The quark anti-quark potential and the cusp anomalous dimension from a TBA equation

We revisit the strong coupling limit of the cusp anomalous dimension in planar N = 4 super Yang-Mills theory. It is known that the strong coupling expansion is asymptotic and non-Borel summable. As a consequence, the cusp anomalous dimension receives non-perturbative corrections, and the complete strong coupling expansion should be a resurgent transseries. We reveal that the perturbative and non-perturbative parts in the transseries are closely interrelated. Solving the Beisert-Eden-Staudacher equation systematically, we analyze in detail the large order behavior in the strong coupling perturbative expansion and show that the non-perturbative information is indeed encoded there. An ambiguity of (lateral) Borel resummations of the perturbative expansion is precisely canceled by the contributions from the non-perturbative sectors, and the final result is real and unambiguous.

Section: Discussionmentioning

confidence: 84%

Resurgence of the cusp anomalous dimension

Dorigoni¹,

Hatsuda²

2015

“…(3.61) 16 We also expect the same system of equations to be applicable for β-deformed case and for the integrable observables with boundary (like cusp anomalous dimension [25,26] or DD-brane system [27]). Generalization to these cases can be done through modification of the asymptotic by relaxing power-like behavior at infinity.…”

Section: Asymptotics At Large Umentioning

confidence: 98%

“…25 One should also properly regularise the above sum which is in general divergent. For instance, one can differentiate it a sufficient number of 24 Again, this is very easy to check starting from (4.1).…”

Section: Jhep09(2015)187mentioning

confidence: 99%

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

Gromov

Казаков

Leurent

et al. 2015

195

519

We give a derivation of quantum spectral curve (QSC) -a finite set of Riemann-Hilbert equations for exact spectrum of planar N = 4 SYM theory proposed in our recent paper Phys. Rev. Lett. 112 (2014). We also generalize this construction to all local single trace operators of the theory, in contrast to the TBA-like approaches worked out only for a limited class of states. We reveal a rich algebraic and analytic structure of the QSC in terms of a so called Q-system -a finite set of Baxter-like Q-functions. This new point of view on the finite size spectral problem is shown to be completely compatible, though in a far from trivial way, with already known exact equations (analytic Y-system/TBA, or FiNLIE). We use the knowledge of this underlying Q-system to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.

“…In [8,18,19] it was shown that the anomalous dimension of the cusped MaldacenaWilson line admits an integrability-based description in terms of an infinite system of integral equations (known as Thermodynamic Bethe Ansatz equations). This anomalous…”

Section: Quantum Spectral Curve For the Quark-anti-quark Potentialmentioning

confidence: 99%

Quark-anti-quark potential in N $$ \mathcal{N} $$ = 4 SYM

Gromov

Levkovich-Maslyuk

2016

We construct a closed system of equations describing the quark-anti-quark potential at any coupling in planar N = 4 supersymmetric Yang-Mills theory. It is based on the Quantum Spectral Curve method supplemented with a novel type of asymptotics. We present a high precision numerical solution reproducing the classical and one-loop string predictions very accurately. We also analytically compute the first 7 nontrivial orders of the weak coupling expansion.Moreover, we study analytically the generalized quark-anti-quark potential in the limit of large imaginary twist to all orders in perturbation theory. We demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger equation. In the process we establish a link between the Q-functions and the solution of the Bethe-Salpeter equation.