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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 $SO(7)\times SO(3)$ 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., Comment: 22 pages + appendices, 3 figures

We initiate the S-matrix bootstrap analysis of theories with non-invertible symmetries in (1+1) dimensions. Our previous work 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 $\mathscr C^{*}_{\mathscr{M}}$ and Symmetry Topological Field Theory (SymTFT). This highlights the utility of SymTFT in the analysis of scattering amplitudes., Comment: 33 pages plus appendices, v3: references added, typos corrected, appendix added

We extend our study of integrable structures in large $N_c$ QCD$_2$ to a broad class of theories called the generalized QCD, which are given by the Lagrangian $\mathcal{L}\propto {\rm tr}\,B\wedge F- {\rm tr}\,V(B)$ coupled to quarks in the fundamental representation. We recast the Bethe-Salpeter equation for the meson spectrum into a TQ-Baxter equation and determine a transfer matrix in a closed form for any given polynomial $V(B)$. Using this reformulation, we derive the asymptotic expansion of energy levels and wavefunctions. Examining the analytic structure of the spectrum as a function of the coefficients of $V(B)$, we determine the region of couplings where the theory admits a positive and discrete spectrum of mesons. Furthermore, we uncover a multi-sheeted structure with infinitely many multi-critical points, where several mesons become simultaneously massless. Lastly, we illustrate that this structure persists in the large-representation limit of the generalized QCD with the SU(2) gauge group., Comment: 62 pages; v2: Added Appendix E: "Non-critical spontaneous symmetry breaking of PT-symmetry", typos corrected

We study correlation functions on the Coulomb branch of planar $\mathcal{N} = 4$ super-Yang- Mills theory (SYM), and their relationship with integrability, the operator product expansion (OPE), the sum rule, the large charge expansion, and holography. First, we compute one-point functions of arbitrary scalar operators at weak coupling and derive a compact spin-chain representation. We next study the two-point functions of chiral primaries at one loop and find that the radius of convergence of OPE in position space is infinite. We estimate the asymptotic growth of the OPE data based on this finding. Finally, we propose a concrete nonperturbative formula that connects the correlation functions on the Coulomb branch with the correlation functions with large charge insertions at the conformal point and provide a holographic interpretation based on a large D3-brane in AdS. The formula extends the known connection between the large charge sector and the Coulomb branch for rank-1 theories to the large $N$ limit., Comment: 51 pages

We show that crossing symmetry of S-matrices is modified in certain theories with non-invertible symmetries or anomalies. Focusing on integrable flows to gapped phases in two dimensions, we find that S-matrices derived previously from the bootstrap approach are incompatible with non-invertible 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., Comment: 7 pages plus supplemental material, v2: references added, typos corrected

We revisit the Berenstein-Maldacena-Nastase (BMN) conjecture relating M-theory on a PP-wave background and Matrix Quantum Mechanics (MQM) of $N\times N$ matrices. In particular, we study the BMN MQM at strong coupling and finite $N$ 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., Comment: 40 pages + appendices, 6 figures