Dualities between string theories/supergravities and gauge theories

Lise Meitner Position M 597 Dualities between string theories / supergravities and gauge theories Jian-Ge ZHOU 09.10.2000 We plan to study dualities between string theories /supergravities and gauge theories from three directions: 1) M(atrix) theory; 2) AdS/CFT correspondence; 3) Noncommutative string theory. 1) As we know, there is an integrated picture of the strongly coupled dynamics for string theories. In various limits, there is an effective description in terms of one or another weakly coupled string theory. The most interesting thing is M-theory whose low energy physics is described by 11D supergravity, and whose short distance physics is assumed to be M(atrix) theory. In M(atrix) theory, we plan to find a way to isolate the dynamics of the states with Discrete Light Cone Quantization (DLCQ) energy 11N and to write a Lagrangian for dnoncompact 5 for the infinite N system. Another interesting problem which we plan to study is the formulation of DLCQ M theory on Calabi-Yau threefolds. 2) In all the known cases of the AdS/CFT correspondence the gravity solution has a timelike boundary. It would be interesting to understand how the correspondence works when the boundary is light-like. It seems that holography must work quite differently in these cases. We plan to see how holography works in other spacetimes, where we do not have this notion of time. We also plan to study the physics of quantum gravity in flat space by taking the large radius limit of physics in AdS space.In this case, the field theory is very strongly coupled and energies are also very high, and there are no known `ways to do any computation on the field theory side. I would be interesting to compute anything explicitly in this limit, for example, to study the dynamics of D-branes in the presence of NS-5- branes. 3) Recently, Seiberg and Witten argued that ordinary gauge fields should be equivalent to noncommutative gauge theory, which acts as the low energy effective theory of open strings. The advantage of noncommutative geometry is that T-dualit acts within the noncommutative Yang-Mills framework, rather than mixing the modes of noncommutative Yang-Mills theory with string winding states and other stringy excitation. This makes the framework of noncommutative Yang-Mills theory very powerful. In this direction, there are so many problems we plan to study. For example, instantons on noncommutative spacetime, string creation in the presence B-field, noncommutative version of the six dimensional (2, 0) theory and so on.