Branes on \(G\)-manifolds. (English) Zbl 1370.57015

Viña, Andrés

J. Geom. Symmetry Phys. 43, 47-71 (2017).

Author’s abstract: Let \(X\) be a Calabi-Yau manifold acted on by a group \(G\). We give a definition of \(G\)-equivariance for branes on \(X\), and assign to each equivariant brane an element of the equivariant cohomology of \(X\) that can be considered as a charge of the brane. We prove that the spaces of strings stretching between equivariant branes support representations of \(G\). This fact allows us to give formulas for the dimension of some of such spaces, when \(X\) is a flag manifold of \(G\).

Reviewer: Cenap Özel (Bolu)

MSC:

57S20	Noncompact Lie groups of transformations
55N91	Equivariant homology and cohomology in algebraic topology
14F05	Sheaves, derived categories of sheaves, etc. (MSC2010)
81T30	String and superstring theories; other extended objects (e.g., branes) in quantum field theory

Keywords:

B-branes; equivariant cohomology; derived categories of sheaves