Semiclassical quantization of circular strings in de Sitter and anti–de Sitter spacetimes

Abstract

We compute the exact equation of state of circular strings in the (2+1) dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting and expanding) strings. The string equation of state has the perfect fluid form P = (γ − 1)E, with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient γ depending on the elliptic modulus. We semi-classically quantize the oscillating circular strings. The string AdS ≈ 4H2 n 2 (large n ∈ N 0 ) and N AdS = ∞ in anti de Sitter spacetime. The level spacing grows with n in AdS spacetime, while is approximately constant (although larger than in Minkowski spacetime) in dS spacetime. The massive states in dS spacetime decay through tunnel effect and the semi-classical decay probability is computed. The semiclassical quantization of exact (circular) strings and the canonical quantization of generic string perturbations around the string center of mass strongly agree.

Pulsating strings on (AdS3 × S3) ϰ

“…Here we wish to study pulsating string solution in the sub sectors of the deformed background as they are more stable than rotating ones [37]. After the inception of the pulsating string in [38], they have been studied both in AdS and non-AdS background [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56].…”

Pulsating strings in Lunin-Maldacena backgrounds

“…However one important class of strings, pulsating strings, have not received much attention so far. They have been studied in AdS 5 × S 5 [18,19,20,21,22,23,24,25], AdS 4 × CP 3 [26,27] and other backgrounds [28], [29], [30], [31]. In the context of deformed geometry it was found that pulsating and rotating strings in AdS 5 × S 5 are images of point like strings living in the deformed space [32].…”

Rotating Strings in Confining AdS/CFT Backgrounds

“…One particular example where one can go much beyond the semiclassical approximation is that of highly boosted point-like strings, corresponding to states of large R-charge [7]. Other examples include truly extended classical string states, such as folded strings in the leading Regge trajectory, stabilized by a large spin S, and/or large R-charge quantum number J (see also [8]- [13] and [14] for an earlier work.). In particular, for very large rotating strings in AdS 5 in global coordinates, there is a dispersion relation…”