Generalized Schur partition functions Z_USp(2N)(q; alpha) for 4d N=2 USp(2N) theories satisfy order-(N+1) MLDEs with vanishing Wronskian index, alpha fixing MLDE parameters, with links to RCFT characters and a conjecture on quantum monodromy traces.
Three-dimensional gauge theories with supersymmetry enhancement
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abstract
We conjecture infrared emergent $\mathcal{N}=4$ supersymmetry for a class of three-dimensional $\mathcal{N}=2$ $U(1)$ gauge theories coupled with a single chiral multiplet. One example is the case where $U(1)$ gauge group has the Chern-Simons level $-\frac{3}2$ and the chiral multiplet has gauge charge $+1$. Other examples are related to this example either by known dualities or rescaling the Abelian gauge field. We give three independent evidences for the conjecture: 1) exact match between the central charges of the $U(1)$ R-symmetry current and the $U(1)$ topological symmetry current, 2) semi-classical construction of the $\mathcal{N}=4$ stress-tensor multiplet, and 3) an IR duality between a direct product of the two copies of the 3d theory on the one hand, and an $\mathcal{N}=4$ theory obtained by gauging the diagonal $SU(2)$ flavor symmetry of the $T[SU(2)]$ theory, on the other. The duality in 3) follows from geometrical aspects of the 3d-3d correspondence.
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A refined 3D index is defined by adding flavor symmetry gradings to the superconformal index of T[M], yielding an explicit infinite-sum formula from Dehn surgery that is claimed to be a strictly stronger invariant than the standard 3D index.
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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Generalised 4d Partition Functions and Modular Differential Equations
Generalized Schur partition functions Z_USp(2N)(q; alpha) for 4d N=2 USp(2N) theories satisfy order-(N+1) MLDEs with vanishing Wronskian index, alpha fixing MLDE parameters, with links to RCFT characters and a conjecture on quantum monodromy traces.
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Refined 3D index
A refined 3D index is defined by adding flavor symmetry gradings to the superconformal index of T[M], yielding an explicit infinite-sum formula from Dehn surgery that is claimed to be a strictly stronger invariant than the standard 3D index.
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Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
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.