Leading quantum correction to energy of "short" spiky strings

TL;DR

This paper calculates the leading quantum correction to the energy of short, spiky strings in AdS_3, providing explicit formulas for the correction coefficient in terms of harmonic sums, which aids in understanding quantum string spectra.

Contribution

It introduces a new explicit computation of the 1-loop quantum correction for short spiky strings using integrability methods, extending previous results to more general string configurations.

Findings

Explicit 1-loop correction coefficient expressed via harmonic sums

Special case for n=2 matches known results for folded strings

General formulas applicable to various spiky string configurations

Abstract

We consider semiclassical quantization of spiky strings spinning in AdS_3 part of AdS_5 X S^5 using integrability-based (algebraic curve) method. In the "short string" (small spin) limit the expansion of string energy starts with its flat-space expression. We compute the leading quantum string correction to "short" spiky string energy and find the explicit form of the corresponding 1-loop coefficient a_01. It turns out to be rational and expressed in terms of the harmonic sums as functions of the number n of spikes. In the special case of n=2 when the spiky string reduces to the single-folded spinning string the coefficient a_01 takes the value (-1/4) found in arXiv:1102.1040. We also consider a similar computation for the m-folded string and more general spiky string with an extra "winding" number, finding similar expressions for a_01. These results may be useful for a description of energies of higher excited states in the quantum AdS_5 X S^5 string spectrum, generalizing earlier discussions of the string counterparts of the Konishi operator.