T-duality in gauged linear sigma-models with torsion

Abstract

(0,2) gauged linear sigma models with torsion, corresponding to principal torus bundles over warped CY bases, provide a useful framework for getting exact statements about perturbative dualities in the presence of fluxes. In this context we first study dualities mapping the torus fiber onto itself, implying the existence of quantization constraints on the torus moduli for consistency. Second, we investigate dualities mixing the principal torus bundle with the gauge bundle, relating the torsional GLSMs to ordinary ones corresponding to CY compactifications with non-standard embeddings, namely two classes of models with different target-space topologies.

Heterotic fluxes and supersymmetry

“…The 8-dimensional perspective makes it apparent that there is a large redundancy in the nominal classification of solutions -this is simply a consequence of the O(2, 18) duality of the T 2 -compactification: there are O(2, 18) transformations that allow us to exchange the "physical" U(1)s associated to the Kaluza-Klein reduced metric and B-field with the "gauge" U(1)s. Such T-duality relations have been explored in [30,31]. This does not mean that every compactification with a non-trivial T 2 -fibration is on a T -duality orbit of a T 2 × K3 compactification.…”

T4 fibrations over Calabi–Yau two-folds and non-Kähler manifolds in string theory

“…It may be interesting to perform T-duality transformations along T 4 . The examples in this paper may serve as useful examples for performing T-dualities [45,46] along higher dimensional tori.…”

T-dual solutions of the Hull–Strominger system on non-Kähler threefolds

“…This has the effect that the bundles act as mere spectators in the T-dualization of the solution. In a more general situation, as explored in the physics literature [16,35,39] and independently proposed in [4], one would expect that the Chern classes of the bundle in the original solution contribute to the topology of the T-dual. It would be interesting to find examples of solutions of the Hull-Strominger system which exhibit this phenomenon.…”

“…T-duality for perturbative solutions of (1.1) on torus bundles over K3 surfaces has been studied in the string theory literature in [16,35]. These solutions were predicted in [13] via a chain of dualities, known as heterotic/F-theory duality, for which solid mathematical underpinnings have not yet been provided (see [23,32] for some interesting progress in this direction).…”