Aspects of (2,2) and (0,2) hybrid models

Abstract

In this work we study the topological rings of two dimensional (2,2) and (0,2) hybrid models. In particular, we use localization to derive a formula for the correlators in both cases, focusing on the B-and B 2 -twists. Although our methods apply to a vast range of hybrid CFTs, we focus on hybrid models suitable for compactifications of the heterotic string. In this case, our formula provides unnormalized Yukawa couplings of the spacetime superpotential. We apply our techniques to hybrid phases of linear models, and we find complete agreement with known results in other phases. We also obtain a prediction for a certain class of correlators involving twisted operators in (2,2) Landau-Ginzburg orbifolds. For (0,2) theories, our argument does not rely on the existence of a (2,2) locus. Finally, we derive vanishing conditions concerning worldsheet instanton corrections in (0,2) B 2 -twisted hybrid models.

Testing the (0,2) mirror map

“…A systematic study along this lines might help unveiling the structure of the non-reflexive subset of the moduli space. For instance, techniques to evaluate B and B/2 model correlators in hybrid models [25,26] have been recently developed [24], and these could be employed to gain insights into this larger set of theories. While we expect a dependence on non-diagonal, but linear, E-parameters, nonlinear E-parameters seem not to affect A/2-twisted V model correlators [27][28][29].…”

A (0,2) mirror duality

“…On the other hand, this interchange nevertheless implies an isomorphism between the A/2 subring of the chiral ring of the (0,2) theory and the B/2 subring of the mirror model. Recent advances in the development of techniques to compute correlators in the corresponding twisted theories [39,40] are likely to shed light on the moduli dependence on at least some subsectors of the theory. For instance, some indications that a splitting between Kähler and complex structure moduli occurs already appeared in the class of (0,2) theories studied in [11,12].…”

(0,2) hybrid models

“…The contribution is then 10 1 2 -hypers in the (32 ′ , 1, 1)∈ so(12) ⊕ u(1) L ⊕ u(1) R . In the twisted k = 2 sector the vacuum has again zero energy and there are no zero modes, hence the only contribution is from the vacuum |2 1,−1 , which together with the CPT conjugate state to be found in k = 12, teams up with the states describe above to complete the representation (32,2,2).…”