Local models of heterotic flux vacua: spacetime and worldsheet aspects

Abstract

We report on some recent progress in understanding heterotic flux compactifications, from a worldsheet perspective mainly. We consider local models consisting in torus fibration over warped Eguchi-Hanson space and non-K\"ahler resolved conifold geometries. We analyze the supergravity solutions and define a double-scaling limit of the resolved singularities, defined such that the geometry is smooth and weakly coupled. We show that, remarkably, the heterotic solutions admit solvable worldsheet CFT descriptions in this limit. This allows in particular to understand the important role of worldsheet non-perturbative effects.Comment: Proceedings from a seminar given during the XVIth European Workshop on String Theory 2010, Madrid, 14--18 June 2010; v2:refs adde

Heterotic fluxes and supersymmetry

“…Essentially all known heterotic flux vacua are variations on a single theme inspired by a dual F/M-theory compactification on K3 × K3 [5]. There have been a number of generalizations, including attempts to check that the equations of motion are satisfied; see, for example, [18][19][20][21][22][23][24]. For simplicity we will focus on a particularly simple configuration and comment on the additional bells and whistles below.…”

T-duality in gauged linear sigma-models with torsion

“…In supergravity one gets the same anomaly equation (see e.g. in [40]) by considering the pullback of an Abelian bundle over K3 of the form F = 2πk n ·T n ̟ [2] , where ̟ [2] ∈ H 2 (S, Z) ∩ H 1,1 (S) is anti-self dual, and {T n , n = 1, . .…”

“…which is automatically satisfied using the quantization condition (19a). 2 When the base is an Eguchi-Hanson space, in which case a worldsheet CFT is known, this requirement is indeed absolutely necessary and quite easy to understand [40]. The existence of chiral generators of an extended algebra is needed in order to define the super-Liouville potential that appears in these constructions.…”

Heterotic flux backgrounds and their IIA duals

“…We are interested in compact backgrounds; there has also been recent work on related non-compact heterotic backgrounds, e.g [30,31]10.…”

“…In this section we will concentrate on the vector moduli associated to the torus.These are clearly modified since the left-moving symmetries δφ I = v I (z) are explicitly broken by the non-trivial curvatures F I 11. On the other hand, nothing in our construction9 We are interested in compact backgrounds; there has also been recent work on related non-compact heterotic backgrounds, e.g [30,31]10.…”