Related papers: Partition functions, mapping class groups and Drin…

We show how to use D and NS fivebranes in Type IIB superstring theory to construct large classes of finite N=1 supersymmetric four dimensional field theories. In this construction, the beta functions of the theories are directly related to…

Let $X$ be a smooth projective and geometrically irreducible curve over the finite field $\mathbb{F}_q$ with $q$ elements and $K$ be its function field. Let $\infty$ be a fixed closed point on $X$ and $A$ be the ring of functions regular…

Complete sets of bases of differential invariants, operators of invariant differentiation and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of…

The requirements of conformal invariance for two and three point functions for general dimension $d$ on flat space are investigated. A compact group theoretic construction of the three point function for arbitrary spin fields is presented…

We present a summary of the progress made in the last few years on topological quantum field theory in four dimensions. In particular, we describe the role played by duality in the developments which led to the Seiberg-Witten invariants and…

We constrain the spectrum of $\mathcal{N}=(1, 1)$ and $\mathcal{N}=(2, 2)$ superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the $\Gamma_\theta$ congruence subgroup of the…

Let ${\mathbb F}_q$ be a finite field of characteristic two and ${\mathbb F}_q(X_1,...,X_n)$ a rational function field. We use matrix methods to obtain explicit transcendental bases of the invariant subfields of orthogonal groups and…

It is shown that the Topological Massive and ``Self-dual'' theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically…

We present a summary of the applications of duality to Donaldson-Witten theory and its generalizations. Special emphasis is made on the computation of Donaldson invariants in terms of Seiberg-Witten invariants using recent results in N=2…

Recently, Gekeler proved that the group of invertible analytic functions modulo constant functions on Drinfeld's upper half space is isomorphic to the dual of an integral generalized Steinberg representation. In this note we show that the…

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…

By means of the Drinfeld twists, we derive the determinant representations of the partition functions for the $gl(1|1)$ and $gl(2|1)$ supersymmetric vertex models with domain wall boundary conditions. In the homogenous limit, these…

Modular invariance imposes rigid constrains on the partition functions of two-dimensional conformal field theories. Many fundamental results follow strictly from modular invariance, giving rise to the numerical modular bootstrap program.…

Generalized Halphen systems are solved in terms of functions that uniformize genus zero Riemann surfaces, with automorphism groups that are commensurable with the modular group. Rational maps relating these functions imply subgroup…

We study the two-fold dimensional dependence of the electromagnetic duality groups. We introduce the dual projection operation that systematically discloses the presence of an internal space of potentials where the group operation is…

It is shown that the higher genus vacuum amplitudes of a meromorphic conformal field theory determine the affine symmetry of the theory uniquely, and we give arguments that suggest that also the representation content with respect to this…

We discuss partition functions of N=(4,4) type IIA string theory on the pp-wave background. This theory is shown to be modular invariant. The boundary states are constructed and possible D-brane instantons are classified. Then we calculate…

We argue that rational conformally invariant quantum field theories in two dimensions are closely related to torsion elements of the algebraic K-theory group K_3(C). If such a theory has an integrable matrix perturbation with purely elastic…

Double Field Theory (DFT) is an attempt to make the O(d,d) T-duality symmetry of string theory manifest, already before reducing on a d-torus. It is known that supergravity can be formulated in an O(D,D) covariant way, and remarkably this…

We consider indecomposable representations of the Klein four group over a field of characteristic $2$ and of a cyclic group of order $pm$ with $p,m$ coprime over a field of characteristic $p$. For each representation we explicitly describe…