Final Activity Report Summary - HOLOGRAPHIC DUALITY (Gauge theories, cosmology and holography)
The objectives of the research program were divided in two parts. The first part focussed on the construction of a realistic holographic gravitational dual theory for the strong interactions, namely QCD.
The main tool for this investigation is the AdS/CFT duality that naturally works in the framework of 10 dimensional critical string theory. The main problem that we planned to address was how to eliminate the effects of the unrealistic extra 5 dimensions in the gravitational dual backgrounds (the gravitational dual of a 4D field theory is naturally 5 dimensional: 4 dimensions for Minkowski space + 1 dimension for the energy scale), in particular the effects of the Kaluza-Klein modes. Our proposal to attack this problem was two-fold:
I-1) To study the effects of the Kaluza-Klein modes by using the so-called gamma-deformation technique, and search for universal quantities, invariant under the gamma transformations.
I-2) To directly construct a 5D dual gravity theory in 5D non-critical string theory.
The second part of the research proposal concerned the study of gravitational singularities in space-time from the point of view of holography. Our proposed method of study was the construction of toy models for two-dimensional cosmology and their investigation in the dual picture, using 2D matrix models. Instead of closely following this strategy, the project preferred to study the problem of gravitational singularities, in particular the black-hole singularities using the original formulation of the AdS/CFT correspondence, namely the duality between the 4D maximally super-symmetric gauge theory and IIB string theory on the AdS5 x S5 background. In particular, the project mapped the structure of the extreme curvature limit of the AdS5 black holes, to a 6D matrix model that stem from the 6 scalar fields in the dual gauge theory.
The main tool for this investigation is the AdS/CFT duality that naturally works in the framework of 10 dimensional critical string theory. The main problem that we planned to address was how to eliminate the effects of the unrealistic extra 5 dimensions in the gravitational dual backgrounds (the gravitational dual of a 4D field theory is naturally 5 dimensional: 4 dimensions for Minkowski space + 1 dimension for the energy scale), in particular the effects of the Kaluza-Klein modes. Our proposal to attack this problem was two-fold:
I-1) To study the effects of the Kaluza-Klein modes by using the so-called gamma-deformation technique, and search for universal quantities, invariant under the gamma transformations.
I-2) To directly construct a 5D dual gravity theory in 5D non-critical string theory.
The second part of the research proposal concerned the study of gravitational singularities in space-time from the point of view of holography. Our proposed method of study was the construction of toy models for two-dimensional cosmology and their investigation in the dual picture, using 2D matrix models. Instead of closely following this strategy, the project preferred to study the problem of gravitational singularities, in particular the black-hole singularities using the original formulation of the AdS/CFT correspondence, namely the duality between the 4D maximally super-symmetric gauge theory and IIB string theory on the AdS5 x S5 background. In particular, the project mapped the structure of the extreme curvature limit of the AdS5 black holes, to a 6D matrix model that stem from the 6 scalar fields in the dual gauge theory.