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

Abstract

We consider heterotic string theory on Eguchi-Hanson space, as a local model of a resolved A 1 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. †

Heterotic Hyper-Kähler flux backgrounds

“…The primary backgrounds we consider are of the form R 1,5 × HK 4 where HK 4 is a warped Hyper-Kähler-four manifold. We consider a non-trivial three-form flux H (3) , dilaton Φ and Heterotic gauge field F . The background metric ansatz is:…”

“…where T ∈ U(1) 16 is in the Cartan subalgebra of E 8 × E 8 or SO (32) and q i the corresponding charge vectors, and solve (4), we get the general solution 3 :…”

“…corresponding to mobile neutral five-brane sources inserted at x α . In appendix A we show how the two center solution is related to the Eguchi-Hanson solution that was discussed in particular in [3].…”

The Abelian heterotic conifold

“…The intuition one has from the gauged CHS solution is that zero size instantons are given by explicit five-brane sources. Indeed in the local heterotic solutions of [19] the blow down limit is precisely the Z 2 orbifold of the zero size CHS solution and thus corresponds to explicit five-brane sources. When the blow up parameter of our solutions is taken to zero size (see section 3.2.2) the dilaton and thus the Einstein frame metric is singular at r = 0.…”

“…Our current work is very much in the same vein as [16,17] except that we will be studying heterotic strings, and that the main class of our solutions will require a Z 2 orbifold of the conifold. It builds on earlier articles by one of the authors [19,20], where solutions of this type, first based on Eguchi-Hanson space (hence providing local models of Fu-Yau compactifications, see also [21]), second on the conifold. An important step towards obtaining these solutions was to define a large charge limit, in which the contribution of the tangent bundle curvature to the Bianchi identity can be consistently neglected.…”