Related papers: Modular properties of full 5D SYM partition functi…
The 6d (2,0) theory of $N$ M5 branes compactified on the product geometry $T^2\times S$, where $S$ is a K\"ahler 4-manifold, can be studied in two different limits. In one limit, the size of $T^2$ is taken to zero and together with a…
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 construct ${\cal N}=2$ supersymmetric low-energy effective action of $5D, {\cal N}=2$ supersymmetric Yang-Mills theory in $5D, {\cal N}=1$ harmonic superspace. It is obtained as a hypermultiplet completion of the leading $W \ln W$-term…
We study $U(N)$ SYM theories on spaces with orbifold singularities via an equivalent description in terms of gauge theories on smooth manifolds with insertions of Gukov-Witten and twist defects. The combined effect of the defects is to…
We deconstruct the fifth dimension of the 5D SYM theory with SU(M) gauge symmetry and Chern-Simons level k=M and show how the 5D moduli space follows from the non-perturbative analysis of the 4D quiver theory. The 5D coupling h=1/(g_5)^2 of…
Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces. The partition function…
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 show that both perturbative and non-perturbative parts of universal partition functions of Chern-Simons theory on 3d sphere are ratios of four over four Barnes' quadruple gamma functions with arguments given by linear combinations of…
An exact formula for partition functions in 3d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific $q$-hypergeometric integrals whose key building block is the…
We consider a topological quiver matrix model which is expected to give a dual description of the instanton dynamics of topological U(N) gauge theory on D6 branes. The model is a higher dimensional analogue of the ADHM matrix model that…
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 compute the exact thermal partition functions of a massive scalar field on flat spacetime backgrounds of the form $\mathbb R^{d-q}\times \mathbb T^{q+1}$ and show that they possess an ${\rm SL}(q+1,\mathbb Z)$ symmetry. Non-trivial…
We consider a class of super-conformal beta-deformed N=1 gauge theories dual to string theory on $AdS_5 \times X$ with fluxes, where $X$ is a deformed Sasaki-Einstein manifold. The supergravity backgrounds are explicit examples of…
We construct modular invariants on the moduli space of quantum vacua of N=2 SYM with gauge group SU(2). We also introduce a nonchiral function K which is expressed in terms of the Seiberg-Witten and Poincare' metrics. It turns out that K…
We propose a set of novel expansions of Nekrasov's instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on $\mathbb{C}^2_{q,t^{-1}} \times \mathbb{S}^1$, we show that the instanton…
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 study super Yang-Mills theories on five-dimensional Sasaki-Einstein manifolds. Using localisation techniques, we find that the contribution from the vector multiplet to the perturbative partition function can be calculated by counting…
We undertake a comprehensive analysis of the supersymmetric partition function of the $\text{U}(N)_k\times\text{U}(N)_{-k}$ ABJM theory on a Seifert manifold, evaluating it to all orders in the $1/N$-perturbative expansion up to…
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 $SU(2)$ gauge theories coupled to $(A_1,D_N)$ theories with or without a fundamental hypermultiplet. For even $N$, a formula for the contribution of $(A_1,D_N)$ to the Nekrasov partition function was recently obtained by us with…