Chiral operators in two-dimensional (0,2) theories and a test of triality

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In this paper we compute spaces of chiral operators in general two-dimensional (0,2) nonlinear sigma models, both in theories twistable to the A/2 or B/2 model, as well as in non-twistable theories, and apply them to check recent duality conjectures.

• The fact that in a nonlinear sigma model, the Fock vacuum can act as a section of a line bundle on the target space plays a crucial role in our (0,2) computations, so we begin with a review of this property.
• We also take this opportunity to show how even in (2,2) theories, the Fock vacuum encodes in this way choices of target space spin structures, and discuss how such choices enter the A and B model topological field theories.
• We then compute chiral operators in general (0,2) nonlinear sigma models, and apply them to test the recent Gadde-Gukov-Putrov triality proposal, which says that certain triples of (0,2) GLSMs should RG flow to nontrivial IR fixed points.