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One of the strongest evidence for the existence of super-conformal field theories is the explicit construction of their gravity duals through the AdS/CFT or Gauge/Gravity correspondence. In this way, holographic techniques have been very successfully applied to the study of 5d fixed point theories, four-dimensional field theories without perturbative Lagrangian descriptions, and conformal field theories in lower number of dimensions. Indeed, a large number of these have been discovered using holographic methods.
Generalized complex geometry is a well-established and broadly used method to generate new AdS solutions. More recently, String Theory duality symmetries have also been used to generate new solutions in supergravity. Contrary to what happens through its Abelian counterpart, solutions generated through non- Abelian T-duality are not equivalent to the original solution, but represent new physics. This opens up an interesting new avenue for the study of new CFTs through Holography.
This Scientific Program puts together the recently developed ideas on various aspects of conformal field theories (with different amounts of supersymmetry and in different dimensions), together with experience on U-dualities, non- Abelian T-duality and geometrical methods in supergravity theories to attack long-standing open problems: the definition of new conformal field theories, the explicit calculation of their observables and, breaking conformality, the application of these ideas to realistic physical systems.