Spinning strings in AdS_5 x S^5: one-loop correction to energy in SL(2) sector

TL;DR

This paper computes the one-loop correction to the energy of a spinning string in AdS_5 x S^5 within the SL(2) sector, revealing a match with gauge theory anomalous dimensions and analyzing fluctuation contributions.

Contribution

It provides the first explicit calculation of the one-loop string correction in the SL(2) sector and explores the connection with gauge theory spin chain results.

Findings

The leading zero-mode correction matches the 1/J gauge theory result.

Non-zero string modes contribute significantly to the correction.

The 'fast string' expansion aligns with the SL(2) spin chain at first order.

Abstract

We consider a circular string with spin $S$ in $AdS_5$ wrapped around big circle of $S^5$ and carrying also momentum $J$. The corresponding N=4 SYM operator belongs to the SL(2) sector, i.e. has tr$(D^S Z^J)+...$ structure. The leading large $J$ term in its 1-loop anomalous dimension can be computed using Bethe ansatz for the SL(2) spin chain and was previously found to match the leading term in the classical string energy. The string solution is stable at large $J$, and the Lagrangian for string fluctuations has constant coefficients, so that the 1-loop string correction to the energy $E_1$ is given simply by the sum of characteristic frequencies. Curiously, we find that the leading term in the zero-mode part of $E_1$ is the same as a 1/J correction to the one-loop anomalous dimension on the gauge theory (spin chain) side that was found in hep-th/0410105. However, the contribution of non-zero string modes does not vanish. We also discuss the ``fast string'' expansion of the classical string action which coincides with the coherent state action of the SL(2) spin chain at the first order in $\l$, and extend this expansion to higher orders clarifying the role of the $S^5$ winding number.