Global aspects of T-duality, gauged sigma models and T-folds

By C. Hull. 2006

499 citations recorded by the source corpus.

The gauged sigma-model argument that string backgrounds related by T-duality give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to T-duality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fibrewise in the general case in which there are no globally-defined Killing vector fields, so that there is no isometry symmetry that can be gauged; the derivation of T-duality is extended to this case. The T-duality transformations are presented in terms of globally-defined quantities. The generalisation to non-geometric string backgrounds is discussed, the conditions for the T-dual background to be geometric found and the topology of T-folds analysed.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0db045e253ff4ff457594dd7141e0c165d87ee16

How researchers see this paper

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

In Mathematical Physics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Spheres, Generalised Parallelisability and Consistent Truncations (2014, background): “If we keep the full degrees of freedom of the Type IIB theory, the GL+(6, R) generalised geometry embeds in a larger (exceptional) E6(6) × R+ generalised geometry.[19,23] This is summarised in appendix B, partly using results of Ashmore.”
T-duality, generalized geometry and non-geometric backgrounds (2008, unknown): “There are however global obstructions in performing the above procedure [14,15].”
M-theory, exceptional generalised geometry and superpotentials (2008, methodology): “In either case, the geometry of M7 is restricted, and some discussion of the latter case appears in [49].”
Duality invariant actions and generalised geometry (2011, background): “This is the same metric as in [45, 46, 34] except for the factor of g1/5.”
Extended geometry and gauged maximal supergravity (2013, methodology): “One of them are configurations obeying the section condition (3.18), which implies that the fields only depend on coordinates spanning a 7-dimensional slice of the extended space, therefore allowing to make contact with supergravity and Exceptional Generalized Geometry.”
Exploring double field theory (2013, methodology): “More general U-duality covariant frameworks have been constructed in [20–30] and [31– 36], and the relation between some of these theories and DFT was explained in [37].”
Lectures on nongeometric flux compactifications (2007, unknown): “See [47] for one argument; another is that one can work with the covering space where the Killing vector is well defined, and quotient by a translation plus T-duality.”
Supergravity as generalised geometry II: Ed(d) × ℝ+ and M theory (2014, methodology): “In the following paper [12], we defined the analogous concepts in Ed(d)×R generalised geometry, also known as exceptional or extended generalised geometry [15, 16].”
Background independent action for double field theory (2010, background): “Generalisations of generalised geometry were proposed in [23] and developed in [24] in which O(D,D) was replaced by U-duality groups; see also [33].”
Generalized geometry and M theory (2010, methodology): “The recent work of Hohm, Hull and Zwiebach [38] reaches similar conclusions for the doubled geometry of the string.”
The gauge structure of generalised diffeomorphisms (2012, background): “Such ideas, where space-time is enlarged to accommodate the extra “momenta”, found its geometric formulation in the work of Hull, first for T-duality [22] and later for Uduality [23, 24].”
Double field theory formulation of heterotic strings (2011, background): “, [30, 31]), we are not aware of investigations of the structures discussed here, and so it would be interesting to further study their mathematical aspects.”
Double field theory: a pedagogical review (2013, methodology): “More recently, Hull and Zwiebach combined their expertise on double geometry [14] and string field theory [15] to build DFT [3].”
Asymmetric orbifolds, non-geometric fluxes and non-commutativity in closed string theory (2012, unknown): “However, it has been argued [25] that, in certain cases, one might still be allowed to perform a T-duality, using the Buscher rules (5), even in the absence of such isometries.”
Duality Symmetric String and M-Theory (2013, background): “These exceptional generalised geometries have been developed in [15] and [16].”
A ten-dimensional action for non-geometric fluxes (2011, background): “Such fluxes are not contained in GCG, which focuses on the NSNS sector, but they could be described in a framework such as Exceptional Generalized Geometry (EGG) [79, 80, 81, 82, 83], or following [84, 85].”
Supergravity as generalised geometry I: type II theories (2011, background): “In a forthcoming companion paper [8], we define the corresponding structures in the Ed(d) version of generalised geometry [9, 10] relevant to restrictions of eleven-dimensional supergravity to a d-dimensional manifold.”
Generalized flux vacua (2006, unknown): “(2)Strictly speaking, the isometry in the direction b is not globally defined, but it seems that the T-duality in this direction can be understood, at least in the dimensionally reduced theory, in terms of an orbifold by a combination of a shift and a T-duality symmetry; see also [16].”