Looking for R-symmetries using generalised geometry

Tue, Jun. 18th 2024, 14:15

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

The AdS/CFT correspondence, first proposed by J. Maldacena in 1997, predicts an equivalence between conformal field theories and certain gravitational theories on Anti-de-Sitter backgrounds when the degree of the CFT’s gauge group is large. This correspondence allows us to study CFT’s from a geometric perspective by going to the “dual” gravity theory. (I used the word dual in its loose sense) That is to say, quantities characterising a CFT, sometimes inaccessible in the field theory language, can be computed in the geometry.
All N=1 SCFT’s have a U(1) R-symmetry which is an important property of the theory. Indeed, the operators of the theory fall into irreducible representations of this symmetry group and their R-charges are related to the a and c central charges by a ’t Hooft anomaly. a-maximisation, developed by Intriligator and Wecht, is a procedure by which the R-symmetry can be extracted from the global symmetry group of a 4D SCFT dual to an AdS5 background. The geometric analogue of this computation was first addressed by Martelli, Sparks and Yau in the case of Sasaki-Einstein geometries in type IIB string theory. In this talk, I will introduce relevant concepts in generalised geometry for constructing such backgrounds. I will then show how Martelli, Sparks and Yau’s proposal fits into a larger story of extremising the appropriate invariant of the generalised structure group. It can therefore be applied to more general backgrounds in various dimensions.

Contact : Valentin
REYS