“Short” spinning strings and structure of quantumAdS5×S5spectrum

Abstract

Using information from the marginality conditions of vertex operators for the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ superstring, we determine the structure of the dependence of the energy of quantum string states on their conserved charges and the string tension $\ensuremath{\sim}\sqrt{\ensuremath{\lambda}}$. We consider states on the leading Regge trajectory in the flat space limit which carry one or two (equal) spins in ${\mathrm{AdS}}_{5}$ 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 ${\mathrm{AdS}}_{5}$ 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 nontrivial 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.