Exact computation of one-loop correction to the energy of pulsating strings in AdS₅×S⁵

Abstract

In the present paper, which is a sequel to arXiv:1001:4018, we compute the one-loop correction to the energy of pulsating string solutions in AdS 5 × S 5 . We show that, as for rigid spinning string elliptic solutions, the fluctuation operators for pulsating solutions can be also put into the single-gap Lamé form. A novel aspect of pulsating solutions is that the one-loop correction to their energy is expressed in terms of the stability angles of the quadratic fluctuation operators. We explicitly study the "short string" limit of the corresponding one-loop energies, demonstrating a certain universality of the form of the energy of "small" semiclassical strings. Our results may help to shed light on the structure of strong-coupling expansion of anomalous dimensions of dual gauge theory operators.

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].…”

Superstrings in AdS2×S2×T6

“…The resulting mass sum rule that checks the 1-loop UV finiteness of the GS string in the static gauge is then universal in n (see [75])…”

“…For a superstring in AdS n × S n × T 10−2n (n = 5, 3, 2) the corresponding quadratic fluctuation spectrum in the static gauge is again a truncation of the AdS 5 × S 5 spectrum in [75]:…”

Semiclassical short strings in AdS5 × S 5

“…This is an important feature allowing to compute the one-loop correction to the string energy exactly for any value of semiclassical spin parameter S. Here we have extended the calculation to the pulsating string in R × S 2 . Additional details as well as the extensions to the pulsating string in AdS 3 and the folded spinning string in R × S 2 can be found in [17]. In all cases where there is only one charge/adiabatic invariant besides the energy, namely, an oscillator number or spin (in S 5 or AdS 5 ), the fluctuation operators can be decoupled and put into a single-gap Lamé type form.…”

“…The semiclassical approximation is based on assumption that √ λ 1 with semiclassical parameters characterizing the various solutions (see [17], for the precise definitions) like…”