T-duality of Singular Spacetime Compactifications in an H-flux
Publication Date
3-29-2018
Document Type
Article
Organizational Units
College of Natural Science and Mathematics, Mathematics
Keywords
Singular compactifications, Equivariant, Generalized, Geometry, Equivariant exact Courant algebroids, Twisted equivariant de Rham complex, Equivariant T-duality
Abstract
We begin by presenting a symmetric version of the circle equivariant T-duality result in a joint work of the second author with Siye Wu, thereby generalizing the results there. We then initiate the study of twisted equivariant Courant algebroids and equivariant generalized geometry and apply it to our context. As before, T-duality exchanges type II" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">IIA and type II" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">IIB string theories. In our theory, both spacetime and the T-dual spacetime can be singular spaces when the fixed point set is non-empty; the singularities correspond to Kaluza–Klein monopoles. We propose that the Ramond–Ramond charges of type II" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">II string theories on the singular spaces are classified by twisted equivariant cohomology groups, consistent with the previous work of Mathai and Wu, and prove that they are naturally isomorphic. We also establish the corresponding isomorphism of twisted equivariant Courant algebroids.
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Recommended Citation
Linshaw, Andrew, and Mathai, Varghese. “T-Duality of Singular Spacetime Compactifications in an H-Flux.” Journal of Geometry and Physics, vol. 129, 2018, pp. 269–278. doi: 10.1016/j.geomphys.2018.03.017.