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Interfaces and Quantum Algebras, II: Cigar Partition Function

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arxiv 2306.16434 v1 pith:JF3NOBP4 submitted 2023-06-28 hep-th math-phmath.AGmath.MPmath.QA

classification hep-thmath-phmath.AGmath.MPmath.QA
keywords cigarpartitionquantumfunctionsupersymmetricvariousalgebrascaptures
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abstract

The supersymmetric cigar (half-)index or cigar partition function of 3d $\mathcal{N}=2$ gauge theories contains a wealth of information. Physically, it captures the spectrum of BPS states, the non-perturbative corrections to various partition functions, the effective twisted superpotential and the data of supersymmetric vacua. Mathematically, it defines the K-theoretic Vertex counting vortices/quasimaps, and connects to quantum K-theory, as well as elliptic cohomology and stable envelopes. We explore these topics from the physics standpoint, systematically developing the foundations and explaining various mathematical properties using the quantum field theory machinery.

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Cited by 1 Pith paper

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  1. $Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory

    hep-th 2025-07 conditional novelty 7.0 of 10

    In 5d N=1 U(N) gauge theory, codimension-two defects produce Q-operators whose q-difference equations are the Baxter TQ equations of XXZ spin chains built on bi-infinite evaluation modules of quantum affine algebras.

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