Abstract by Joseph Ward
A First Look at Nonabelian Mirror Symmetry
Mirror symmetry predicts a surprising relationship between two string theory models known as the A-model and the B-model. Given a polynomial W in n variables, a symmetry of W is a linear transformation that leaves the polynomial unchanged when applied to the variables. The A-model construction depends on W and the choice of symmetry group G. Mirror symmetry occurs when the A-model construction for the pair (W, G) is isomorphic to the B-model construction for another pair. This is well understood for symmetry groups represented by diagonal matrices - i.e. G is abelian - but almost nothing is known about mirror symmetry in the nonabelian case. We are studying one example of mirror symmetry for a pair (W, G) with a nonabelian symmetry group. In this talk, I will introduce this example and discuss what we have discovered so far.