Dualities of corner configurations and supersymmetric indices

2019

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We propose dual pairs of N = (0, 4) half-BPS boundary conditions for 3d N = 4 Abelian gauge theories related to mirror symmetry and S-duality by showing the matching of boundary 't Hooft anomalies and supersymmetric indices. We find simple N = (0, 4) mirror symmetry between 2d N = (0, 4) Abelian gauge theories and free Fermi multiplets that generalizes N = (0, 2) Abelian duality. We also propose a prescription for computing half-index of enriched Neumann boundary condition including 2d boundary bosonic matters by gauging the 2d boundary flavor symmetry of Dirichlet boundary condition. By coupling N = (0, 4) half-BPS boundary configurations of 3d N = 4 gauge theories to quarter-BPS corner configurations of 4d N = 4 Super Yang-Mills theories, we further obtain a new type of 4d-3d-2d duality that may involve 3d non-Abelian gauge symmetry.

Section: Resultsmentioning

confidence: 63%

Section: Resultsmentioning

confidence: 99%

Section: Future Workmentioning

confidence: 99%

“…We define the quarter-index as the trace over the cohomology of the preserved supercharges [31] IV(t, x; q) := Tr Op (−1) F q J+ H+C…”

Section: Indicesmentioning

confidence: 99%

Section: Introduction and Conclusionmentioning

confidence: 99%

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Abelian dualities of $$ \mathcal{N} $$ = (0, 4) boundary conditions

2019

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

Hatsuda

2023

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We find closed-form expressions for the Schur indices of 4d $$ \mathcal{N} $$ 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.

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

2021

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We evaluate half-indices of $$ \mathcal{N} $$ N = (2, 2) half-BPS boundary conditions in 3d $$ \mathcal{N} $$ 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.