Abstract
We consider a cusped Wilson line with J insertions of scalar fields in mathcal{N} = 4 SYM and prove that in a certain limit the Feynman graphs are integrable to all loop orders. We identify the integrable system as a quantum fishchain with open boundary conditions. The existence of the boundary degrees of freedom results in the boundary reflection operator acting non-trivially on the physical space. We derive the Baxter equation for Q-functions and provide the quantisation condition for the spectrum. This allows us to find the non-perturbative spectrum numerically.
Highlights
Integrability in D > 2 quantum field theories takes its roots in quantum chromodynamics where it was first observed that in the BFKL limit the evolution kernel admits integrability [1, 2]
The only insight we borrow from the QSC approach is a simple quantisation condition, which would require further efforts to derive from first principles. Another motivation behind the work we present in this paper is due to the recent study of structure constants by the separation of variables (SoV) method [16, 19, 25, 26], where the explicit form of the Baxter equation was shown to be at the heart of the SoV
In order to enforce this symmetry we introduce an auxiliary field γ transforming as γ
Summary
Integrability in D > 2 quantum field theories takes its roots in quantum chromodynamics where it was first observed that in the BFKL limit the evolution kernel admits integrability [1, 2]. The only insight we borrow from the QSC approach is a simple quantisation condition, which would require further efforts to derive from first principles Another motivation behind the work we present in this paper is due to the recent study of structure constants by the separation of variables (SoV) method [16, 19, 25, 26], where the explicit form of the Baxter equation was shown to be at the heart of the SoV. In this paper we show that for the general J > 0 case the diagrams which survive are those of the fishnet type with a boundary corresponding to the two rays of the Wilson line (see figure 1) This drastic simplification in Feynman graphs allows us to construct the resummation procedure involving a graph-building operator.
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