Cosmologies with Null Singularities and their Gauge Theory Duals

TL;DR

This work analyzes Type IIB backgrounds with null singularities and proposes a holographic dual in terms of ${\mathcal{N}}=4$ SYM on a curved spacetime with a light-like varying coupling $g_{YM}^2=e^\Phi$. The authors demonstrate that the dual gauge theory is nonsingular by exploiting the vanishing conformal anomaly for null backgrounds and by working with gauge-invariant observables built from the tilde variables, which have canonical kinetic terms when $e^\Phi$ vanishes near the singularity. They show that, although bulk supergravity calculations of two-point functions near the singularity encounter breakdowns and potential α' corrections, the gauge theory description remains well defined, and they extend the analysis to Penrose limits and Matrix Membrane theory to connect with pp-waves and DLCQ duals. The paper also derives the bulk two-point function via two complementary methods and discusses the implications for string dynamics in these time-dependent backgrounds, highlighting that a nonsingular gauge-theory description can effectively resolve or extend past the bulk singularity.

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.