Summing the instantons in half-twisted linear sigma models

Abstract

We study half-twisted linear sigma models relevant to (0,2) compactifications of the heterotic string. Focusing on theories with a (2,2) locus, we examine the linear model parameter space and the dependence of genus zero half-twisted correlators on these parameters. We show that in a class of theories the correlators and parameters separate into A and B types, present techniques to compute the dependence, and apply these to some examples. These results should bear on the mathematics of (0,2) mirror symmetry and the physics of the moduli space and Yukawa couplings in heterotic compactifications.

The leading quantum corrections to stringy Kähler potentials

“…Much less is understood about the Kähler potential which appears to be less constrained. We suspect, however, that much more can be said about stringy Kähler potentials largely through a heterotic generalization of mirror symmetry to (0, 2) rather than (2, 2) world-sheet theories [4][5][6][7][8][9][10][11][12]. One of the basic tests of the original (2, 2) mirror conjecture was reproducing the known (α ′ ) 3 correction to the space-time…”

Rational curves and (0, 2)-deformations

“…They have been much-studied in the context of the gauged linear σ-model [9,23,24]. These do not depend on the choice of resolution and we will see in section 4.3 that they never suffer from instanton corrections.…”

Supersymmetric localization in GLSMs for supermanifolds

“…(See e.g. [35][36][37] for a discussion of (0, 2) deformations of tangent bundles of products of projective spaces and results in quantum sheaf cohomology.) Then the M 's are given by:…”