Related papers: $\mathcal{N}{=}1$ supersymmetric indices and the f…
The twisted index of 3d $\mathcal{N}=2$ gauge theories on $S^1 \times \Sigma$ has an algebro-geometric interpretation as the Witten index of an effective supersymmetric quantum mechanics. In this paper, we consider the contributions to the…
We study the twisted indices of $\mathcal{N}=4$ supersymmetric gauge theories in three dimensions on spatial $S^{2}$ with an angular momentum refinement. We demonstrate factorisation of the index into holomorphic blocks for the $T[SU(N)]$…
We compute the supersymmetric partition function of the six-dimensional $(2,0)$ theory of type $A_{N-1}$ on $S^1 \times S^5$ in the presence of both codimension two and codimension four defects. We concentrate on a limit of the partition…
We study surface defects in 4d $\mathcal{N}=1$ $SU(N)$ superconformal gauge theories of class $\mathcal{S}_k$ obtained from the 6d (1,0) theories of type $A_{N-1}$, which are worldvolume theories on $N$ M5-branes at…
We study three-dimensional supersymmetric quiver gauge theories with a non-simply laced global symmetry primarily focusing on framed affine $B_{N}$ quiver theories. Using a supersymmetric partition function on a three sphere, and its…
In this paper we compute the superconformal index of 2d (2,2) supersymmetric gauge theories. The 2d superconformal index, a.k.a. flavored elliptic genus, is computed by a unitary matrix integral much like the matrix integral that computes…
We study 4d superconformal indices for a large class of N=1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we call a…
We consider four-dimensional Omega-deformed N=2 supersymmetric SU(2) gauge theory on A1 space and its lift to five dimensions. We find that the partition functions can be reproduced via special geometry and the holomorphic anomaly equation.…
We study three dimensional $\mathcal{N}=2$ supersymmetric theories on $I \times M_2$ with 2d $\mathcal{N}=(0,2)$ boundary conditions at the boundaries $\partial (I \times M_2)=M_2 \sqcup M_2$, where $M_2=\mathbb{C}$ or $ T^2$. We introduce…
We use localization to compute the partition function of a four dimensional, supersymmetric, abelian gauge theory on a hemisphere coupled to charged matter on the boundary. Our theory has eight real supercharges in the bulk of which four…
The most recent studies on the supersymmetric localization reveal many non-trivial features of supersymmetric field theories in diverse dimensions, and 3d gauge theory provides a typical example. It was conjectured that the index and the…
We study the hemisphere partition function of a three-dimensional $\mathcal{N}=4$ supersymmetric $U(N)$ gauge theory with one adjoint and one fundamental hypermultiplet -- the ADHM quiver theory. In particular, we propose a distinguished…
We use supersymmetric localization to compute the partition function of N=2 super-Yang-Mills on S^4 in the presence of a gauged linear sigma model surface defect on a S^2 subspace. The result takes the form of a standard partition function…
We study N=2 supersymmetric four dimensional gauge theories, in a certain N=2 supergravity background, called Omega-background. The partition function of the theory in the Omega-background can be calculated explicitly. We investigate…
We compute the supersymmetric partition function of an $\mathcal{N}=1$ chiral multiplet coupled to an external Abelian gauge field on complex manifolds with $T^2 \times S^2$ topology. The result is locally holomorphic in the complex…
We construct the gravity duals of large N supersymmetric gauge theories defined on squashed five-spheres with SU(3) x U(1) symmetry. These five-sphere backgrounds are continuously connected to the round sphere, and we find a one-parameter…
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,…
We compute the exact path integral of $\mathcal{N}=2$ supersymmetric gauge theories with general gauge group on $\mathbb{RP}^4$ and a $\mathbb{Z}_2$-quotient of the hemi-$S^4$. By specializing to $SU(2)$ superconformal quivers, we show that…
We study the 6-dimensional N=2 supersymmetric grand unified theories with gauge group SU(N) and $ SO(M)$ on the extra space orbifolds $T^2/(Z_2)^3$ and $T^2/(Z_2)^4$, which can be broken down to the 4-dimensional N=1 supersymmetric…
We rederive the recently introduced $N=2$ topological gauge theories, representing the Euler characteristic of moduli spaces ${\cal M}$ of connections, from supersymmetric quantum mechanics on the infinite dimensional spaces ${\cal A}/{\cal…