Related papers: Elliptic modular double and 4d partition functions
Partition function of beta-gamma systems on the orbifolds C^2/Z_N and C^3/Z_M x Z_N are obtained as the invariant part of that on the respective affine spaces, by lifting the geometric action of the orbifold group to the fields.…
We study two types of discrete operations on Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories using both abelianisation and the monopole formula. We generalise previous work on discrete quotients of Coulomb branches and…
The goal of the present paper is to calculate the complex structure moduli space K\"ahler potentials for hypersurfaces in weighted projective spaces and compare with the partition functions of their mirror GLSMs. We explicitly perform the…
We present a family of solvable multi-matrix models associated with an arbitrary embedded graph $\Gamma$ with a single vertex. The graph with $n$ edges is equipped with $2n$ corner matrices. The partition function of each member of the…
We continue the development of the topological membrane approach to open and unoriented string theories. We study orbifolds of topologically massive gauge theory defined on the geometry $[0,1]\times\Sigma$, where $\Sigma$ is a generic…
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 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 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 vacua in spontaneously broken N=4 electrically gauged supergravities in four space-time dimensions. We argue that the classification of all such solutions amounts to solving a system of purely algebraic equations. We then…
We analyze the subdivision properties of certain lattice gauge theories for the discrete abelian groups $Z_{p}$, in four dimensions. In these particular models we show that the Boltzmann weights are invariant under all $(k,l)$ subdivision…
In this paper we give some evidence for the Tate (and Hodge) conjecture(s) for a class of Hilbert modular fourfolds X, whose connected components arise as arithmetic quotients of the fourfold product of the upper half plane by congruence…
In this note, using Nekrasov's gauge origami framework, we study two different versions of the the BPS/CFT correspondence - first, the standard AGT duality and, second, the quiver W algebra construction which has been developed recently by…
We compute the supersymmetric partition function of $\mathcal{N}{=}1$ supersymmetric gauge theories with an $R$-symmetry on $\mathcal{M}_4 \cong \mathcal{M}_{g,p}\times S^1$, a principal elliptic fiber bundle of degree $p$ over a genus-$g$…
Let $\Gamma$ be a quiver on n vertices $v_1, v_2, ..., v_n$ with $g_{ij}$ edges between $v_i$ and $v_j$, and let $\alpha \in \N^n$. Hua gave a formula for $A_{\Gamma}(\alpha, q)$, the number of isomorphism classes of absolutely…
This review paper contains a concise introduction to highest weight representations of infinite dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera…
We study BPS surface observables of $\mathcal{N}=2$ four dimensional $SU(2)$ gauge theory in gravitational $\Omega$-background at perturbative and at Argyres-Douglas superconformal fixed points. This is done by formulating the equivariant…
Non-simply laced quivers, despite the lack of complete Lagrangian descriptions, play an important role in characterising moduli spaces of supersymmetric field theories. Notably, the moduli space of instantons in non-simply laced gauge…
The relation between the Seiberg-Witten prepotentials, Nekrasov functions and matrix models is discussed. We derive quasiclassically the matrix models of Eguchi-Yang type, describing the instantonic contribution to the deformed partition…
We propose a universal manipulation to obtain Seiberg-like dualities of 3d $\mathcal{N}=2$ general quiver gauge theories with unitary, symplectic and orthogonal gauge groups coupled to fundamental and bifundamental matter fields. We…
We realize the fundamental representations of quantum algebras via the supersymmetric Higgs mechanism in gauge theories with 8 supercharges on an $\Omega$-background. We test our proposal for quantum affine algebras, by probing the Higgs…