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

TL;DR

This paper uses algebraic curve methods to quantize folded strings in AdS5xS5, deriving explicit formulas for anomalous dimensions, including the Konishi state, and exploring finite-size effects at strong coupling.

Contribution

It provides a novel one-loop quantization of the folded string solution and explicit strong coupling expansions for short operators, including finite-size corrections.

Findings

Derived explicit one-loop quantization results for folded strings.

Obtained strong coupling expansion coefficients for the Konishi operator.

Reproduced numerical predictions for the Konishi anomalous dimension.

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 2\lambda^{1/4}-4+2/\lambda^{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.