Journal of Geometry and Symmetry in Physics

Branes on $G$-Manifolds

Andrés Viña

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Abstract

Let $X$ be Calabi-Yau manifold acted 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 $G$.

Article information

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

Dates
First available in Project Euclid: 12 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.jgsp/1494605780

Digital Object Identifier
doi:10.7546/jgsp-43-2017-47-71

Mathematical Reviews number (MathSciNet)
MR3644814

Zentralblatt MATH identifier
1370.57015

Subjects
Primary: 57S20: Noncompact Lie groups of transformations
Secondary: 55N91: Equivariant homology and cohomology [See also 19L47] 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]

Keywords
$B$-branes equivariant cohomology derived categories of sheaves

Citation

Viña, Andrés. Branes on $G$-Manifolds. J. Geom. Symmetry Phys. 43 (2017), 47--71. doi:10.7546/jgsp-43-2017-47-71. https://projecteuclid.org/euclid.jgsp/1494605780


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