A Two-loop Test of Buscher's T-duality I

We study the two loop quantum equivalence of sigma models related by Buscher's T-duality transformation. The computation of the two loop perturbative free energy density is performed in the case of a certain deformation of the SU(2) principal sigma model, and its T-dual, using dimensional regularization and the geometric sigma model perturbation theory. We obtain agreement between the free energy density expressions of the two models.Comment: 28 pp, Latex, references adde

Triangulated Surfaces in Twistor Space: A Kinematical Set up for Open/Closed String Duality

We exploit the properties of the three-dimensional hyperbolic space to discuss a simplicial setting for open/closed string duality based on (random) Regge triangulations decorated with null twistorial fields. We explicitly show that the twistorial N-points function, describing Dirichlet correlations over the moduli space of open N-bordered genus g surfaces, is naturally mapped into the Witten-Kontsevich intersection theory over the moduli space of N-pointed closed Riemann surfaces of the same genus. We also discuss various aspects of the geometrical setting which connects this model to PSL(2,C) Chern-Simons theory.Comment: 35 pages, references added, slightly revised introductio

The twisted open string partition function and Yukawa couplings

We use the operator formalism to derive the bosonic contribution to the twisted open string partition function in toroidal compactifications. This amplitude describes, for instance, the planar interaction between g+1 magnetized or intersecting D-branes. We write the result both in the closed and in the open string channel in terms of Prym differentials on the appropriate Riemann surface. Then we focus on the g=2 case for a 2-torus. By factorizing the twisted partition function in the open string channel we obtain an explicit expression for the 3-twist field correlator, which is the main ingredient in the computation of Yukawa couplings in D-brane phenomenological models. This provides an alternative method for computing these couplings that does not rely on the stress-energy tensor technique.Comment: 32 pages, 5 figures, Latex; v2: typos correcte

Duality of Graphical Models and Tensor Networks

In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a hypergraph exactly corresponds to the graphical model given by the dual hypergraph. We translate various notions under duality. For example, marginalization in a graphical model is dual to contraction in the tensor network. Algorithms also translate under duality. We show that belief propagation corresponds to a known algorithm for tensor network contraction. This article is a reminder that the research areas of graphical models and tensor networks can benefit from interaction