Dualities between string theories/supergravities and gauge theories in the large N limit

To understand the large N behaviour of SU(N) gauge theories is long-standing problems, which is related to the understanding of quark confinement in gauge theories. On the other hand, the goal of quantum gravity is to smooth out, or resolve, the singularities of classical general relativity. It is known that many space-times which are singular from the standpoint of general relativity axe in fact non-singular when viewed as solutions to string theory. To explore the relation between gauge theories (there is quark confinement) and string theories/supergravities (there is geometrical singularity) in large N limit is our main goal which we hope to pursue. In this research project, we shall study the following problems: 1. The duality between 6D supergravity with nL + nR = 1 and sigma model with (4, 0) supersymmetry. 2. The duality between 5D supergravity on S2 x AdS 3 (which is from M-theory compactified on M x S2 x AdS 3 with M some Calabi-Yau manifold) and the (0, 4) superconformal field theory on the boundary of AdS 3 . 3. The relation between two kinds of 2D conformal field theories from world-sheet point of view of perturbative string theory propagating on AdS 3 x S3 x T4 target space-time. 4. Apply AdS 3 /CFT correspondence to study BTZ black hole physics.