Quantum folded string and integrability: from finite size effects to Konishi dimension

TL;DR

The paper develops an algebraic-curve quantization framework to compute the one-loop energy of the folded string in $AdS_5\times S^5$ for arbitrary spins $S$ and charges $J$, deriving a short-operator strong-coupling expansion that yields the Konishi anomalous dimension $\gamma_K = 2\lambda^{1/4}-4+2\lambda^{-1/4}$ and matching existing Y-system numerics. It also analyzes long-string regimes, obtaining finite-size corrections in $1/\log S$ and showing consistency between the algebraic-curve results and wrapping corrections from the Y-system, including the massless anomaly contribution. The work connects quasi-classical string quantization with exact integrability-based finite-size data, clarifying the role of wrapping effects and providing a robust cross-check with numerical results in the Y-system. Overall, it demonstrates that the algebraic-curve approach is a reliable bridge between semi-classical string theory and nonperturbative integrability predictions for finite charges and large-spin limits.

Abstract

Using the algebraic curve approach we one-loop quantize the folded string solution for the type IIB superstring in AdS(5)xS(5). We obtain an explicit result valid for arbitrary values of its Lorentz spin S and R-charge J in terms of integrals of elliptic functions. Then we consider the limit S ~ J ~ 1 and derive the leading three coefficients of strong coupling expansion of short operators. Notably, our result evaluated for the anomalous dimension of the Konishi state gives 2λ^{1/4}-4+2/λ^{1/4}. This reproduces correctly the values predicted numerically in arXiv:0906.4240. Furthermore we compare our result using some new numerical data from the Y-system for another similar state. We also revisited some of the large S computations using our methods. In particular, we derive finite--size corrections to the anomalous dimension of operators with small J in this limit.