numerically compute the six-point function using the Nambu-Goto action in static gauge, finding agreement with the conformal gauge answer.

United States

Simone Giombi

Bendeguz Offertaler

Jieru Shan

Boundary reparametrizations and six-point functions on the AdS2 string

Anti–de Sitter space acts as an infrared cutoff for asymptotically free theories, allowing interpolation between a weakly coupled small-sized regime and a strongly coupled flat-space regime. We scrutinize the interpolation for theories in two dimensions from the perspective of boundary conformal theories. We show that the appearance of a singlet marginal operator destabilizes a gapless phase existing at a small size, triggering a boundary renormalization group flow to a gapped phase that smoothly connects to flat space. We conjecture a similar mechanism for confinement in gauge theories.