Related papers: From 4d superconformal indices to 3d partition fun…
We study the $S^1\times\Sigma_{\mathfrak g}$ topologically twisted index and the squashed sphere partition function of various 3d $\mathcal N\geq2$ holographic superconformal field theories arising from M2-branes. Employing numerical…
In this work, we investigate new solutions to the decoration transformation in terms of various special functions, including the hyperbolic gamma function, the basic hypergeometric function, and the Euler gamma function. These solutions to…
We develop techniques for computing superconformal blocks in 4d superconformal field theories. First we study the super-Casimir differential equation, deriving simple new expressions for superconformal blocks for 4-point functions…
We construct the hyperbolic and trigonometric solutions to the star-star relation via the gauge/YBE correspondence by using the three-dimensional lens partition function and superconformal index for a certain N=2 supersymmetric gauge dual…
This is the 10th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It reviews correspondences between three-dimensional gauge theories and complex Chern-Simons theory on suitable…
In this paper, we explore supersymmetric and 2d analogs of the SYK model. We begin by working out a basis of (super)conformal eigenfunctions appropriate for expanding a four-point function. We use this to clarify some details of the 1d…
We discuss the Cardy limit of 3d supersymmetric partition functions which allow the factorization into the hemisphere indices: the generalized superconformal index, the refined topologically twisted index and the squashed sphere partition…
We probe the 3d-3d correspondence for mapping cylinder/torus using the superconformal index. We focus on the case when the fiber is a once-punctured torus (\Sigma_{1,1}). The corresponding 3d field theories can be realized using duality…
Recent years have witnessed lots of progress in the computation of supersymmetric partition functions of SCFTs on curved manifolds via localization. The twisted partition function on product manifolds of the form $S^1 \times \Sigma_g$,…
Starting with the superconformal indices for 4d N=2 and N=1 supersymmetric gauge theories, which are related by superpotential deformation, we perform the contour integrations and isolate the residue contributions which can be attributed to…
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…
We compute the 4d superconformal index for N=1,2 gauge theories on S^1 x L(p,1), where L(p,1) is a lens space. We find that the 4d N=1,2 index on S^1 x L(p,1) reduces to a 3d N=2,4 index on S^1 x S^2 in the large p limit, and to a 3d…
We discuss the degeneration limits of d=4 superconformal indices that relate Seiberg duality for the d=4 N=1 SQCD theory to Aharony and Giveon-Kutasov dualities for d=3 N=2 SQCD theories. On a mathematical level we argue that this 3d/4d…
This is the 8th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. The article reviews the superconformal index. It is often simpler to calculate than instanton partition functions,…
Besides solving the spectral problem of $\mathcal{N}=4$ Super-Yang-Mills (SYM) theory, integrability also provides us with tools to compute the structure constants of the theory, most prominently through the hexagon formalism. We show that,…
We give a pedagogical introduction to the study of supersymmetric partition functions of 3D $\mathcal{N}{=}2$ supersymmetric Chern-Simons-matter theories (with an $R$-symmetry) on half-BPS closed three-manifolds---including $S^3$, $S^2…
We present a unifying theme relating BPS partition functions and superconformal indices. In the case with complex SUSY central charges (as in N=2 in d=4 and N=(2,2) in d=2) the known results can be reinterpreted as the statement that the…
This is the 9th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. We review the exact computations in 3D N=2 supersymmetric gauge theories on the round or squashed $S^3$ and the…
We study the partition functions of topologically twisted 3d $\mathcal{N}=2$ gauge theories on a hemisphere spacetime with boundary $HS^2 \times S^1$. We show that the partition function may be localised to either the Higgs branch or the…
We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field theories. In a gauge theory the partition function is the sum of the contributions of sectors specified by holonomies, and we should carefully choose the relative…