A new shell formula unifies and delivers explicit closed-form expressions plus recursions for instanton partition functions in 5d SYM and multiple gauge origami configurations using arbitrary-dimensional Young diagrams.
Elliptic genera of 2d N=2 gauge theories
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We compute the elliptic genera of general two-dimensional N=(2,2) and N=(0,2) gauge theories. We find that the elliptic genus is given by the sum of Jeffrey-Kirwan residues of a meromorphic form, representing the one-loop determinant of fields, on the moduli space of flat connections on T^2. We give several examples illustrating our formula, with both Abelian and non-Abelian gauge groups, and discuss some dualities for U(k) and SU(k) theories. This paper is a sequel to the authors' previous paper arXiv:1305.0533.
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Proposes comet-shaped quiver gauge theories for surface defects with nested instantons in 4D gauge theories on T^2 × T*C_{g,k} and gives conjectural explicit formulae for the virtual equivariant elliptic genus of bundles over nested Hilbert schemes of points on the affine plane.
Exact partition functions for N=(2,2) theories on spindles are computed via localisation for both twist and anti-twist, yielding a unified formula.
Derives a distributional real-line integral formula for abelian observables in A-twisted N=(2,2) theories on S², verifies it on the CP^{N-1} GLSM correlator, and uses hyperfunctions to equate it with contour integrals matching the Jeffrey-Kirwan prescription.
High-temperature limits on higher sheets of the superconformal index for (A1,A2n) Argyres-Douglas theories yield Gang-Kim-Stubbs 3d N=2 theories whose boundaries support Virasoro minimal model VOAs M(2,2n+3) and associated MTCs.
Computes boundary-to-boundary elliptic kernels via localization for 4d N=1 theories and proves rank-changing Seiberg dualities as Jeffrey-Kirwan residue identities.
Pedagogical crash-course notes on supersymmetric field theory across 2–10 dimensions, organized around recurring structures such as holomorphy, dualities, indices, BPS data, and anomalies.
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A new shell formula unifies and delivers explicit closed-form expressions plus recursions for instanton partition functions in 5d SYM and multiple gauge origami configurations using arbitrary-dimensional Young diagrams.
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Defects, nested instantons and comet shaped quivers
Proposes comet-shaped quiver gauge theories for surface defects with nested instantons in 4D gauge theories on T^2 × T*C_{g,k} and gives conjectural explicit formulae for the virtual equivariant elliptic genus of bundles over nested Hilbert schemes of points on the affine plane.
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Exact partition functions for N=(2,2) theories on spindles are computed via localisation for both twist and anti-twist, yielding a unified formula.
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High-temperature limits on higher sheets of the superconformal index for (A1,A2n) Argyres-Douglas theories yield Gang-Kim-Stubbs 3d N=2 theories whose boundaries support Virasoro minimal model VOAs M(2,2n+3) and associated MTCs.
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Localization, Factorization and Dualities for Elliptic Kernels
Computes boundary-to-boundary elliptic kernels via localization for 4d N=1 theories and proves rank-changing Seiberg dualities as Jeffrey-Kirwan residue identities.
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Pedagogical crash-course notes on supersymmetric field theory across 2–10 dimensions, organized around recurring structures such as holomorphy, dualities, indices, BPS data, and anomalies.