相关论文: Two loop superstring amplitudes and S_6 representa…
Let $\mathfrak{g}$ be a simple Lie algebra. We study 1/2-BPS Wilson loops of supersymmetric 5d $\mathfrak{g}$-type quiver gauge theories on a circle, in a non-trivial instanton background. The Wilson loops are codimension 4 defects of the…
Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…
Building upon the Jones-Wassermann program of studying Conformal Field Theory using operator algebraic tools, and the work of A. Wassermann on the loop group of LSU(n) (Invent. Math. 133 (1998), 467-538), we give a solution to the problem…
We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…
General properties of ternary semigroups and groups are considered. The bi-element representation theory in which every representation matrix corresponds to a pair of elements is built, connection with the standard theory is considered and…
We systematically apply semisimplification functors in modular representation theory. Motivated by the Duflo--Serganova functor in Lie superalgebras, we construct various functors of interest. In the setting of finite groups, we refine the…
The representation theory of the quantum group su$_q(2)$ is used to introduce $q$-analogues of the Wigner rotation matrices, spherical functions, and Legendre polynomials. The method amounts to an extension of variable separation from…
Following the idea of Refs.[1,2], the double-copy-like decomposition of exchanged internal states in the world-line limit of one-loop string amplitudes is systematically formulated and generalized to both bosonic and heterotic string…
In this paper we present three new families of smooth Type II string theory backgrounds. These are dual to supersymmetry-preserving deformations of 4d SCFTs. The deformations include a VEV for a global current and a `twisted…
We derive the representation theory of $SU(2)$ from the expository theory of Lie groups and Lie algebras. Based on this, the mathematics of non-relativistic quantum mechanics of a spin $\frac{1}{2}$ particle are described from a…
The dilatation operator of planar N=4 super Yang-Mills in the pure scalar SO(6) sector is derived at the two-loop order. Representation theory allows for eight free coefficients in an ansatz for the corresponding spin-chain hamiltonian…
The non-minimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative $R^4$ conjectures of Green, Russo and Vanhove. The first theorem states that when $0<n<12$,…
In this paper, we extend the work in "Morita's Theory for the Symplectic Groups" to split reductive groups. We construct and study the holomorphic discrete series representation and the principal series representation of a split reductive…
This paper investigates relationships between low-energy four-particle scattering amplitudes with external gauge particles and gravitons in the E_8 X E_8 and SO(32) heterotic string theories and the type I and type IA superstring theories…
The theory of representations of a crossed module is a direct generalization of the theory of representations of groups. For a finite group G, the Drinfeld quantum double of the group G is a Hopf algebra that represents a special case of…
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…
After a brief overview of the operator formalism for conventional string theory, an operator formalism for ambitwistor string theory is presented. It is shown how tree level supergravity scattering amplitudes are recovered in this…
We explore gauge fields - strings duality by means of the loop equations and the zigzag symmetry. The results are striking and incomplete. Striking - because we find that the string ansatz proposed in [A.M. Polyakov, hep-th/9711002]…
We continue our investigation of the modular graph functions and string invariants that arise at genus-two as coefficients of low energy effective interactions in Type II superstring theory. In previous work, the non-separating degeneration…
We discuss the prepotential describing the effective field theory of N=2 heterotic superstring models. At the one loop-level the prepotential develops logarithmic singularities due to the appearance of charged massless states at particular…