Related papers: Modularity of supersymmetric partition functions
Scaling black holes are solutions of supergravity with multiple black hole singularities, which can be adiabatically connected to a single center black hole solution. We develop techniques to determine partition functions for such scaling…
We compute the ${\cal N}=2$ supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the K\"ahler form with jumps…
We study properties of the full partition function for the $U(1)$ 5D $\mathcal{N}=2^*$ gauge theory with adjoint hypermultiplet of mass $M$. This theory is ultimately related to abelian 6D (2,0) theory. We construct the full…
Supersymmetric black holes provide an excellent theoretical laboratory to test ideas about quantum gravity in general and black hole entropy in particular. When four-dimensional supergravity is interpreted as the low-energy approximation of…
We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z_M. Our primary focus is the dependence of Z_M on the geometry of M, as well as background…
We compute the supersymmetric partition function on L(r,1)xS^1, the lens space index, for 4d gauge theories related by supersymmetric dualities and involving non simply-connected groups. This computation is sensitive to the global…
We investigate 3d $\mathscr{N}=2$ supersymmetric gauge theories on $S^1 \times S^2$ and the corresponding 2d effective field theories arising in the limit of small ratio of radii, $\beta=R_{S^1}/R_{S^2}\to 0$. We evaluate the exact…
We discuss the large $N$ factorization properties of five-dimensional supersymmetric partition functions for CFT with a holographic dual. We consider partition functions on manifolds of the form $\mathcal{M}= \mathcal{M}_3 \times…
We consider 4d supersymmetric (special) unitary $\Gamma$ quiver gauge theories on compact manifolds which are $T^2$ fibrations over $S^2$. We show that their partition functions are correlators of vertex operators and screening charges of…
In the three-dimensional sl(N) Chern-Simons higher-spin theory, we prove that the conical surplus and the black hole solution are related by the S-transformation of the modulus of the boundary torus. Then applying the modular group on a…
Searching for the integrable structures of supersymmetric gauge theories and topological strings, we study melting crystal, which is known as random plane partition, from the viewpoint of integrable systems. We show that a series of…
We consider 4d $\mathcal{N}=1$ gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry…
We study aspects of Calabi-Yau four-folds as compactification manifolds of F-theory, using mirror symmetry of toric hypersurfaces. Correlation functions of the topological field theory are determined directly in terms of a natural ring…
We study the supersymmetric partition function of a 2d linear $\sigma$-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a K\"ahler modulus that varies along the other. This setup is…
We derive new closed form expressions for the partition functions of free conformally-coupled scalars on $S^{2D-1}\times S^1$ which resum the exact high-temperature expansion. The derivation relies on an identification of the partition…
We derive the relation between the Hilbert space of certain geometries under the Bohr-Sommerfeld quantization and the perturbative prepotentials for the supersymmetric five-dimensional SU(N) gauge theories with massive fundamental matters…
We present a prototype for Wilsonian analysis of asymptotics of supersymmetric partition functions of non-abelian gauge theories. Localization allows expressing such partition functions as an integral over a BPS moduli space. When the limit…
We calculate the instanton partition function of the four-dimensional N=2* SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show…
We study partition function of four-dimensional $\mathcal{N}=1$ supersymmetric field theory on $T^2 \times S^2$. By applying supersymmetry localization, we show that the $T^2 \times S^2$ partition function is given by elliptic genus of…
Previous studies have shown that supersymmetric partition function on $T^2 \times S^2$ is related to elliptic genus of two dimensional supersymmetric theory. In this short note we find a four dimensional supersymmetric theory, whose…