On the one-loop curvature function in the sector of SYM
arXiv:1404.0893 · doi:10.1007/JHEP06(2014)141
Abstract
We consider twist operators with spin in the sector of SYM. The small spin expansion of their anomalous dimension defines the so-called slope functions. Much is known about the linear term, but the study of the quadratic correction, the curvature function, started only very recently. At any fixed , the curvature function can be extracted at all loops from the -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 and small winding 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 and can be evaluated with minor effort for any fixed . The result is an explicit series in odd-index values. Our approach provides a complete reconciliation between the -system predictions and the large approach.
arXiv comment21 pages
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