A note on AdS cosmology and gauge theory correlator

Abstract

Using AdS/CFT prescription, we compute two point Yang-Mills correlator on a constant time slice for the Kasner background. Pushing the surface close to the initial singularity, we find, in some cases, the correlator does not develop pole. We further numerically calculate similar correlator where the bulk is a Kasner AdS soliton. We find that the qualitative behaviour of the correlator remains unchanged.

Further holographic investigations of big bang singularities

“…This implies that for t > 0, the turning point occurs at t * = (−c) −1/2p . The function x(t) can be obtained from u(t) by direct integration; the result below agrees with the earlier work of [16]: 3…”

“…We conclude this section by treating the separate case in which p = − 1 2n+1 . By setting p = − 1 2n+1 in the equations of motion (3.5), we may implement a variable redefinition y = −t −2p c −1 , which allows us to obtain a solution for these particular values of p via the same methodology described above: 16) where the constants c 3 and c 4 are determined as above:…”

Nonvacuum AdS cosmology and comments on gauge theory correlator

“…It was found that if the direction along which the operators were separated carries a negative Kasner exponent, the correlators developed divergences in their IR. Subsequently, in [15], by solving the space-like geodesic equations for arbitrary exponents, it was noticed that for correlators separated along the positive Kasner exponents, correlation vanishes even if one pushes the space-like surface close to the singularity. While the reason for such behaviour is not yet obvious to us, in the present work we consider a larger class of time dependent geometries in AdS, study their symmetries, embeddings in flat space of higher dimensions, space-like geodesics in the geometries and nature two point correlators at the boundary.…”

Time-dependent AdS backgrounds from S-branes

“…In [15] a more general solution where the D3-brane worldvolume is replaced by Friedmann-Robertson-Walker (FRW) metric with a conformal factor was obtained and its properties were analyzed [16]. For the M5-brane only the Kasner deformation has been investigated [17,18].…”