Related papers: Two loop superstring amplitudes and S_6 representa…

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge…

Motivated by their role for integrality and integrability in topological string theory, we introduce the general mathematical notion of "s-functions" as integral linear combinations of poly-logarithms. 2-functions arise as disk amplitudes…

We make a further step in the analytically exact quantization of spinning string states in semiclassical approximation, by evaluating the exact one-loop partition function for a class of two-spin string solutions for which quadratic…

The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been…

Using the pure spinor formalism in part I [1] we compute the complete tree-level amplitude of N massless open strings and find a striking simple and compact form in terms of minimal building blocks: the full N-point amplitude is expressed…

We compare two classes of functions arising from genus-one superstring amplitudes: modular and holomorphic graph functions. We focus on their analytic properties, we recall the known asymptotic behaviour of modular graph functions and we…

Motivated by recent advances in the categorification of quantum groups at prime roots of unity, we develop a theory of 2-representations for 2-categories enriched with a p-differential which satisfy finiteness conditions analogous to those…

Representation theory of the symmetric group $\mathfrak{S}_n$ has a very distinctive combinatorial flavor. The conjugacy classes as well as the irreducible characters are indexed by integer partitions $\lambda \vdash n$. We introduce class…

We inspect the excitation energy spectrum of a confining string in terms of solitons in an effective field theory model. The spectrum can be characterized by a spectral function, and twisting and bending of the string is manifested by the…

Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

We study integrals appearing in one-loop amplitudes in string theory, and in particular their analytic continuation based on a string theoretic analog of the $i\varepsilon$-prescription of quantum field theory. For various zero- and…

In this paper, we develop 2-dimensional algebraic theory which closely follows the classical theory of modules. The main results are giving definitions of 2-module and the representation of 2-ring. Moreover, for a 2-ring $\cR$, we prove…

We find the precise relationship between the loop gas method and the matrix quantum mechanics approach to two-dimensional string theory. The two systems are distinguished by different target spaces ($\Z$ and $\R$, respectively) as far as…

In this paper we consider the restriction of a unitary irreducible representation of type $A_{\mathfrak q}(\lambda)$ of $GL(4,{\mathbb R})$ to reductive subgroups $H$ which are the fixpoint sets of an involution. We obtain a formula for the…

Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…

A field theory approach to summing threshold effects to the gauge couplings in a two-torus compactification is presented and the link with the (heterotic) string calculation is carefully investigated. We analyse whether the complete UV…

Invariance of Type IIB superstring theory under SL(2,Z) or S-duality implies dependence on the complex coupling T through real and complex modular forms in T. Their structure may be understood explicitly in an expansion of superstring…

We show that a rank reduction technique for string C-group representations first used for the symmetric groups generalizes to arbitrary settings. The technique permits us, among other things, to prove that orthogonal groups defined on…

Superstring theories at low energy limit are described by the corresponding supergravities, and their non-perturbative D-brane/O-plane excitations are described by DBI and WZ actions. Higher derivative corrections to these effective actions…