Related papers: Generalised 4d Partition Functions and Modular Dif…

We revisit a double-scaled limit of the superconformal index of ${\cal N}=2$ superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, $\hat {\cal Z}(q,\alpha)$, has a standard $q$-expansion…

We study a set of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) $\widehat{\Gamma}(G)$ labeled by a pair of simply-laced Lie groups $\Gamma$ and $G$. They are constructed out of gauging a number of $\mathcal{D}_p(G)$…

We consider a family of Argyres-Douglas theories, which are 4D $\mathcal N=2$ strongly coupled superconformal field theories (SCFTs) but share many features with 4D $\mathcal N=4 $ super-Yang-Mills theories. In particular, the two central…

We consider 4d supersymmetric (special) unitary $\Gamma$ quiver gauge theories on compact manifolds which are $T^2$ fibrations over $S^2$. We show that their partition functions are correlators of vertex operators and screening charges of…

There is a well-known map from 4d $\mathcal{N}=2$ superconformal field theories (SCFTs) to 2d vertex operator algebras (VOAs). The 4d Schur index corresponds to the VOA vacuum character, and must be a solution with integral coefficients of…

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 give geometric descriptions of the category C_k(n,d) of rational polynomial representations of GL_n over a field k of degree d for d less than or equal to n, the Schur functor and Schur-Weyl duality. The descriptions and proofs use a…

Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…

Aiming at a complete classification of unitary N=2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate of a partition function for such a theory is indeed the…

Let $k$ be a commutative $\mathbb{Q}$-algebra. We study families of functors between categories of finitely generated $R$-modules which are defined for all commutative $k$-algebras $R$ simultaneously and are compatible with base changes.…

This is the first in a series of papers on the search for the 2D CFT description of a large class of 4D $\mathcal{N} = 1$ gauge theories. Here, we identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks of…

Recently we explained that the classical $Q$ Schur functions stand behind various well-known properties of the cubic Kontsevich model, and the next step is to ask what happens in this approach to the generalized Kontsevich model (GKM) with…

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…

We study properties of the full partition function for the $U(1)$ 5D $\mathcal{N}=2^*$ gauge theory with adjoint hypermultiplet of mass $M$. This theory is ultimately related to abelian 6D (2,0) theory. We construct the full…

We define Schur categories, $\Gamma^d \mathcal C$, associated to a $\Bbbk$-linear category $\mathcal C$, over a commutative ring $\Bbbk$. The corresponding representation categories, $\mathbf{rep}\, \Gamma^d\mathcal C$, generalize…

We consider the $\Omega$-deformed $\mathcal{N}=2$ $SU(2)$ gauge theory in four dimensions with $N_{f}=4$ massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters $\varepsilon_{1},…

Making use of the exact solutions of the $N=2$ supersymmetric gauge theories we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. SCFTs we have…

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…

We define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups $\Gamma_\vartheta$, $\Gamma^0(2)$ and $\Gamma_0(2)$ of $\text{SL}_2(\mathbb Z)$. Each subgroup corresponds to one of the spin structures on the…

We give alternative computations of the Schur multiplier of $Sp(2g,\mathbb Z/D\mathbb Z)$, when $D$ is divisible by 4 and $g\geq 4$: a first one using $K$-theory arguments based on the work of Barge and Lannes and a second one based on the…