Related papers: S^3/Z_n partition function and dualities
We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix…
A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this…
We explicitly apply localization results to study the interpolation between three and two dimensional mirror symmetry for Abelian gauge theories with four supercharges. We first use the ellipsoid S_b^3 partition functions to verify the…
In Hawking's Euclidean path integral approach to quantum gravity, the partition function is computed by summing contributions from all possible topologies. The behavior such a sum can be estimated in three spacetime dimensions in the limit…
We provide non-trivial checks of $\mathcal{N}=4, D=3$ mirror symmetry in a large class of quiver gauge theories whose Type IIB (Hanany-Witten) descriptions involve D3 branes ending on orbifold/orientifold 5-planes at the boundary. From the…
Using localization techniques, we compute the path integral of $N=2$ SUSY gauge theory coupled to matter on the hemisphere $HS^4$, with either Dirichlet or Neumann supersymmetric boundary conditions. The resulting quantities are…
We consider a one-dimensional Osp($N|2M$) pseudoparticle mechanical model which may be written as a phase space gauge theory. We show how the pseudoparticle model naturally encodes and explains the two-dimensional zero curvature approach to…
We consider N=3 supersymmetric Chern-Simons (CS) theories that contain product U(N) gauge groups and bifundamental matter fields. Using the matrix model of Kapustin, Willett and Yaakov, we examine the Euclidean partition function of these…
The partition function of an N=2 gauge theory in the Omega-background satisfies, for generic value of the parameter beta=-eps_1/eps_2, the, in general extended, but otherwise beta-independent, holomorphic anomaly equation of special…
We present a new expression for the partition function of refined Chern-Simons theory on $S^3$ with arbitrary gauge group, which is explicitly equal to $1$, when the coupling constant is zero. Using this form of partition function we show…
We show that the supersymmetric partition function of three-dimensional N=2 R-symmetric Chern-Simons-matter theories on the squashed S^3 and on S^2 x S^1 can be computed with the so-called Higgs branch localization method, alternative to…
S-folds are generalizations of orientifolds in type IIB string theory, such that the geometric identifications are accompanied by non-trivial S-duality transformations. They were recently used by Garcia-Etxebarria and Regalado to provide…
We formulate new gauge principles for n supersymmetric particles in a worldline formalism with N supersymmetries. The models provide realizations of the more general supersymmetries that are encountered in sectors of S-theory or Matrix…
Five-dimensional $\mathcal{N}=1$ theories with gauge group $U(N)$, $SU(N)$, $USp(2N)$ and $SO(N)$ are studied at large rank through localization on a large sphere. The phase diagram of theories with fundamental hypermultiplets is universal…
The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit of the q-deformed partition function…
The 't~Hooft partition function~$\mathcal{Z}_{\text{tH}}[E;B]$ of an $SU(N)$ gauge theory with the $\mathbb{Z}_N$ 1-form symmetry is defined as the Fourier transform of the partition function~$\mathcal{Z}[B]$ with respect to the…
The theory of symmetric functions has been extended to the case where each variable is paired with an anticommuting one. The resulting expressions, dubbed superpolynomials, provide the natural N=1 supersymmetric version of the classical…
Gauge theory defined on the orbifold $M^4 \times (S^1/Z_2)$ is investigated from the viewpoint of the Hosotani mechanism. Rearrangement of gauge symmetry takes place due to the dynamics of Wilson line phases. The physical symmetry of the…
We apply the method of Higgs branch localization to the $\mathcal{N}=1$ supersymmetric partition function on $S^3\times S^1.$ As a result, we show that it can be written as the product of an elliptic vortex and anti-vortex partition…
We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to…