A new coordinate system forq-deformed AdS₅×S⁵and classical string solutions

Abstract

We study a GKP-like classical string solution on a q-deformed AdS 5 ×S 5 background and argue the spacetime structure by using it as a probe. The solution cannot stretch beyond the singularity surface and this result may suggest that the holographic relation is realized inside the singularity surface. This observation leads us to introduce a new coordinate system which describes the spacetime only inside the singularity surface. With the new coordinate system, we study minimal surfaces and derive a deformed Neumann-Rosochatius system with a rigid string ansatz.

Deformations of the Almheiri-Polchinski model

“…Hence the location of the holographic screen and the choice of the counter-term are far from trivial. Although the holographic screen was supposed to be the singularity, inversely speaking, this agreement of the entropies here supports that the proposal in [69][70][71] would work well. As for the geometrical meaning of the counter-term (5.4), we have no definite idea.…”

“…Now that we know the classical r-matrix which leads to the black hole geometry, it would be interesting to consider a Yang-Baxter deformation of higher-dimensional AdS with this r-matrix. In the study of Yang-Baxter deformations, it has been a long standing problem to determine where the holographic screen is, while there was a proposal for the η-deformed AdS 5 [69][70][71] but it has not been supported by concrete evidence before this paper. It is JHEP03(2017)173 significant to find out more supports to clarify the holographic interpretation for general Yang-Baxter deformations.…”

“…3 However, the holographic duals of the deformed geometries have been poorly understood. In particular, even the location of the holographic screen has not been clarified, though there is a proposal [69][70][71]. Hence it is important to get much deeper understanding of the simplest case like AdS 2 .…”

“…Now that the boundary structure is drastically changed, the first thing is to determine the location of the holographic screen. In the following, we take the screen on the singularity by following the proposal of [69][70][71]. More precisely, by introducing a UV cut-off , the boundary is taken just before the singularity (Z = Z 0 + ).…”

Stringy correlations on deformed AdS3 × S 3

“…As a consequence of this, the deformed target space metric corresponding to AdS 5 appears to be with no boundary in the usual sense [78]. Instead one could think of a holographic screen [84]- [85] and solve stringy dynamics within the region bounded by this holographic screen. It turns out that the region bounded by this holographic screen is the only allowed physical region in the bulk where the classical string solutions as well as the holographic correspondence make sense [84]- [85].…”