Hybrid conformal field theories

Abstract

We describe a class of (2,2) superconformal field theories obtained by fibering a Landau-Ginzburg orbifold CFT over a compact Kähler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model, our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of linear models and comparing spectra among the phases.

(0,2) hybrid models

“…While conceptually this framework parallels the (2,2) case, there is a substantial technical difference, which we mention here and we will tackle later in this section. As pointed out in [24] the cohomology groups H • Q 0 (Y , H q,h ) are generically infinite-dimensional due to the non-compact geometry of Y . The strategy to obtain a well-defined counting problem is the following:…”

“…The geometric interpretation of this fact is the appearance of obstructions to the states being massless. In (2,2) models such obstructions are required to vanish in order for CPT invariance to hold as a symmetry in Q 0 -cohomology [24]. In (0,2) models there can be obstructions compatible with CPT invariance, although we do not have an example in which these are nontrivial.…”

“…V determines a vertical U(1)-action on Y , and a lift of this action to E. The last piece of data is given by the (0,2) superpotential J ∈ Γ(E * ). We assume that this satisfies the potential condition of [24], i.e., J −1 (0) = B.…”

“…In this section we are going to describe the techniques to compute the massless spectrum for a compactification of the E 8 × E 8 heterotic string based on a (0,2) hybrid CFT satisfying (3.21), generalizing the methods of [24].…”

“…, r n ). In the case E = T Y it has been shown in [24] that the SES defining T Y can be graded with respect to r as follows…”