arXiv subjects

Shota Komatsu

Publications and source records attributed to Shota Komatsu.

At least 19 recordsLinked to original sources

arXiv2026

Matrix Theory from Holography

We propose a setup that embeds Matrix Theory for M-theory into the AdS/CFT correspondence, allowing the former to be tested using the latter. The central claim is a triality among the BMN matrix model of rank $m$, a large-charge monopole sector of ABJM theory with charge $J$, and M-theory on the maximally supersymmetric eleven-dimensional pp-wave with a compact lightlike direction. The relevant ABJM limit sends $N,k,J\to\infty$ while keeping $N/k^2$ and $m=J/k$ fixed. We provide quantitative evidence for this triality by showing that, in this triple-scaling limit, the ABJM superconformal index agrees precisely with a grand-canonical sum of Witten indices of the $U(m)$ BMN matrix model. This relation also yields a compact grand-canonical expression for the BMN index, which we use to revisit its large-$m$ behavior. Our analytic and numerical results reveal strong boson--fermion cancellations and show no evidence for the previously claimed $e^{O(m^2)}$ growth when the BMN charge scales as $Q \sim m^2$. We further study the correspondence between the BPS cohomologies of the two theories by constructing a letter-level dictionary. This leads to a new notion of BPS fortuity in ABJM theory that survives even at strict $N=\infty$: although the usual fortuity associated with finite-$N$ trace relations disappears in the triple-scaling limit, each fixed-monopole sector is governed by the effective rank $m$, and finite-$m$ trace relations generate fortuitous states that map directly to fortuitous states of the BMN matrix model. Finally, we discuss connections to related concepts such as large-charge matrix models, open--closed--open triality, and worldline holography.

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arXiv2026

Time-Dependent Integrability from Gauge Theory, I

Solvable time-dependent systems provide important settings for studying non-equilibrium physics, where exact results are rare. They are also useful for benchmarking quantum simulations, which can directly probe real-time dynamics beyond the reach of conventional numerical approaches. In this paper, we show that the four-dimensional Chern-Simons theory offers a natural and unifying framework for constructing such systems. Focusing on classically integrable field theories, we consider a generalization of the four-dimensional Chern-Simons theory in which the usual holomorphic one-form is replaced by a more general, spacetime-dependent one-form. This yields a systematic procedure for generating time-dependent integrable field theories and establishes a universal relation: for every theory obtained in this way, the allowed time dependence coincides with the one-loop renormalization group flow. Despite the explicit time dependence, these theories retain Lax integrability and remain solvable by inverse scattering methods. Our construction applies to both ultralocal and non-ultralocal theories and extends previously known time-dependent sigma models to a much broader class of integrable systems. It also admits rewriting as dilaton gravity coupled to matter, producing a large family of classically integrable dilaton gravity theories in two dimensions. We also comment on connections to time-dependent integrable models studied recently in condensed matter physics and non-autonomous integrable systems arising from dimensionally-reduced Einstein gravity.

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arXiv2026

Worldsheet for Generalized Veneziano Amplitudes

We present a worldsheet action that reproduces a class of dual resonance amplitudes discussed in the literature, which generalize the Veneziano amplitude for open strings. Our proposal builds on the chiral composite linear dilaton introduced recently. We further compute higher-point extensions and closed-string analogs, which exhibit partial crossing symmetry.

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arXiv2026

Crosscap Defects

We introduce a novel class of defects, termed crosscap defects, in conformal field theory (CFT) in general dimensions. These arise from quotienting the spacetime by a $Z_2$ automorphism, and provide higher-codimension generalisations of CFT on real projective space ($RP^{d}$). Crosscap defects extend along a $p$-dimensional fixed locus of the $Z_2$ action and preserve an $SO(p+1,1)\times PO(d-p)$ subgroup of the conformal group. The two-point functions of operators in this setup exhibit three operator product expansion channels: bulk, image, and defect. These lead to several crosscap crossing equations, which we present. We analyse conformal block decompositions and show that the blocks are identical to defect CFT blocks up to a redefinition of cross ratios. As concrete examples, we study crosscap defects in the $O(N)$ model at the Gaussian and Wilson--Fisher fixed points in the $\varepsilon$-expansion. We compute explicitly the associated CFT data as a function of $p$ and find that, unlike standard defects, displacement and tilt operators are absent for generic $p$. They provide examples of defect conformal manifolds without exactly marginal operators.

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arXiv2026

Continuous Family of Conformal Field Theories and Exactly Marginal Operators

Does a conformal manifold imply the existence of exactly marginal operators? We answer this question affirmatively under the assumption that there exists a conformal interface with certain properties connecting nearby CFTs. We show that the exactly marginal operator that connects the CFTs can be reconstructed from the interface displacement operator. Our construction is model-independent and based on the general principles of conformal symmetry.

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arXiv2026

Dressing and Screening in Anti-de Sitter

Motivated by a question of defining gauge-invariant observables in cosmology and by the close connection between perturbation theory in de Sitter (dS) and Anti-de Sitter (AdS), we study scalar electrodynamics in AdS in setups that are largely unexplored but relevant for dS physics. For photons with standard (Dirichlet) boundary conditions, we analyze charged scalars whose boundary conditions break the $U(1)$ symmetry. This leads to a nonstandard Higgs mechanism in which the gauge field acquires a one-loop mass without a classical vacuum expectation value. Using recent advances in perturbation theory in AdS, we compute this mass explicitly and evaluate charged-scalar four-point functions. We also provide an alternative derivation based on boundary Ward identities. For photons with alternate (Neumann) boundary conditions, where local charged operators are not gauge invariant, we construct physical observables by dressing charged fields with geodesic Wilson lines. These dressed operators have well-behaved conformal properties and unphysical photon modes decouple from their correlation functions. Explicit one-loop computations further reveal the decoupling of boundary field strengths, for which we provide a nonperturbative argument based on higher-form symmetry. Along the way, we explain the physical consequences of spontaneous breaking of higher-form symmetry in AdS, including the role of the tilt operator, the relation between one-form symmetry and endpoints of Wilson lines at the boundary, and a generalized-symmetry interpretation of conserved currents dual to bulk gauge fields.

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arXiv2026

Analyticity and Unitarity for Cosmological Correlators

We study the fundamentals of quantum field theory on a rigid de Sitter space. We show that the perturbative expansion of late-time correlation functions to all orders can be equivalently generated by a non-unitary Lagrangian on a Euclidean AdS geometry. This finding simplifies dramatically perturbative computations, as well as allows us to establish basic properties of these correlators, which comprise a Euclidean CFT. We use this to infer the analytic structure of the spectral density that captures the conformal partial wave expansion of a late-time four-point function, to derive an OPE expansion, and to constrain the operator spectrum. Generically, dimensions and OPE coefficients do not obey the usual CFT notion of unitarity. Instead, unitarity of the de Sitter theory manifests itself as the positivity of the spectral density. This statement does not rely on the use of Euclidean AdS Lagrangians and holds non-perturbatively. We illustrate and check these properties by explicit calculations in a scalar theory by computing first tree-level, and then full one-loop-resummed exchange diagrams. An exchanged particle appears as a resonant feature in the spectral density which can be potentially useful in experimental searches.

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arXiv2025

F-theorem for Quantum Field Theories in Anti-de Sitter Space

We introduce a regularized free energy $\mathcal{F}_{\text{AdS}}$ for massive quantum field theories (QFTs) on Anti-de Sitter space (AdS). We conjecture this quantity to be monotonic under the renormalization group (RG) flow induced by boundary perturbations, generalizing the known boundary $F$-theorem to non-conformal setups. We test this conjecture in several examples and provide a proof in two dimensions. We also discuss applications to long-range critical points, obtaining bounds on the sphere free energy of long- and short-range Ising models in three dimensions.

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arXiv2025

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

We propose a bosonic string dual to large $N$ chiral Yang-Mills in two dimensions at finite 't Hooft coupling. The worldsheet theory is a $β$-$γ$ 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 CFTs with $c<24$ and their $T\bar{T}$-, $J\bar{T}$-deformations. The results hint at interrelations among confining, nonrelativistic and matrix strings, and AdS$_3/$CFT$_2$.

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arXiv2025

Chiral Composite Linear Dilaton as String Dual to Two-Dimensional Yang-Mills

Two-dimensional Yang-Mills theory (2d YM) is arguably the simplest confining gauge theory and its large $N_c$ expansion has a structure of the genus expansion in string theory. Nevertheless various aspects of its worldsheet description have not been fully understood. In this paper, we elaborate on a bosonic string dual to large $N_c$ chiral 2d YM at finite 't Hooft coupling, proposed in our earlier work. The worldsheet theory consists of $β$-$γ$ system deformed by linear dilaton action built from a composite of $γ$. It can be seen as a noncritical version of nonrelativistic string theory introduced by Gomis and Ooguri. We provide a detailed analysis of the worldsheet operator product expansion and the computation of three- and four-point scattering amplitudes.

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arXiv2025

Coulomb Branch and Integrability

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 $AdS_5\times S^{5}$. 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.

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arXiv2025

Exact Three-Point Functions in $\mathcal{N}=2$ Superconformal Field Theories: Integrability vs. Localization

We propose an integrability approach for planar three-point functions at finite coupling in $\mathcal{N}=2$ superconformal field theories obtained as $\mathbb{Z}_K$ 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.

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arXiv2025

Einstein gravity from a matrix integral -- Part I

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.

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arXiv2025

Einstein gravity from a matrix integral -- Part II

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.

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arXiv2025

Cosmological Correlators at Finite Coupling

We study finite-coupling effects of QFT on a rigid de Sitter (dS) background taking the $O(N)$ vector model at large $N$ as a solvable example. Extending standard large $N$ techniques to the dS background, we analyze the phase structure and late-time four-point functions. Explicit computations reveal that the spontaneous breaking of continuous symmetries is prohibited due to strong IR effects, akin to flat two-dimensional space. Resumming loop diagrams, we compute the late-time four-point functions of vector fields at large $N$, demonstrating that their spectral density is meromorphic in the spectral plane and positive along the principal series. These results offer highly nontrivial checks of unitarity and analyticity for cosmological correlators.

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arXiv2024

Strings from Feynman Diagrams

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 $1/N$ 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.

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arXiv2024

2d QCD and Integrability, Part II: Generalized QCD

We extend the study of integrable structures and analyticity of the spectrum 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 an associated Fredholm equation, we numerically study the analytic structures 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.

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arXiv2024

2d QCD and Integrability, Part I: 't Hooft model

We study analytic properties and integrable structures of the meson spectrum in large $N_c$ QCD$_2$. 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 $m=m_1=m_2$, 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.

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