1,059 research outputs found
Algebraic Curve for a Cusped Wilson Line
We consider the classical limit of the recently obtained exact result for the
anomalous dimension of a cusped Wilson line with the insertion of an operator
with L units of R-charge at the cusp in planar N=4 SYM. The classical limit
requires taking both the 't Hooft coupling and L to infinity. Since the formula
for the cusp anomalous dimension involves determinants of size proportional to
L, the classical limit requires a matrix model reformulation of the result. We
construct such matrix model-like representation and find corresponding
classical algebraic curve. Using this we derive the classical value of the cusp
anomalous dimension and the 1-loop correction to it. We check our results
against the energy of the classical solution and numerically by extrapolating
from the quantum regime of finite L.Comment: 15 pages, 2 figure
BFKL Spectrum of N=4 SYM: non-Zero Conformal Spin
We developed a general non-perturbative framework for the BFKL spectrum of
planar N=4 SYM, based on the Quantum Spectral Curve (QSC). It allows one to
study the spectrum in the whole generality, extending previously known methods
to arbitrary values of conformal spin . We show how to apply our approach to
reproduce all known perturbative results for the Balitsky-Fadin-Kuraev-Lipatov
(BFKL) Pomeron eigenvalue and get new predictions. In particular, we re-derived
the Faddeev-Korchemsky Baxter equation for the Lipatov spin chain with non-zero
conformal spin reproducing the corresponding BFKL kernel eigenvalue. We also
get new non-perturbative analytic results for the Pomeron eigenvalue in the
vicinity of point and we obtained an explicit formula for
the BFKL intercept function for arbitrary conformal spin up to the 3-loop order
in the small coupling expansion and partial result at the 4-loop order. In
addition, we implemented the numerical algorithm of arXiv:1504.06640 as an
auxiliary file to this arXiv submission. From the numerical result we managed
to deduce an analytic formula for the strong coupling expansion of the
intercept function for arbitrary conformal spin.Comment: 70 pages, 5 figures, 1 txt, 2 nb and 2 mx files; v2: references
added, typos fixed and nb file with Mathematica stylesheet attached; v3: more
typos fixed; v4: the text edited according to the report of the refere
- β¦