Equivariant branes

الأصل · EN

Given a Calabi-Yau manifold X acted by a group G and considering the B-branes on X as objects in the derived category of coherent sheaves, we give a definition of equivariant branes, which generalizes the concept of equivariant sheaves. We also propose a definition of equivariant charge of an equivariant brane. The spaces of strings joining the branes F and G, are the groups Extⁱ(F,G). We prove that the spaces of strings between two G-equivariant branes support representations of G. Thus, these spaces can be decomposed in direct sum of invariant spaces for the G-action. We show some particular decompositions, when X is a toric variety and when X is a flag manifold of a semisimple Lie group.