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CONFORMAL COURANT ALGEBROIDS AND ORIENTIFOLD T-DUALITY

DAVID BARAGLIA

Mathematical Sciences Institute, The Australian National University, Canberra, Australian Capital Territory 0200, Australia

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https://doi.org/10.1142/S0219887812500843Cited by:10 (Source: Crossref)

Abstract

We introduce conformal Courant algebroids, a mild generalization of Courant algebroids in which only a conformal structure rather than a bilinear form is assumed. We introduce exact conformal Courant algebroids and show they are classified by pairs (L, H) with L a flat line bundle and H ∈ H³(M, L) a degree 3 class with coefficients in L. As a special case gerbes for the crossed module (U(1) → ℤ₂) can be used to twist TM ⊕ T*M into a conformal Courant algebroid. In the exact case there is a twisted cohomology which is 4-periodic if L² = 1. The structure of Conformal Courant algebroids on circle bundles leads us to construct a T-duality for orientifolds with free involution. This incarnation of T-duality yields an isomorphism of 4-periodic twisted cohomology. We conjecture that the isomorphism extends to an isomorphism in twisted KR-theory and give some calculations to support this claim.

Keywords:

AMSC: 53D18, 53C08, 81T30, 19L50

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