Strings and D-branes in curved space-time

TL;DR

This thesis investigates the AdS3 WZNW model, analyzing operator product expansions, fusion rules, and modular properties, and explores D-branes and their relation to conformal field theory structures.

Contribution

It provides a detailed analysis of the AdS3 WZNW model's operator algebra, fusion rules, and modular properties, extending understanding of D-branes in curved space-time.

Findings

Fusion rules close on the Hilbert space due to symmetry-induced truncation.

Regularization of characters on Lorentzian torus recovers spectral information.

Generalized modular properties relate to D-brane one-point functions.

Abstract

In this thesis we study the AdS3 Wess-Zumino-Novikov-Witten model. We compute the Operator Product Expansion of primary fields as well as their images under the spectral flow automorphism in all sectors of the model by considering it as a Wick rotation of the H3+ coset model. We argue that the symmetries of the affine algebra require a truncation which establishes the closure of the fusion rules on the Hilbert space of the theory. These results are then used to discuss the factorization of four point functions by applying the bootstrap approach. We also study the modular properties of the model. Although the Euclidean partition function is modular invariant, the characters on the Euclidean torus diverge and the regularization proposed in the literature removes information on the spectrum, so that the usual one to one map between characters and representations of rational models is lost. Reconsidering the characters defined on the Lorentzian torus and focusing on their structure as distributions, we obtain expressions that recover those properties. We then study their generalized modular properties and use them to discuss the relation between modular data and one point functions associated to symmetric D-branes, generalizing some results from Rational Conformal Field Theories in the particular cases of point like and dS2 branes, such as Cardy type solutions or Verlinde like formulas.