# Conform symmetry and T-duality in the σ model for closed strings.

Name: Rheymisson Prado Pereira

Type: MSc dissertation

Publication date: 06/04/2020

Advisor:

Name | Role |
---|---|

Galen Mihaylov Sotkov | Advisor * |

Examining board:

Name | Role |
---|---|

Andre Luiz Alves Lima | Internal Examiner * |

Galen Mihaylov Sotkov | Advisor * |

Igor Figueiredo Justo | External Examiner * |

Marian Stanishkov | External Examiner * |

Ulysses Camara da Silva | External Examiner * |

Summary: Conformal symmetries determine the specific form of the curved space-time string action, as well as its dimension D. When there are isometric dimensions, the obtained action manifests the T-Duality phenomenon, from which distinct equivalent backgrounds can be obtained.

This dissertation studies said T-Duality in the case when the isometries are abelian. A review is made about the classical closed string and its quantization, both in the light cone and conformal gauge. The way each gauge deals with ghosts, fix the space-time dimension and the massless spectrum are derived in detail. The sigma model is derived as an effective action resulting from the inclusion of the massless spectrum in the at space-time. It is shown that imposing conformal symmetry in the model implies equations of motion for the background fields and, in particular, an extended version of Einstein's equations in D dimensions. The T-Duality phenomenon is demonstrated in the Polyakov action. For the more general sigma model, it is shown that abelian T-Duality occurs and can be understood as a canonical transformation connecting two distinct systems which describe the same physics, in this process, the Buscher Rules are also derived. Three examples of interest in contemporary research are presented, two illustrating the use of TDuality to obtain equivalent backgrounds and the last one extending the method for non-isometric

dimensions. We conclude by proposing to use the methods described in the text to investigate the possibility of deriving symmetries of scale factor inversion in asymptotically AdS gravitational theories.