Related papers: Fusion rules for N=2 superconformal modules

We present the first polytope volume formulas for the multiplicities of affine fusion, the fusion in Wess-Zumino-Witten conformal field theories, for example. Thus, we characterise fusion multiplicities as discretised volumes of certain…

Generalizing our ideas in [arXiv:1006.3313], we explain how topologically-twisted N=2 gauge theory on a four-manifold with boundary, will allow us to furnish purely physical proofs of (i) the Atiyah-Floer conjecture, (ii) Munoz's theorem…

We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…

We determine the mass dependence of the coupling constant for N=2 SYM with N_f=1,2,3 and 4 flavours. All these cases can be unified in one analytic expression, given by a Schwarzian triangle function. Moreover we work out the connection to…

In this note we give a new construction of the N=2 superconformal algebra using currents of the affine superalgebra $\hat{sl}(2 | 1)$ and free bosonic fields, and also the N=4 superconformal algebra without central charge in terms of…

Let $V$ be a simple vertex operator algebra, and $G$ a finite automorphism group of $V$ such that $V^G$ is regular. The definition of entries in $S$-matrix on $V^G$ is discussed, and then is extended. The set of $V^G$-modules can be…

A modular category is a braided category with some additional algebraic features. The interest of this concept is that it provides a Topological Quantum Field Theory in dimension 3. The Verlinde formulas associated with a modular category…

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…

In this note we discuss several properties of the Schur index of N=2 superconformal theories in four dimensions. In particular, we study modular properties of this index under SL(2,Z) transformations of its parameters.

Two dimensional N=2 supersymmetric nonlinear sigma models on hermitian symmetric spaces are formulated in terms of the auxiliary superfields. If we eliminate auxiliary vector and chiral superfields, they give D- and F-term constraints to…

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…

The non-commutative algebraic analog of the moduli of vector and covector fields is built. The structure of moduli of derivations of non-commutative algebras are studied. The canonical coupling is introduced and the conditions for…

We present a manifestly $N=2$ supersymmetric formulation of $N=2$ super-$W_3$ algebra (its classical version) in terms of the spin 1 and spin 2 supercurrents. Two closely related types of the Feigin-Fuchs representation for these…

We discuss an N=2 quantum mechanics with or without a central charge. A representation is constructed with the number of bosonic degrees of freedom less that one half of the fermionic degrees of freedom. We suggest a systematic method of…

We use localization techniques to study the non-perturbative properties of an N=2 superconformal gauge theory with gauge group SU(3) and six fundamental flavours. The instanton corrections to the prepotential, the dual periods and the…

We study the non-perturbative properties of N=2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic epsilon-background, with four fundamental…

We construct super vertex operator algebras which lead to modules for moonshine relations connecting the four smaller sporadic simple Mathieu groups with distinguished mock modular forms. Starting with an orbifold of a free fermion theory,…

In paper, we study the representation theory of super $W(2,2)$ algebra ${\mathfrak{L}}$. We prove that ${\mathfrak{L}}$ has no mixed irreducible modules and give the classification of irreducible modules of intermediate series. We…

N-extended massless arbitrary integer and half-integer spin supermultiplets in four dimensional flat space are studied in the framework of light-cone gauge formalism. For such multiplets, by using light-cone momentum superspace, we build…

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…