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Tadashi Okazaki

Publications and source records attributed to Tadashi Okazaki.

At least 37 records · Page 2Linked to original sources
arXiv2024

Asymptotic degeneracies of M2-brane SCFTs

We study the asymptotic growth of the degeneracy of the BPS local operators with scaling dimension $n/2$ in the three-dimensional superconformal field theories describing $N$ M2-branes. From the large $N$ supersymmetric indices we obtain the asymptotic formulas for degeneracies of the M2-brane SCFTs according to the Meinardus theorem. We observe an intriguing universal $n^{2/3}$ growth of the degeneracies in various theories of M2-brane SCFTs. We also determine the coefficients of $n^{2/3}$ growth as well as further corrections in these theories explicitly.

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arXiv2024

Line defect half-indices of $SU(N)$ Chern-Simons theories

We study the Wilson line defect half-indices of 3d $\mathcal{N}=2$ supersymmetric $SU(N)$ Chern-Simons theories of level $k\le -N$ with Neumann boundary conditions for the gauge fields, together with 2d Fermi multiplets and fundamental 3d chiral multiplets to cancel the gauge anomaly. We derive some exact results and also make some conjectures based on expansions of the $q$-series. We find several interesting connections with special functions known in the literature, including Rogers-Ramanujan functions for which we conjecture integral representations, and the appearance of Appell-Lerch sums for certain Wilson line half-index grand canonical ensembles which reveal an unexpected appearance of mock modular functions. We also find intriguing $q$-difference equations relating half-indices to Wilson line half-indices. Some of these results also have a description in terms of a dual theory with Dirichlet boundary conditions for the vector multiplet in the dual theory.

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arXiv2023

3d exceptional gauge theories and boundary confinement

We find boundary confining dualities of 3d $\mathcal{N}=2$ supersymmetric gauge theories with exceptional gauge groups. The half-indices which enumerate the boundary BPS local operators in the presence of Neumann and Dirichlet boundary conditions for gauge fields are identified with the Askey-Wilson type $q$-beta integrals and Macdonald type sums respectively. New conjectural identities of $E_6$ and $E_7$ integrals and sums are derived from the boundary confining dualities. We also consider theories with a vector multiplet and adjoint chiral, which correspond to an $\mathcal{N}=4$ vector multiplet, with appropriate boundary conditions. We argue for the boundary confinement of the $\mathcal{N}=4$ vector multiplet and comment on such theories also with classical gauge groups.

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arXiv2023

Excitations of bubbling geometries for line defects

The half-BPS Wilson line operators in the irreducible representations labeled by the Young diagrams for $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory have gravity dual descriptions. When the number $k$ of boxes of the diagram grows as $k\sim N^2$, the bubbling geometries emerge. We evaluate the spectra of quantum fluctuations on the bubbling geometries from the large $N$ and large $k$ limit of the supersymmetric indices decorated by the Wilson lines. The spectra of excitations over multi-particle $1/8$- and $1/2$-BPS states agree with the numbers of conjugacy classes of general linear group over finite fields while degeneracies of single particle BPS states are given by the general necklace polynomial. The bubbling geometry exhibits a new class of asymptotic degeneracy of states.

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arXiv2023

Large $N$ and large representations of Schur line defect correlators

We study the large $N$ and large representation limits of the Schur line defect correlators of the Wilson line operators transforming in the (anti)symmetric, hook and rectangular representations for $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory. By means of the factorization property, the large $N$ correlators of the Wilson line operators in arbitrary representations can be exactly calculated in principle. In the large representation limit they turn out to be expressible in terms of certain infinite series such as Ramanujan's general theta functions and the $q$-analogues of multiple zeta values ($q$-MZVs). Several generating functions for combinatorial objects, including partitions with non-negative cranks and conjugacy classes of general linear groups over finite fields, emerge from the large $N$ correlators. Also we find conjectured properties of the automorphy and the hook-length expansion satisfied by the large $N$ correlators.

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arXiv2023

Boundary confining dualities and Askey-Wilson type $q$-beta integrals

We propose confining dualities of $\mathcal{N}=(0,2)$ half-BPS boundary conditions in 3d $\mathcal{N}=2$ supersymmetric $SU(N)$, $USp(2n)$ and $SO(N)$ gauge theories. Some of these dualities have the novel feature that one (anti)fundamental chiral has Dirichlet boundary condition while the rest have Neumann boundary conditions. While some of the dualities can be extended to 3d bulk dualities, others should be understood intrinsically as 2d dualities as they seem to hold only at the boundary. The gauge theory Neumann half-indices are well-defined even for theories which contain monopole operators with non-positive scaling dimensions and they are given by Askey-Wilson type $q$-beta integrals. As a consequence of the confining dualities, new conjectural identities of such integrals are found.

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arXiv2023

Exact $\mathcal{N}=2^{*}$ Schur line defect correlators

We study the Schur line defect correlation functions in $\mathcal{N}=4$ and $\mathcal{N}=2^*$ $U(N)$ super Yang-Mills (SYM) theory. We find exact closed-form formulae of the correlation functions of the Wilson line operators in the fundamental, antisymmetric and symmetric representations via the Fermi-gas method in the canonical and grand canonical ensembles. All the Schur line defect correlators are shown to be expressible in terms of multiple series that generalizes the Kronecker theta function. From the large $N$ correlators we obtain generating functions for the spectra of the D5-brane giant and the D3-brane dual giant and find a correspondence between the fluctuation modes and the plane partition diamonds.

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arXiv2022

Dualities and flavored indices of M2-brane SCFTs

We study various conjectural dual descriptions of a stack of M2-branes in M-theory including ADHM, ABJ(M), BLG, discrete gauge theories and quiver Chern-Simons (CS) theories and propose several new dualities of the M2-brane SCFTs by analyzing flavored supersymmetric indices in detail. The mapping of local operators, Coulomb, Higgs and mixed branch operators as well as global symmetries under the dualities are obtained from the precise matching of the indices. Furthermore, we find closed form expressions for the Coulomb limit of the indices of the $U(N)$ ADHM theory and the dual quiver CS theory for arbitrary $N$ and propose a refined generating function for plane partitions with trace $N$. For the quiver CS theories we also find an infinite-sum expression for the Higgs limit of the indices which is more useful than the original expression.

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arXiv2022

$\mathcal{N}=2^{*}$ Schur indices

We find closed-form expressions for the Schur indices of 4d $\mathcal{N}=2^{*}$ super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with spectral zeta functions of an ideal Fermi-gas system. These functions are expressed in terms of the twisted Weierstrass functions, generating functions for quasi-Jacobi forms. The indices lie in the polynomial ring generated by the Kronecker theta function and the Weierstrass functions which contains the polynomial ring of the quasi-Jacobi forms. The grand canonical ensemble allows for another simple exact form of the indices as infinite series. In addition, we find that the unflavored Schur indices and their limits can be expressed in terms of several generating functions for combinatorial objects, including sum of triangular numbers, generalized sums of divisors and overpartitions.

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arXiv2022

M2-branes and plane partitions

There is a correspondence between the protected local operators in the 3d SCFTs describing the geometry $\mathbb{C}^2$ probed by a stack of $N$ M2-branes and plane partitions of trace $N$. We give combinatorial expressions of the indices which count the local operators parametrizing $\mathbb{C}^2/\mathbb{Z}_k$ probed by $N$ M2-branes in the canonical and grand canonical ensembles in terms of generating functions for plane partitions. We derive the asymptotic behaviors of the grand potential in the high-temperature limit and the scaling dimension in the large $N$ limit.

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arXiv2022

Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers

We propose a universal manipulation to obtain Seiberg-like dualities of 3d $\mathcal{N}=2$ general quiver gauge theories with unitary, symplectic and orthogonal gauge groups coupled to fundamental and bifundamental matter fields. We illustrate this with several examples of linear, circular and star-shaped quiver gauge theories. We examine the local operators in the theories by computing supersymmetric indices and also find precise matching for the proposed dualities as strong evidence. We also generalize the dualities in the presence of a boundary on which the theories obey $\mathcal{N}=(0,2)$ chiral half-BPS boundary conditions.

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arXiv2022

Fermi-gas correlators of ADHM theory and triality symmetry

We analytically study the Fermi-gas formulation of sphere correlation functions of the Coulomb branch operators for 3d $\mathcal{N}=4$ ADHM theory with a gauge group $U(N)$, an adjoint hypermultiplet and $l$ hypermultiplets which can describe a stack of $N$ M2-branes at $A_{l-1}$ singularities. We find that the leading coefficients of the perturbative grand canonical correlation functions are invariant under a hidden triality symmetry conjectured from the twisted M-theory. The triality symmetry also helps us to fix the next-to-leading corrections analytically.

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arXiv2021

Abelian mirror symmetry of $\mathcal{N}=(2,2)$ boundary conditions

We evaluate half-indices of $\mathcal{N}=(2,2)$ half-BPS boundary conditions in 3d $\mathcal{N}=4$ supersymmetric Abelian gauge theories. We confirm that the Neumann boundary condition is dual to the generic Dirichlet boundary condition for its mirror theory as the half-indices perfectly match with each other. We find that a naive mirror symmetry between the exceptional Dirichlet boundary conditions defining the Verma modules of the quantum Coulomb and Higgs branch algebras does not always hold. The triangular matrix obtained from the elliptic stable envelope describes the precise mirror transformation of a collection of half-indices for the exceptional Dirichlet boundary conditions.

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arXiv2021

Singular BPS boundary conditions in $\mathcal{N} = (2,2)$ supersymmetric gauge theories

We derive general BPS boundary conditions in two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $\mathcal{N}=(2,2)$ supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in $\mathbb{C}^2$ with a special Lagrangian 3-cycle in $\mathbb{C}^3$.

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arXiv2019

Sphere correlation functions and Verma modules

We propose a universal IR formula for the protected three-sphere correlation functions of Higgs and Coulomb branch operators of ${\cal N}=4$ supersymmetric quantum field theories with massive, topologically trivial vacua.

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arXiv2019

Dualities of Corner Configurations and Supersymmetric Indices

We compute supersymmetric indices which count local operators at certain half-BPS interfaces and quarter-BPS junctions of interfaces in four-dimensional $\mathcal{N}=4$ Super Yang-Mills theory. We use the indices as very stringent tests of a variety of string theory-inspired conjectures about the action of S-duality on such defects.

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arXiv2019

Mirror symmetry of 3d $\mathcal{N}=4$ gauge theories and supersymmetric indices

We compute supersymmetric indices to test mirror symmetry of three-dimensional $\mathcal{N}=4$ gauge theories and dualities of half-BPS enriched boundary conditions and interfaces in four-dimensional $\mathcal{N}=4$ Super Yang-Mills theory. We find the matching of indices as strong evidences for various dualities of the 3d interfaces conjectured by Gaiotto and Witten under the action of S-duality in Type IIB string theory.

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