arXiv subjects

Sanefumi Moriyama

Publications and source records attributed to Sanefumi Moriyama.

At least 19 recordsLinked to original sources

arXiv2026

Factorized Quantum Curves and Minuscule Vertices in 3D Duality Cascades with FI Parameters

In the study of duality cascades in three-dimensional gauge theories without FI parameters, an important role is played by a fundamental domain whose vertices correspond to brane configurations with vanishing relative ranks. Through the Fermi gas formalism, such brane configurations are known to be represented by factorized quantum curves. In this paper, we show that this factorized description extends naturally to quantum curves associated with del Pezzo geometries possessing exceptional Weyl-group symmetries in the presence of FI parameters. We find that the vertices of the fundamental domain corresponding to the weights of minuscule representations are realized as factorized quantum curves built from canonical operators interpreted as 5-branes dressed with FI parameters. This reveals an unexpected relation between factorized quantum curves and minuscule representations, providing a physical realization of these vertices in terms of ``extremal'' brane configurations.

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arXiv2026

An M2/M5 Duality from the Giant Graviton Expansion

We conjecture a precise relation between the superconformal indices of two theories defined in different spacetime dimensions. The first is the three-dimensional ABJM theory describing the worldvolume of parallel M2-branes in M-theory on $\mathbb{R}^{10,1}$. The second is the $\mathcal{N}=(2,0)$ theory in six dimensions which describes the worldvolume of parallel M5-branes in the same background. As we review, the existence of such a duality is closely related to Imamura's proposal for the giant graviton expansion of the three-dimensional index. We check our conjecture against various results for the two indices available in the literature. Using an existing proposal of Hristov for the ABJM superconformal index, we verify our conjecture to the first three orders in an expansion around the six-dimensional Cardy limit.

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arXiv2025

Giant Gravitons and Volume Minimisation

We establish a precise correspondence between the giant graviton expansion of the superconformal index of field theories in $D\leq 4$, and the master volume formalism of Gauntlett, Martelli and Sparks (GMS) which determines the near horizon geometries of certain BPS black holes and black strings in supergravity. We focus on 4d $\mathcal{N}=1$ superconformal field theories arising on the world volume of $N$ D3 branes placed at the tip of a cone over a toric Sasaki-Einstein manifold SE$_{5}$, the simplest example of which is $S^5$, corresponding to $\mathcal{N}=4$ super-Yang-Mills. The giant graviton expansion realises the superconformal index as the sum of contributions from wrapped D3 branes in the dual AdS$_{5}\times \text{SE}_{5}$. We argue that, for large wrapping numbers, the asymptotics of each such contribution is governed by the master volume of a particular metric deformation of $\text{SE}_5$ (suitably fibred over $S^{3}$). In particular, the wrapping numbers of a generic giant graviton configuration are identified with Kähler moduli of the corresponding metric. We further show that at large $N$ the entropy function of the relevant AdS$_5\times \text{SE}_5$ BPS rotating black hole is recovered by extremising over these moduli. Our results suggest that the complex Euclidean geometries corresponding to rotating BPS black holes in AdS$_{5}$ are determined by a close analogue of GMS volume minimisation, and that conversely, the off-shell geometries considered in such minimisation procedures should be understood as the near-horizon geometries of back-reacted giant gravitons. We present analogous results for 3d $\mathcal{N}=2$ theories holographically dual to M-theory on AdS$_4\times \text{SE}_7$.

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arXiv2024

Finiteness and Uniqueness of Duality Cascades in Three Dimensions for Affine Quivers

For three-dimensional circular-quiver supersymmetric Chern-Simons theories, the questions, whether duality cascades always terminate and whether the endpoint is unique, were rephrased into the question whether a polytope defined in the parameter space of relative ranks for duality cascades is a parallelotope, filling the space by discrete translations. By regarding circular quivers as affine Dynkin diagrams, we generalize the arguments into other affine quivers. We find that, after rewriting properties into the group-theoretical language, most arguments work in the generalizations. Especially, we find that, instead of the original relation to parallelotopes, the corresponding polytope still fills the parameter space but with some gaps. This indicates that, under certain restrictions, duality cascades still terminate uniquely.

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arXiv2024

Affine Symmetries for ABJM Partition Function and its Generalization

Partially motivated by the fact that the grand partition function of the ABJM theory or its generalization is expressed by a spectral operator enjoying symmetries of the Weyl group, it was found that the grand partition function satisfies the q-Painleve equation, which is constructed from the affine Weyl group. In this paper we clarify the affine symmetries of the grand partition function. With the affine symmetries, we find that the grand partition function extends naturally outside the fundamental domain of duality cascades and once the Painleve equation holds in the fundamental domain, so does it outside.

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arXiv2023

40 Bilinear Relations of q-Painleve VI from N=4 Super Chern-Simons Theory

We investigate partition functions of the circular-quiver supersymmetric Chern-Simons theory which corresponds to the q-deformed Painleve VI equation. From the partition functions with the lowest rank vanishing, where the circular quiver reduces to a linear one, we find 40 bilinear relations. The bilinear relations extend naturally to higher ranks if we regard these partition functions as those in the lowest order of the grand canonical partition functions in the fugacity. Furthermore, we show that these bilinear relations are a powerful tool to determine some unknown partition functions. We also elaborate the relation with some previous works on q-Painleve equations.

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arXiv2022

Duality Cascades and Parallelotopes

Duality cascades are a series of duality transformations in field theories, which can be realized as the Hanany-Witten transitions in brane configurations on a circle. In the setup of the ABJM theory and its generalizations, from the physical requirement that duality cascades always end and the final destination depends only on the initial brane configuration, we propose that the fundamental domain of supersymmetric brane configurations in duality cascades can tile the whole parameter space of relative ranks by translations, hence is a parallelotope. We provide our arguments for the proposal.

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arXiv2022

Duality Cascades and Affine Weyl Groups

Brane configurations in a circle allow subsequent applications of the Hanany-Witten transitions, which are known as duality cascades. By studying the process of duality cascades corresponding to quantum curves with symmetries of Weyl groups, we find a hidden structure of affine Weyl groups. Namely, the fundamental domain of duality cascades consisting of all the final destinations is characterized by the affine Weyl chamber and the duality cascades are realized as translations of the affine Weyl group, where the overall rank in the brane configuration associates to the grading operator of the affine algebra. The structure of the affine Weyl group guarantees the finiteness of the processes and the uniqueness of the endpoint of the duality cascades. In addition to the original duality cascades, we can generalize to the cases with Fayet-Iliopoulos parameters. There we can utilize the Weyl group to analyze the fundamental domain similarly and find that the fundamental domain continues to be the affine Weyl chamber. We further interpret the Weyl group we impose as a "half" of the Hanany-Witten transition.

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arXiv2021

Quantum Representation of Affine Weyl Groups and Associated Quantum Curves

We study a quantum (non-commutative) representation of the affine Weyl group mainly of type $E_8^{(1)}$, where the representation is given by birational actions on two variables $x$, $y$ with $q$-commutation relations. Using the tau variables, we also construct quantum "fundamental" polynomials $F(x,y)$ which completely control the Weyl group actions. The geometric properties of the polynomials $F(x,y)$ for the commutative case is lifted distinctively in the quantum case to certain singularity structures as the $q$-difference operators. This property is further utilized as the characterization of the quantum polynomials $F(x,y)$. As an application, the quantum curve associated with topological strings proposed recently by the first named author is rederived by the Weyl group symmetry. The cases of type $D_5^{(1)}$, $E_6^{(1)}$, $E_7^{(1)}$ are also discussed.

math.QA↗

arXiv2021

Brane Transitions from Exceptional Groups

It is a well-known result by Hanany and Witten that, when two five-branes move across each other, D3-branes stretching between them are generated. Later the same brane configurations played a crucial role in understanding the worldvolume theory of multiple M2-branes. Recently the partition function of multiple M2-branes was transformed to the Fredholm determinant for quantum algebraic curves, where the characteristic 3/2 power law of degrees of freedom is reproduced and the determinant enjoys a large symmetry given by exceptional Weyl groups. The large exceptional Weyl group reproduces the Hanany-Witten brane transitions and, besides, contains brane transitions unknown previously. Aiming at understanding the new brane transitions better, we generalize our previous study on the D5 quantum curve to the E7 case, which requires delicate handling of degeneracies. By combining the results of these two cases, we propose a "local" rule for the brane transitions.

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arXiv2020

Quantum Mirror Map for Del Pezzo Geometries

Mirror maps play an important role in studying supersymmetric gauge theories. In these theories the dynamics is often encoded in an algebraic curve where two sets of periods enjoy the symplectic structure. The A-periods contribute to redefinitions of chemical potentials known as mirror maps. Using the quantization of the $D_5$ del Pezzo geometry, which enjoys the symmetry of the $D_5$ Weyl group, we are able to identify clearly the group-theoretical structure and the multi-covering structure for the mirror map. With the structures, we can apply the mirror map to superconformal Chern-Simons theories describing the worldvolume of multiple M2-branes on various backgrounds, where we find that the redefinition of the chemical potential is obtained directly from the mirror map. Besides, we have interesting observations for the mirror map: The representations appearing in the quantum mirror map are the same as those appearing in the BPS indices except for the trivial case of degree 1 and the coefficients are all integers.

hep-th↗

arXiv2020

Spectral Theories and Topological Strings on del Pezzo Geometries

Motivated by understanding M2-branes, we propose to reformulate partition functions of M2-branes by quantum curves. Especially, we focus on the backgrounds of del Pezzo geometries, which enjoy Weyl group symmetries of exceptional algebras. We construct quantum curves explicitly and turn to the analysis of classical phase space areas and quantum mirror maps. We find that the group structure helps in clarifying previous subtleties, such as the shift of the chemical potential in the area and the identification of the overall factor of the spectral operator in the mirror map. We list the multiplicities characterizing the quantum mirror maps and find that the decoupling relation known for the BPS indices works for the mirror maps. As a result, with the group structure we can present explicitly the statement for the correspondence between spectral theories and topological strings on del Pezzo geometries.

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arXiv2019

Hanany-Witten Transition in Quantum Curves

It was known that the U$(N)^4$ super Chern-Simons matrix model describing the worldvolume theory of D3-branes with two NS5-branes and two $(1,k)$5-branes in IIB brane configuration (dual to M2-branes after taking the T-duality and the M-theory lift) corresponds to the $D_5$ quantum curve. For deformations of these two objects, on one hand the super Chern-Simons matrix model has three degrees of freedom (of relative rank deformations interpreted as fractional branes in brane configurations), while on the other hand the $D_5$ curve has five degrees of freedom (characterized by point configurations of asymptotic values). To identify the three-dimensional parameter space of brane configurations in the five-dimensional space of point configurations, we propose the necessity to cut the compact T-duality circle (or the circular quiver diagram) open, which is similar to the idea of "fixing a reference frame" or "fixing a local chart". Since the parameter space of curves enjoys the $D_5$ Weyl group beautifully, we are naturally led to conjecture that M2-branes are not only deformed by fractional branes but more obscure geometrical backgrounds.

hep-th↗

arXiv2019

ABJM Matrix Model and 2D Toda Lattice Hierarchy

It was known that one-point functions in the ABJM matrix model (obtained by applying the localization technique to one-point functions of the half-BPS Wilson loop operator in the ABJM theory) satisfy the Jacobi-Trudi formula, which strongly indicates the integrable structure of the system. In this paper, we identify the integrable structure of two-point functions in the ABJM matrix model as the two-dimensional Toda lattice hierarchy. The identification implies infinitely many non-linear differential equations for the generating function of the two-point functions.

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arXiv2018

Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models

It was known that quantum curves and super Chern-Simons matrix models correspond to each other. From the viewpoint of symmetry, the algebraic curve of genus one, called the del Pezzo curve, enjoys symmetry of the exceptional algebra, while the super Chern-Simons matrix model is described by the free energy of topological strings on the del Pezzo background with the symmetry broken. We study the symmetry breaking of the quantum cousin of the algebraic curve and reproduce the results in the super Chern-Simons matrix model.

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arXiv2018

Jacobi-Trudi Identity in Super Chern-Simons Matrix Model

It was proved by Macdonald that the Giambelli identity holds if we define the Schur functions using the Jacobi-Trudi identity. Previously for the super Chern-Simons matrix model (the spherical one-point function of the superconformal Chern-Simons theory describing the worldvolume of the M2-branes) the Giambelli identity was proved from a shifted version of it. With the same shifted Giambelli identity we can further prove the Jacobi-Trudi identity, which strongly suggests an integrable structure for this matrix model.

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arXiv2018

Two-Point Functions in ABJM Matrix Model

We introduce non-trivial two-point functions of the super Schur polynomials in the ABJM matrix model and study their exact values with the Fermi gas formalism. We find that, although defined non-trivially, these two-point functions enjoy two simple relations with the one-point functions. One of them is associated with the Littlewood-Richardson rule, while the other is more novel. With plenty of data, we also revisit the one-point functions and study how the diagonal BPS indices are split asymmetrically by the degree difference.

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arXiv2017

Superconformal Chern-Simons Theories from del Pezzo Geometries

We present an explicit expression for the grand potential of the U(N)^3 superconformal Chern-Simons theory with the Chern-Simons levels being (k,0,-k). From the viewpoint of the Newton polygon, it is expected that the grand potential is given by the free energy of the topological string theory on the local D_5 del Pezzo geometry, though the explicit identification was a puzzle for years. We show how the expectation is realized explicitly. As a bonus, we can also study the Z_2 orbifold of this theory and find the grand potential is now given in terms of the local E_7 del Pezzo geometry.

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