Abstract
We apply the recently proposed quantum spectral curve technique to the study of twist operators in planar N=4 SYM theory. We focus on the small spin expansion of anomalous dimensions in the sl(2) sector and compute its first two orders exactly for any value of the 't Hooft coupling. At leading order in the spin S we reproduced Basso's slope function. The next term of order S^2 structurally resembles the Beisert-Eden-Staudacher dressing phase and takes into account wrapping contributions. This expansion contains rich information about the spectrum of local operators at strong coupling. In particular, we found a new coefficient in the strong coupling expansion of the Konishi operator dimension and confirmed several previously known terms. We also obtained several new orders of the strong coupling expansion of the BFKL pomeron intercept. As a by-product we formulated a prescription for the correct analytical continuation in S which opens a way for deriving the BFKL regime of twist two anomalous dimensions from AdS/CFT integrability.
Highlights
IntroductionFinite-size corrections [3, 4] were later accounted for via the Thermodynamic Bethe Ansatz (TBA)/Y-system technique [5,6,7,8,9,10]
We focus on the small spin expansion of anomalous dimensions in the sl(2) sector and compute its first two orders exactly for any value of the ‘t Hooft coupling
We found a new coefficient in the strong coupling expansion of the Konishi operator dimension and confirmed several previously known terms
Summary
Finite-size corrections [3, 4] were later accounted for via the Thermodynamic Bethe Ansatz (TBA)/Y-system technique [5,6,7,8,9,10]. This approach led to the formulation of an infinite set of integral equations, which are expected to describe the exact spectrum of the theory at any value of the ’t Hooft coupling λ. They, allowed for a detailed numerical study of these simplest operators [11, 13,14,15] and led to a prediction for string theory which was confirmed in [16,17,18]
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