On the short string limit of the folded spinning string in AdS5 x S5

TL;DR

The paper advances the string-theory side of AdS5 x S5 by computing the 1-loop energy correction for the folded spinning string in the short-string (slow) limit with nonzero S5 angular momentum J. Working in a near-flat-space expansion and keeping u = J^2/(S sqrt(lambda)) fixed, the authors derive a precise 1-loop energy correction that appears as the first subleading term in the strong-coupling expansion of short SL(2) sector operators. They provide explicit expressions for the coefficients of the ε^4 and ε^6 corrections, including exact ω-integrals and their dependence on zeta values, yielding E1 ~ c3(u) S^{3/2} + c5(u) S^{5/2} + ..., with c3 and c5 given in terms of zeta constants and u. The results connect short-string quantum corrections to gauge-theory operators like Tr D^S Z^J and illuminate how the flat-space limit persists at the quantum level while introducing new non-BMN-type contributions at large J, thus enriching the dictionary between strong coupling string theory and the SL(2) sector of N=4 SYM.

Abstract

In this paper we generalize the results of arXiv:0806.4758 to non-zero value J of angular momentum in S^5. We compute the 1-loop correction to the energy of the folded spinning string in AdS_5 x S^5 in the particular limit of slow short string approximation. In this limit the string is moving in a near-flat central region of AdS_5 slowly rotating in both AdS_5 and S^5. The one-loop correction should represent the first subleading correction to strong coupling expansion of the anomalous dimension of short gauge theory operators of the form Tr D^S Z^J in the SL(2) sector.