T duality: Topology change from H flux
Jun, 200340 pages
Published in:
- Commun.Math.Phys. 249 (2004) 383-415
e-Print:
- hep-th/0306062 [hep-th]
Report number:
- ADP-03-122-M102,
- IFUP-TH-2003-19
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Abstract:
T-duality acts on circle bundles by exchanging the first Chern class with the fiberwise integral of the H-flux, as we motivate using E_8 and also using S-duality. We present known and new examples including NS5-branes, nilmanifolds, Lens spaces, both circle bundles over RP^n, and the AdS^5 x S^5 to AdS^5 x CP^2 x S^1 with background H-flux of Duff, Lu and Pope. When T-duality leads to M-theory on a non-spin manifold the gravitino partition function continues to exist due to the background flux, however the known quantization condition for G_4 fails. In a more general context, we use correspondence spaces to implement isomorphisms on the twisted K-theories and twisted cohomology theories and to study the corresponding Grothendieck-Riemann-Roch theorem. Interestingly, in the case of decomposable twists, both twisted theories admit fusion products and so are naturally rings.Note:
- 36 pages, latex2e, uses xypic package. Made only a few superficial changes in the manuscript Subj-class: High Energy Physics - Theory: K-Theory and Homology: Differential Geometry Journal-ref: vol 249 no. 2 (2004) 383 - 415 DOI: 10.1007/s00220-004-1115-6
- string model
- supersymmetry
- compactification
- T-duality
- fibre bundle
- topology
- index theorem
- quantization
- anomaly
- flux
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