Quantum spectral curve at work: from small spin to strong coupling in N $$ \mathcal{N} $$ = 4 SYM

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.

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4

“…Due to their simplicity, the equations have found numerous applications in the practical calculations: they were successfully applied to the analysis of weak coupling expansion in the sl(2) sector (Konishi up to 9 loops!) [16,17] as well as at strong coupling [15], for the slope and curvature functions for twist-2 operators at any coupling and pomeron intercept at strong coupling [18]. Recently, the QSC was also found for the ABJM model in [19], which was used [20] to make a well-grounded conjecture for the interpolation function h(λ) entering numerous physically relevant quantities such as cusp anomalous dimension and magnon dispersion relation in this theory.…”

“…We also note that for non-even integer charges there could be an additional sign ambiguity due to a branch cut at infinity (see [18] for some examples).…”

“…It was used to get the most accurate perturbative calculation at weak [16,17] and at strong coupling in [18,20], where also a pomeron intercept was found up to the 6-th order. The method was proven to be very powerful for exact analytic nonperturbative calculations for the generalized cusp anomalous dimension [15,49,50], for slope and curvature function [18,20]. Recently, following our methods, the QSC was also build in the ABJM theory [19,[51][52][53].…”

Resurgence of the cusp anomalous dimension

“…The Quantum Spectral Curve formulation [5,6] will be helpful for this purpose. See [70] for an interesting approach to the strong coupling Konishi dimension, based on [71]. The generalization to the ABJM theory [13] is also interesting.…”

Master symmetry in the AdS 5 × S 5 pure spinor string

“…A more recent development not covered in [1] is the the Quantum Spectral Curve method [2,3]. For some of its applications, including higher loop computations, see [4][5][6][7][8][9].…”