  In this paper we study the quantum sheaf cohomology of Grassmannians with
deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2)
deformation of the ordinary quantum cohomology ring, realized as the OPE ring
in A/2-twisted theories. Quantum sheaf cohomology has previously been computed
for abelian gauged linear sigma models (GLSMs); here, we study (0,2)
deformations of nonabelian GLSMs, for which previous methods have been
intractable. Combined with the classical result, the quantum ring structure is
derived from the one-loop effective potential. We also utilize recent advances
in supersymmetric localization to compute A/2 correlation functions and check
the general result in examples. In this paper we focus on physics derivations
and examples; in a companion paper, we will provide a mathematically rigorous
derivation of the classical sheaf cohomology ring.
