Banca de QUALIFICAÇÃO: Guilherme Ribeiro Gonçalves Barrocas

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : Guilherme Ribeiro Gonçalves Barrocas
DATE: 25/08/2023
TIME: 14:00
LOCAL: Auditório do IF
TITLE:

On a non-geometric approach to noncommutative gauge and gravity theories.

KEY WORDS:

Noncommutative field theory, Noncommutative gravity, Self-Interaction, Groenewold-Moyal star product.

PAGES: 45
BIG AREA: Ciências Exatas e da Terra
AREA: Física
SUMMARY:

Over the past few decades, noncommutative geometry has evolved into a well-established field, bridging pure mathematics and theoretical physics. Its emergence as a model independent limit of quantum gravity and string theory has ignited a quest to explore physics beyond the standard model of particle physics and even beyond the theory of General Relativity in the setting of noncommutative geometry.

One of the most studied noncommutative geometries that has found extensive applications in physics is the noncommutative Groenewold-Moyal (flat) space. At the same time, the study of “curved” noncommutative geometries is rather non-trivial and, very often, ambiguous. Thus, the main objective of this work is to use a “non-geometric” approach to noncommutative theories in the case when either space-time (gravity) or internal space (gauge theories) are curved. For that end, we adopt to the noncommutative setting from Deser's approach (originally designed for the commutative case), in which self-interactions via conserved currents are shown to generate consistent and fully nonlinear geometric theories [Gen. Rel. Grav. 1 (1970) 9, gr-qc/0411023v3].

The doctoral work consists of two stages:

1) First, we want to study a somewhat simpler case of gauge fields on Groenewold-Moyal space. In the case of non-abelian, i.e. Yang-Mills, gauge fields, several approaches to noncommutative generalization exist. We expect that our approach will expand our understanding of how noncommutative gauge symmetry emerges naturally from the requirement of consistent self-interaction. For instance, even in the simplest case of abelian U(1) theory, we have already shown that this approach leads to a non-geometric construction of the noncommutative U(1) theory due to the existence of a noncommutative non-local conserved current, which is absent in the commutative case. Also, this study serves as a serious preparation to the second, much less trivial case of noncommutative gravity.

2) The construction of noncommutative gravity is much less settled than that of noncommutative Yang-Mills. Extending the techniques studied at the previous stage, we want to generalize Deser’s non-geometric derivation of General Relativity from the flat Fierz-Pauli theory. The starting point again is the Fierz-Pauli theory, but now defined on Groenewold-Moyal space. This leads to a non-trivial deformation of the conserved current, i.e., the energy-momentum tensor. Effectively, this corresponds to changing the local isometries of the space-time from the usual Poincare symmetry to the so-called twisted Poincare. We expect that going through the procedure of the consistent coupling of this twisted current to the original fields will lead to a well-defined theory of noncommutative gravity. Whether we will succeed in deriving the full theory or just noncommutative corrections remains to be seen. We then plan to compare our results with existing models.

COMMITTEE MEMBERS:
Externo ao Programa - 1715572 - ARSEN MELIKYAN - nullExterna ao Programa - 4177635 - CAROLINA MATTE GREGORY - nullExterno ao Programa - 2316482 - JOSE FRANCISCO DA ROCHA NETO - nullPresidente - 2993768 - MARIANA PENNA LIMA VITENTI