Abstract

ABSTRACT: We consider twist J operators with spin S in the sl(2) sector of N = 4 SYM. The small spin expansion of their anomalous dimension defines the so-called slope func-tions. Much is known about the linear term, but the study of the quadratic correction, the curvature function, started only very recently. At any fixed J, the curvature function can be extracted at all loops from the Pµ-system formulation of the Thermodynamical Bethe Ansatz. Here, we work at the one-loop level and follow a different approach. We present a systematic double expansion of the Bethe Ansatz equations at large J and small wind-ing number. We succeed in fully resumming this expansion and obtain a closed explicit simple formula for the one-loop curvature function. The formula is parametric in J and can be evaluated with minor effort for any fixed J. The result is an explicit series in odd-index ζ values. Our approach provides a complete reconciliation between the Pµ-system predictions and the large J approach. ar X iv