On marginal deformations of (0,2) non-linear sigma models

Abstract

An N=1, d=4 supersymmetric compactification of the perturbative heterotic string is described by a d=2 (0,2) superconformal field theory. The first-order marginal deformations of the internal (0,2) SCFT are in 1 to 1 correspondence with massless gaugeneutral scalars in the spacetime theory. Working at tree-level in the α ′ expansion, we describe these first order deformations for SCFTs with a (0,2) non-linear sigma model description. Our results clarify the structure of deformations of heterotic Calabi-Yau compactifications and more general heterotic flux vacua.

Algebroids, heterotic moduli spaces and the Strominger system

“…We derive results valid through first order 1 in α ′ , a technical improvement over the discussion of [5], with our results being in agreement with that work in the limit where α ′ → 0. On the other hand, unlike [5], we 'overcount' the massless degrees of freedom of the compactification as, as we will describe, we shall only analyze a subset of the conditions imposed upon the system by Strominger. Our supergravity deformation analysis will also be restricted to compactifications on spaces satisfying the ∂∂-lemma, which can be stated as follows:…”

“…More precisely, we will show that fluctuations satisfying (2.54) and (2.55) are classified by the cohomology H 1 (H) of a bundle H that we will specify. In section 5 we will see that, in the limit α ′ → 0, the equations above precisely duplicate the cocycle conditions found in the worldsheet analysis of [5].…”

“…As we will show in section 5, the results we have presented above reduce to those of [5], which were derived formally from two-dimensional non-linear sigma models, in the limit where α ′ → 0. In such a limit, as we have seen, the maps involved in defining H become significantly more straightforward and, thus, it is interesting to look at the new features arise when we go beyond such a simplification.…”

“…In addition to Calabi-Yau compactifications, there has also been considerable interest in non-Kähler solutions of the heterotic string, see for example [5][6][7][8]. In particular, as Yau's theorem can no longer be applied to relate metric moduli to deformations of the complex and Kähler structure, a longstanding problem in non-Kähler heterotic compactifications has been to understand their massless degrees of freedom.…”

“…A proposal for the physical moduli of non-Kähler solutions to the Strominger system was given in [5], at zeroth order in α ′ (see e.g. [43,44] for other related work).…”