Quantum corrections to energy of short spinning string in AdS5

TL;DR

The paper analyzes quantum corrections to the energy of a folded spinning string in $AdS_5\times S^5$ in the short-string limit, aiming to illuminate strong-coupling behavior of anomalous dimensions for short gauge-theory operators. Using a near-flat-space expansion and evaluating the $AdS_5\times S^5$ Green-Schwarz string fluctuations, the authors extract the first two 1-loop coefficients in the small-spin expansion of the energy, $E(S,\lambda)=\lambda^{1/4}\sqrt{2S}\,[a_{00}+a_{01}/\sqrt{\lambda}+a_{10}S/\sqrt{\lambda}+\dots]$, finding $a_{01}=3-4\ln 2$ and $a_{11}= -1219/576 + (3/2)\ln 2 + (3/4)\zeta(3)$. The leading correction renormalizes the flat-space result and the next term introduces a $\zeta(3)$ piece, highlighting the intricate transcendental structure of short-string quantum corrections. The work also discusses infrared subtleties, zero-mode regularization, and how these results relate to, but do not directly reproduce, perturbative gauge-theory expansions at small coupling due to resummation challenges. Overall, it demonstrates concrete, calculable quantum corrections in a highly nontrivial curved background and clarifies the near-flat-space regime for AdS/CFT energetics.

Abstract

Motivated by desire to shed light on the strong coupling behaviour of anomalous dimensions of "short" gauge theory operators we consider the famous example of folded spinning string in AdS_5 in the limit of small semiclassical spin parameter §= S/sqrt[lambda]. In this limit the string becomes short and is moving in a near-flat central region of AdS_5. Its energy scales with spin as E = sqrt[2 S] [ a_0 + a_1 S + a_2 S^2 + ...]. We explicitly compute the leading 1-loop quantum AdS_5 x S^5 superstring corrections to the short-string limit coefficients a_0 and a_1 and show, in particular, that a_1 receives a contribution containing ζ(3).