## Periodic Report Summary 1 - T-DUALITIES (Beyond Abelian T-duality)

Dualities, equivalent mathematical descriptions of the same physics, are best understood when isometries are Abelian. Abelian dualities, such as Kramers-Wannier duality in condensed matter, allow one to extend the regime where perturbation theory is valid, so that calculations can be performed. An Abelian duality called T-duality underpins much of our knowledge of string theory, a leading candidate for a theory of quantum gravity, and it is an interesting feature of T-duality that it permits non-Abelian and fermionic generalisations. The goal of this proposal is to study fermionic and non-Abelian T-dualities to better understand their application in string theory. Moreover, we will explore the implications, through the ubiquitous AdS/CFT correspondence, for strongly coupled quantum field theories, where there is no useful formulation of non-Abelian duality.

Thanks to work over the last two years, we now have complete control over solution generation for non-Abelian T-duality in type II supergravity. Building on a series of papers, where it was shown how supergravity backgrounds transform on a case by case basis, my publication, Class.Quant.Grav. 32 (2015) 035014, has demonstrated how the transformation is consistent with supersymmetry for a large class of diagonal Bianchi IX spacetimes. The preservation of supersymmetry is important as it guarantees stability of the T-dual geometries. This work covers all results to date on SU(2) transformations, the simplest extension of non-Abelian T-duality and provides confirmation of the prescription given by K. Sfetsos et al in Nucl.Phys. B873 (2013) 1-64. This paper also serves to back up earlier claims presented in JHEP 1411 (2014) 115.

As an off-shoot of the above work on T-duality, in collaboration with Y. Lozano, J. Montero, N. Macpherson, we realised that new examples of geometries dual to 2D N = (0,4) superconformal field theories could be generated. An interesting feature of these new solutions is that they fall outside the existing classifications of supersymmetric geometries. In recent work, which is only being published now, we have revisited the classifications using some of my earlier work. We have identified a new class of geometries, which we have shown is unique. This class is expected to correspond to the near-horizon of a class of supersymmetric black holes in 7D and will have implications for the microstate counting program.

We have recently witnessed the first example of geometries that are self-dual under fermionic T-duality where the dimensions of the external AdS and internal space differs. Against this backdrop, it is prudent to revisit the AdS4 CP3 calculation of I. Bakhmatov to perform a systematic check of T-duality directions. It is a shortcoming of Bakhmatov's work that he chooses T-duality directions in a rather ad hoc manner.

Thanks to work over the last two years, we now have complete control over solution generation for non-Abelian T-duality in type II supergravity. Building on a series of papers, where it was shown how supergravity backgrounds transform on a case by case basis, my publication, Class.Quant.Grav. 32 (2015) 035014, has demonstrated how the transformation is consistent with supersymmetry for a large class of diagonal Bianchi IX spacetimes. The preservation of supersymmetry is important as it guarantees stability of the T-dual geometries. This work covers all results to date on SU(2) transformations, the simplest extension of non-Abelian T-duality and provides confirmation of the prescription given by K. Sfetsos et al in Nucl.Phys. B873 (2013) 1-64. This paper also serves to back up earlier claims presented in JHEP 1411 (2014) 115.

As an off-shoot of the above work on T-duality, in collaboration with Y. Lozano, J. Montero, N. Macpherson, we realised that new examples of geometries dual to 2D N = (0,4) superconformal field theories could be generated. An interesting feature of these new solutions is that they fall outside the existing classifications of supersymmetric geometries. In recent work, which is only being published now, we have revisited the classifications using some of my earlier work. We have identified a new class of geometries, which we have shown is unique. This class is expected to correspond to the near-horizon of a class of supersymmetric black holes in 7D and will have implications for the microstate counting program.

We have recently witnessed the first example of geometries that are self-dual under fermionic T-duality where the dimensions of the external AdS and internal space differs. Against this backdrop, it is prudent to revisit the AdS4 CP3 calculation of I. Bakhmatov to perform a systematic check of T-duality directions. It is a shortcoming of Bakhmatov's work that he chooses T-duality directions in a rather ad hoc manner.

## Contact

Sega-Buhalis, Maria (Senior European Research Support Officer)

Tel.: +44 1483 683498

Fax: +44 1483 683791

E-mail

Tel.: +44 1483 683498

Fax: +44 1483 683791

## Subjects

Life Sciences**Record Number**: 182296 /

**Last updated on**: 2016-05-23

Information source: SESAM