Related papers: Macdonald Index From Refined Kontsevich-Soibelman …

We refine the statement of the denominator and evaluation conjectures for affine Macdonald polynomials proposed by Etingof-Kirillov Jr. and prove the first non-trivial cases of these conjectures. Our results provide a q-deformation of the…

We study a class of near-BPS operators for a complex 2-parameter family of N=1 superconformal Yang-Mills theories that can be obtained by a Leigh-Strassler deformation of N=4 SYM theory. We identify these operators in the large N and large…

We consider N = 2 superconformal field theory with following properties: a) Coulomb branch operators have fractional scaling dimensions, b) there are exact marginal deformations . The weakly coupled gauge theory descriptions are found by…

We study supersymmetric quarter-indices for corner configurations in 4d $\mathcal{N}=4$ super Yang-Mills theory with orthogonal and symplectic gauge groups. For the basic Y-junctions, we obtain exact closed-form expressions for the indices…

We consider a class of line operators in d=4, N=2 supersymmetric field theories which leave four supersymmetries unbroken. Such line operators support a new class of BPS states which we call "framed BPS states." These include halo bound…

This paper focuses on the analysis of $4d$ $\mathcal{N}=4$ superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is…

Let $M$ be a complete Riemannian manifold and assume that $M$ is partitioned by a hypersurface $N$. In this paper we introduce a novel class of functions $C_{\mathrm{w}}(M)$ on noncompact manifolds, which is slightly larger than the algebra…

Let $L= -\Delta+ V$ be a Schr\"odinger operator on $\mathbb R^d$, $d\geq 3$, where $V$ is a nonnegative potential, $V\ne 0$, and belongs to the reverse H\"older class $RH_{d/2}$. In this paper, we study the commutators $[b,T]$ for $T$ in a…

Whenever available, refined BPS indices provide considerably more information on the spectrum of BPS states than their unrefined version. Extending earlier work on the modularity of generalized Donaldson-Thomas invariants counting D4-D2-D0…

We prove a boundedness criterion for a class of dyadic multilinear forms acting on two-dimensional functions. Their structure is more general than the one of classical multilinear Calder\'{o}n-Zygmund operators as several functions can now…

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…

Vertex operator algebras (VOAs) arise in protected subsectors of supersymmetric quantum field theories, notably in 4d ${\mathcal N}=2$ superconformal field theories (SCFT) via the Schur sector and in twisted 3d ${\mathcal N}=4$ theories via…

We study the index theory of a class of perturbed Dirac operators on non-compact manifolds of the form $\mathsf{D}+\mathrm{i}\mathsf{c}(X)$, where $\mathsf{c}(X)$ is a Clifford multiplication operator by an orbital vector field with respect…

Let $G$ be an almost simple simply connected complex Lie group, and let $G/U_-$ be its base affine space. In this paper we formulate a conjecture, which provides a new geometric interpretation of the Macdonald polynomials associated to $G$…

We consider the matrix model of $U(N)$ refined Chern-Simons theory on $S^3$ for the unknot. We derive a $q$-difference operator whose insertion in the matrix integral reproduces an infinite set of Ward identities which we interpret as…

We study the four-dimensional superconformal N=2 gauge theories engineered by the Type IIB superstring on Arnold's 14 exceptional unimodal singularities (a.k.a. Arnold's strange duality list), thus extending the methods of 1006.3435 to…

Argyres-Douglas theories constitute an important class of superconformal field theories in $4$d. The main focus of this paper is on two infinite families of such theories, known as $D^b_p(\mathrm{SO}(2N))$ and $(A_m, D_n)$. We analyze in…

We study the four-point correlation function of stress-tensor supermultiplets in N=4 SYM using the method of Lagrangian insertions. We argue that, as a corollary of N=4 superconformal symmetry, the resulting all-loop integrand possesses an…

By means of fixed point index theory for multi-valued maps, we provide an analogue of the classical Birkhoff--Kellogg Theorem in the context of discontinuous operators acting on affine wedges in Banach spaces. Our theory is fairly general…

We study ultraviolet (UV) incarnations of deep infrared (IR) physics on the Coulomb branch of the simplest interacting 4D $\mathcal{N}=2$ superconformal field theory: the minimal Argyres-Douglas (MAD) theory. One of the most basic…