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3-Manifolds and 3d Indices
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In this article, a large class R of 3-dimensional N = 2 superconformal field theories is identified, and the equivalence relation among theories in class R is a quantum-field-theoretic 2-3 move.Abstract:
We identify a large class R of three-dimensional N=2 superconformal field theories. This class includes the effective theories T_M of M5-branes wrapped on 3-manifolds M, discussed in previous work by the authors, and more generally comprises theories that admit a UV description as abelian Chern-Simons-matter theories with (possibly non-perturbative) superpotential. Mathematically, class R might be viewed as an extreme quantum generalization of the Bloch group; in particular, the equivalence relation among theories in class R is a quantum-field-theoretic "2-3 move." We proceed to study the supersymmetric index of theories in class R, uncovering its physical and mathematical properties, including relations to algebras of line operators and to 4d indices. For 3-manifold theories T_M, the index is a new topological invariant, which turns out to be equivalent to non-holomorphic SL(2,C) Chern-Simons theory on M with a previously unexplored "integration cycle."read more
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Partition functions of N=(2,2) gauge theories on S^2 and vortices
TL;DR: In this paper, the authors apply localization techniques to compute the partition function of a two-dimensional R-symmetric theory of vector and chiral multiplets on S^2, where the path integral reduces to a sum over topological sectors of a matrix integral over the Cartan subalgebra of the gauge group.
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3d dualities from 4d dualities for orthogonal groups
TL;DR: In this paper, the relation of 4d and 3d IR dualities of supersymmetric gauge theories with four supercharges was studied in the case of orthogonal gauge groups.
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BPS Degeneracies and Superconformal Index in Diverse Dimensions
Amer Iqbal,Cumrun Vafa +1 more
TL;DR: The spectrum of massive supersymmetric (BPS) states that arise in consistent deformations of three and five-dimensional superconformal theories can be classified by the spectrum of BPS states in the deformed ones as mentioned in this paper.
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An E7 Surprise
Tudor Dimofte,Davide Gaiotto +1 more
TL;DR: In this article, the authors explore the implications of Seiberg duality for an SU(2) four-dimensional gauge theory with eight chiral doublets and show that two copies of the theory can be deformed by an exactly marginal quartic superpotential so that they acquire an enhanced Ecffff 7 flavor symmetry.
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3d & 5d gauge theory partition functions as q-deformed CFT correlators
TL;DR: In this paper, a class of q-deformed CFT correlators where conformal blocks are controlled by a deformation of Virasoro symmetry and are paired by Spairing and id-pairing respectively is defined.
References
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TL;DR: By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels.
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Liouville Correlation Functions from Four-dimensional Gauge Theories
TL;DR: In this paper, the authors conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of SCFTs recently defined by one of the authors.