Rational curves and (0, 2)-deformations

Abstract

We compare the count of (0, 2)-deformation moduli fields for N = (2, 2) conformal field theories on orbifolds and sigma-models on resolutions of the orbifold. The latter involves counting deformations of the tangent sheaf. We see there is generally a discrepancy which is expected to be explained by worldsheet instanton corrections coming from rational curves in the orbifold resolution. We analyze the rational curves on the resolution to determine such corrections and discover that irreducible toric rational curves account for some, but not all, of the discrepancy. In particular, this proves that there must be worldsheet instanton corrections beyond those from smooth isolated rational curves.arXiv:1404.7802v1 [hep-th]

(0,2) hybrid models

“…Finally, in the realm of (0,2) theories without a (2,2) locus, the most pressing question is how worldsheet instantons modify the classical picture as we move away from the hybrid limit. In theories with a (2,2) locus, such corrections, although there are indications that they do occur [7,52], are particularly elusive [5]. We expect this behavior to be significantly different in more general (0,2) theories [23].…”

“…for some 0 ≤ q α < 1 and −1 ≤ Q A < 0. 7 The hybrid action is then invariant under a U(1) L × U(1) R symmetry under which the superfields have charges…”

“…In particular, it is reasonable to conjecture that LG accidents carry over to the hybrid structure, which would then suffer from the same pathology. Indeed, we can write (3.16) and (3.20) in terms of the data of the fiber LG theory as 7) and one might conclude that the hybrid IR would inherit the pathology of the LG fiber, prompting the model builder to reject such a hybrid theory.…”

“…Moreover, much of the work concerning (0,2) theories has focused on deformations of theories with (2,2) supersymmetry. While there are certainly notable challenges even in this tamer setting [3][4][5][6][7][8][9], in many instances features of (2,2) theories are more or less straightforwardly inherited by this larger space of deformations. Thus, it is of most interest to pursue the study of (0,2) models which do not admit a (2,2) locus.…”

“…The superscripts on D K and D H stand for "Kähler" and "Hermitian" respectively 6. We use the notation ǫQ · • ≡ [ǫQ, •], where ǫ is an anti-commuting parameter and Q is the operator corresponding to the supercharge Q, and similarly for Q 7. The upper bounds for the charges are determined by the potential condition and unitarity constraints.…”