"Short" spinning strings and structure of quantum AdS_5 x S^5 spectrum

TL;DR

This paper investigates the energy spectrum of quantum strings in AdS_5 x S^5, revealing universal patterns and proposing a semiclassical approach to determine energy coefficients, with implications for string theory and supersymmetry.

Contribution

It introduces a method to analyze the energy dependence of quantum string states using marginality conditions and semiclassical expansion, highlighting universality in energy coefficients across different string configurations.

Findings

Universal transcendental parts in energy coefficients identified.

Consistency with target space supersymmetry confirmed.

Proposed universality of a rational coefficient in energy formulas.

Abstract

Using information from the marginality conditions of vertex operators for the AdS_5 x S^5 superstring, we determine the structure of the dependence of the energy of quantum string states on their conserved charges and the string tension proportional to lambda^(1/2). We consider states on the leading Regge trajectory in the flat space limit which carry one or two (equal) spins in AdS_5 or S^5 and an orbital momentum in S^5, with Konishi multiplet states being particular cases. We argue that the coefficients in the energy may be found by using a semiclassical expansion. By analyzing the examples of folded spinning strings in AdS_5 and S^5 as well as three cases of circular two-spin strings we demonstrate the universality of transcendental (zeta-function) parts of few leading coefficients. We also show the consistency with target space supersymmetry with different states belonging to the same multiplet having the same non-trivial part of the energy. We suggest, in particular, that a rational coefficient (found by Basso for the folded string using Bethe Ansatz considerations and which, in general, is yet to be determined by a direct two-loop string calculation) should, in fact, be universal.