Elsevier

Nuclear Physics B

Volume 827, Issue 3, 11 March 2010, Pages 503-544
Nuclear Physics B

Double-scaling limit of heterotic bundles and dynamical deformation in cft

https://doi.org/10.1016/j.nuclphysb.2009.10.027Get rights and content

Abstract

We consider heterotic string theory on Eguchi–Hanson space, as a local model of a resolved A1 singularity in a six-dimensional flux compactification, with an Abelian gauge bundle turned on and non-zero torsion. We show that in a suitable double scaling limit, that isolates the physics near the non-vanishing two-cycle, a worldsheet conformal field theory description can be found. It contains a heterotic coset whose target space is conformal to Eguchi–Hanson. Starting from the blow-down limit of the singularity, it can be viewed as a dynamical deformation of the near-horizon fivebrane background. We analyze in detail the spectrum of the theory in particular examples, as well as the important role of worldsheet non-perturbative effects.

Section snippets

Introduction and summary of the results

Supersymmetric compactifications of the heterotic string [1] were soon recognized as a very successful approach to string phenomenology. An explicit description at the worldsheet conformal field theory (cft) level is only possible at some very specific points in the moduli space of compactifications, where the geometrical interpretation is usually lost. This includes orbifold toroidal compactifications [2], free-fermionic constructions [3], [4] and Gepner models [5]. The topological data of

Heterotic gauge bundles over Eguchi–Hanson

In this section we consider Abelian gauge bundles over Eguchi–Hanson space in heterotic supergravity. The solution at lowest order in α can be found explicitly [33], and will be analyzed in detail in the following. We shall then define the particular double scaling limit of this solution that will eventually be obtained as an exact worldsheet conformal field theory. We will end this section by discussing some limiting cases in which the Bianchi identity can be solved exactly, and when one must

Sigma-model approach: dynamical deformations

In this section we will uncover the worldsheet sigma-model structure of the supergravity background (2.27a), (2.27b), (2.27c), (2.27d), as a first step towards determining the underlying exact worldsheet conformal field theory. We will find that, starting from the blow-down limit of the gauge bundle over Eguchi–Hanson, one can obtain the resolved singularity with an Abelian gauge bundle by resorting to the method of dynamical promotion of a marginal deformation, called hereafter in short

A coset cft for the heterotic gauge bundle

In this section we consider the worldsheet conformal field theory description of the Abelian bundle over Eguchi–Hanson space, given by the heterotic supergravity solution (2.27a), (2.27b), (2.27c), (2.27d). The sigma-model analysis done in Section 3 suggests that, from the worldsheet perspective, of the solution can be viewed as a dynamical current–current deformation of the SU(2) wzw model. We find here the corresponding exact cft and analyze its spectrum.

Acknowledgements

The authors would like to thank C. Bachas, E. Dudas, S. Groot-Nibbelink, C. Kounnas, V. Niarchos, M. Petrini, N. Prezas, K. Sfetsos, J. Sonnenschein and especially M. Trapletti for numerous scientific discussions. They also acknowledge N. Prezas' contribution at the first stages of the project.

This work was supported in part by the EU under the contracts MEXT-CT-2003-509661, MRTN-CT-2004-005104, MRTN-CT-2004-503369, by the Agence Nationale pour la Recherche, France, under contract

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  • Cited by (12)

    1

    Unité mixte de Recherche 7644, CNRS – École Polytechnique.

    2

    Unité mixte de Recherche 7095, CNRS – Université Pierre et Marie Curie.

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