Related papers: $\mathcal{N}=2^{*}$ Schur indices
We study superconformal indices of four-dimensional $SU(N)$ gauge theories with $\mathcal{N}=1,2,4$ supersymmetry. The usual representation of a gauge theory index involves multiple contour integrals and reflects the BPS spectrum at zero…
A set of functions is introduced which generalizes the famous Schur polynomials and their connection to Grasmannian manifolds. These functions are shown to provide a new method of constructing solutions to the KP hierarchy of nonlinear…
We introduce super-analogues of the Schur functors defined by Akin, Buchsbaum and Weyman. These {\em Schur superfunctors} may be viewed as characteristic-free analogues of the finite dimensional atypical irreducible modules over the Lie…
We consider families of theories with large N=4 superconformal symmetry. We define an index generalizing the elliptic genus of theories with N=2 symmetry. In contrast to the N=2 case, the new index constrains part of the non-BPS spectrum.…
I review the appearence of integrable structures in the formulation of exact nonperturbative solutions to $4d$ supersymmetric quantum gauge theories. Various examples of ${\cal N}\geq 2$ SUSY Yang-Mills nonperturbative solutions are…
We compute, by free field techniques, the scalar product of the SU(2) Chern-Simons states on genus > 1 surfaces. The result is a finite-dimensional integral over positions of ``screening charges'' and one complex modular parameter. It uses…
An expression is given for the plethysm $p_{2}\circ S_{\square}$, where $p_{2}$ is the power sum of degree two and $S_{\square}$ is the Schur function indexed by a rectangular partition. The formula can be well understood from the viewpoint…
Stable Grothendieck polynomials can be viewed as a K-theory analog of Schur polynomials. We extend stable Grothendieck polynomials to a two-parameter version, which we call canonical stable Grothendieck functions. These functions have the…
Recently a prescription to compute the four-dimensional N = 2 superconformal index in the presence of certain BPS surface defects has been given. These surface defects are labelled by symmetric representations of SU(N). In the present paper…
We derive a manifestly superconformal expression for the leading-order two-point functions of all single trace chiral primary operators in 4d $\mathcal{N}=4$ super-Yang-Mills theory with a co-dimension one Nahm pole defect. Notably, our…
We present exact expressions for certain integrated correlators of four superconformal primary operators in the stress tensor multiplet of $\mathcal{N}=4$ supersymmetric Yang--Mills (SYM) theory with classical gauge group, $G_N$ $= SO(2N)$,…
We compute two-loop form factors of operators in the $SU(2|3)$ closed subsector of $N=4$ supersymmetric Yang-Mills. In particular, we focus on the non-protected, dimension-three operators $\mathrm{Tr} (X[Y,Z])$ and $\mathrm{Tr} ( \psi…
We generalize several classical results about Schur functions to the family of cylindric Schur functions. First, we give a combinatorial proof of a Murnaghan--Nakayama formula for expanding cylindric Schur functions in the power-sum basis.…
A class of 4d $\mathcal{N}=3$ SCFTs can be obtained from gauging a discrete subgroup of the global symmetry group of $\mathcal{N}=4$ Super Yang-Mills theory. This discrete subgroup contains elements of both the $SU(4)$ R-symmetry group and…
We establish a strong link between two open problems: determining the Reidemeister spectrum of free nilpotent groups and determining the coefficients in the Schur expansion of plethysms of Schur functions. Specifically, we show that the…
The Kronecker product of two Schur functions $s_{\mu}$ and $s_{\nu}$, denoted by $s_{\mu}*s_{\nu}$, is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the…
We consider a finite-dimensional oscillatory integral which provides a "finite-dimensional model" for analytically continued $SU(2)$ Chern-Simons theory on closed 3-manifolds that are described by plumbing trees. This model allows an…
We show that the equality of 2d $\mathcal{N}$=(2,2) supersymmetric indices in Seiberg-type duality leads to a new integrable Ising-type model. The emergence of the new model is the result of correspondence between the supersymmetric $SU(2)$…
The finiteness properties of the N=4 supersymmetric Yang-Mills theory are reanalyzed both in the component formulation and using N=1 superfields, in order to discuss some subtleties that emerge in the computation of gauge dependent…
We recall the relation between Zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of Zeta…