Cosmologies with Null Singularities and their Gauge Theory Duals

TL;DR

This paper studies Type IIB string backgrounds with null singularities and their dual gauge theories, showing the dual gauge theory remains nonsingular and exploring related pp-wave solutions and Matrix Membrane theory.

Contribution

It demonstrates the nonsingularity of the dual gauge theory for specific null singularity backgrounds and constructs related pp-wave and Matrix Membrane theories.

Findings

Dual gauge theory correlation functions are nonsingular at all times.

Bulk supergravity calculations near singularities are invalid due to corrections.

Constructed Matrix Membrane theory for pp-wave backgrounds.

Abstract

We investigate backgrounds of Type IIB string theory with null singularities and their duals proposed in hep-th/0602107. The dual theory is a deformed N=4 Yang-Mills theory in 3+1 dimensions with couplings dependent on a light-like direction. We concentrate on backgrounds which become AdS_5 x S^5 at early and late times and where the string coupling is bounded, vanishing at the singularity. Our main conclusion is that in these cases the dual gauge theory is nonsingular. We show this by arguing that there exists a complete set of gauge invariant observables in the dual gauge theory whose correlation functions are nonsingular at all times. The two-point correlator for some operators calculated in the gauge theory does not agree with the result from the bulk supergravity solution. However, the bulk calculation is invalid near the singularity where corrections to the supergravity approximation become important. We also obtain pp-waves which are suitable Penrose limits of this general class of solutions, and construct the Matrix Membrane theory which describes these pp-wave backgrounds.