Related papers: From 4d superconformal indices to 3d partition fun…

Working within the path-integral framework we first establish a duality between the partion functions of two $U(1)$ gauge theories with a theta term in $d=4$ space-time dimensions. Then, after a dimensional reduction to $d=3$ dimensions we…

This is a brief account of relations between the theory of special functions, on the one side, and superconformal indices and Seiberg dualities of four-dimensional $\mathcal{N}=1$ supersymmetric gauge field theories, on the other side.

Superconformal indices of four-dimensional $\mathcal{N}=1$ gauge theories factorize into holomorphic blocks. We interpret this as a modular property resulting from the combined action of an $SL(3,\mathbb{Z})$ and $SL(2,\mathbb{Z})\ltimes…

We construct and study the 6D dual superconformal algebra. Our construction is inspired by the dual superconformal symmetry of massless 4D $\mathcal{N}=4$ SYM and extends the previous construction of the enhanced dual conformal algebra for…

We study the 3-point functions of single-trace scalar operators in a four-dimensional $\mathcal{N}=2$ SYM theory with gauge group $\mathrm{SU}(N)$ and matter in the symmetric plus anti-symmetric representation, which has a vanishing…

Supersymmetric gauge theories of certain class possess a large hidden nonperturbative symmetry described by the Ding-Iohara-Miki (DIM) algebra which can be used to compute their partition functions and correlators very efficiently. We lift…

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 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…

In this paper we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of…

We study the superconformal index of 4d $\mathcal{N}=4$ $USp(2N_c)$ and $SO(N_c)$ SYM from a matrix model perspective. We focus on the Cardy-like limit of the index. Both in the symplectic and orthogonal case the index is dominated by a…

We study the expansion near roots of unity of the superconformal index of 4d $SU(N)$ $\mathcal{N}=4$ SYM. In such an expansion, middle-dimensional walls of non-analyticity are shown to emerge in the complex analytic extension of the…

Using the ADM formalism, we demonstrate that the Hamiltonian formulation of Quantum Gravity is exactly in the form of a worldline (WL) formalism in the superspace. We then show that the Keldysh partition function reduces to the partition…

We realize off-shell, local and gauge invariant $N=8$ supergravity in $D=4$, to cubic order in fields, as the double copy of $N=4$ super Yang-Mills theory (SYM). Employing the homotopy algebra approach, we show that, thanks to a redundant…

We evaluate partition functions of matrix models which are given by topologically twisted and dimensionally reduced actions of d=4 N=1 super Yang-Mills theories with classical (semi-)simple gauge groups, SO(2N), SO(2N+1) and USp(2N). The…

The partition function of four dimensional SO(4) Yang-Mills theory is rewritten in terms of variables admitting straightforward relation to the partition function of pure 4D gravity. The gauge action turns into first-order Hilbert-Palatini…

In this paper we consider 4d $\mathrm{SU}(N)$ gauge theories with $N+1$ fundamentals, five antifundamentals and a conjugate two index antisymmetric tensor. The model has been shown to be in a mixed phase in the IR, splitting in an…

We study the dependence of supersymmetric partition functions on continuous parameters for the flavor symmetry group, $G_F$, for 2d $\mathcal{N} = (0,2)$ and 4d $\mathcal{N}=1$ supersymmetric quantum field theories. In any…

We study a superconformal index for ${\cal N}=4$ super Yang-Mills on $S^1 \times S^3$ with a half BPS duality domain wall inserted at the great two-sphere in $S^3$. The index is obtained by coupling the 3d generalized superconformal index…

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times $ time. Our index receives contributions from states invariant under at least one supercharge and captures all…

This thesis is based on the publications arXiv:1106.4253, arXiv:1206.2920, arXiv:1210.2590. We construct warped "AdS_4 x S^2 x S^2 x \Sigma" type IIB supergravity solutions dual to the infrared fixed points of all 3d N=4 linear and circular…