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

Using the algebraic curve approach we one-loop quantize the folded string solution for the type IIB superstring in AdS 5 × S 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.