T-Duality: Topology Change from H-Flux

By P. Bouwknegt, Jarah Evslin, Varghese Mathai. 2003

297 citations recorded by the source corpus.

T-duality acts on circle bundles by exchanging the first Chern class with the fiberwise integral of the H-flux, as we motivate using E8 and also using S-duality. We present known and new examples including NS5-branes, nilmanifolds, lens spaces, both circle bundles over Pn, and the AdS5×S5 to AdS5×P2×S1 with background H-flux of Duff, Lü 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 G4 receives a correction. 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.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/97226641298095a92261d0d4c12e46e0ab31a79d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. M. Graña
2. D. Waldram
3. G. Cavalcanti
4. A. Tomasiello
5. Shengda Hu
6. M. Petrini
7. R. Minasian
8. B. Wecht

In Mathematical Physics

1. M. Graña
2. D. Waldram
3. Shengda Hu
4. G. Cavalcanti
5. A. Tomasiello
6. M. Petrini
7. M. Gualtieri
8. R. Minasian

In Nuclear and High Energy Physics

1. M. Graña
2. B. Wecht
3. D. Waldram
4. A. Tomasiello
5. M. Petrini
6. R. Minasian
7. G. Cavalcanti
8. D. Lust

Citations in the corpus

• A scan for new N = 1 vacua on twisted tori (2006, background): “) The second relation is the well–known inversion of the radius; the first implies, by taking d on both sides (nothing depends on x1), that ι∂x1H ↔ c1 [68–70].”
• New aspects of the ddc-lemma (2005, unknown): “Namely, in order for a torus bundle (E,H) to be T-dualizable, H(X,Y, ·) has to vanish for every pair of vertical vectors X and Y [8].”
• New aspects of the dd c -lemma (2004, methodology): “Namely, in order for a torus bundle (E,H) to be T-dualizable, H(X,Y, ·) has to vanish for every pair of vertical vectors X and Y [8].”
• Flux compactifications in string theory: A Comprehensive review (2005, unknown): “[156, 157] for constructions relevant to this discussion).”
• Mirror Symmetric SU(3)-Structure Manifolds with NS Fluxes (2003, background): “This fact played for example a role in a number of applications and was recently formalized in mathematical terms in [11].”
• T-duality, generalized geometry and non-geometric backgrounds (2008, background): “It is well known that, under a single T-duality, the components of the B-field with no legs along the T-dualized directions stay unchanged, while those with one leg are exchanged with the connection along the T-dualized fiber [26].”
• Lectures on nongeometric flux compactifications (2007, background): “It is worth pointing out here that these fluxes have been studied from a more rigorous mathematical standpoint than we take here [49], where it is argued that the presence of R flux corresponds to some kind of nonassociative geometry.”
• Hamiltonian Symmetries and Reduction in Generalized Geometry (2005, methodology): “Another very interesting example of twisting change accompanied with topology change is the T -duality with H-flux as described by Bouwknegt, et al [3].”
• Generalized complex geometry and T-duality (2011, methodology): “Proposition 2.1 (Bouwknegt–Hannabuss–Mathai [6]).”
• Generalized Complex Geometry (2004, methodology): “This construction is described in the physics literature and especially in the remarkable paper of Bouwknegt, Evslin, and Mathai [7].”