Chaotic strings in a near Penrose limit of AdS5 × T1,1

Abstract

Abstract:We study chaotic motions of a classical string in a near Penrose limit of AdS 5 × T 1,1 . It is known that chaotic solutions appear on R×T 1,1 , depending on initial conditions. It may be interesting to ask whether the chaos persists even in Penrose limits or not. In this paper, we show that sub-leading corrections in a Penrose limit provide an unstable separatrix, so that chaotic motions are generated as a consequence of collapsed KolmogorovArnold-Moser (KAM) tori. Our analysis is based on deriving a reduced system composed of two degrees of freedom by supposing a winding string ansatz. Then, we provide support for the existence of chaos by computing Poincaré sections. In comparison to the AdS 5 ×T 1,1 case, we argue that no chaos lives in a near Penrose limit of AdS 5 ×S 5 , as expected from the classical integrability of the parent system.

Integrability of geodesics and action-angle variables in Sasaki–Einstein space $$T^{1,1}$$ T 1 , 1

“…In [6] an analytical approach is presented of the loss of the integrability using the techniques of differential Galois theory for normal variational equation. It is quite remarkable that, while the point-like string (geodesic) equations are integrable in some backgrounds, the corresponding extended classical string motion is not integrable in general [6,19]. A similar situation encountered in [20] in the study of (non)-integrability of geodesics in Dbrane background.…”

Lax pairs for deformed Minkowski spacetimes

“…Other deformations are associated with classical r-matrices composed of non-commuting generators and lead to deformed backgrounds obtained through a chain of dualities including S-dualities [31,32]. Further remarkably, these deformations may work for non-integrable backgrounds, such as a Sasaki-Einstein manifold T 1,1 [33,34]. TsT transformations of T 1,1 [16,35] are reproduced as Yang-Baxter deformations [36,37].…”

Lax pairs on Yang-Baxter deformed backgrounds

“…There are many examples of non-integrable AdS/CFT correspondences. An example is the case of AdS 5 × T 1,1 [44], for which the non-integrability has been shown by the existence of chaotic string solutions on R×T 1,1 [45][46][47]. Thus TsT transformations of T 1,1 [30,48] are regarded as non-integrable deformations.…”