Scalar insertions in cusped Wilson loops in the ladders limit of planar $$ \mathcal{N} $$ = 4 SYM

Abstract

Compact expressions in terms of the Q-functions of the Quantum Spectral Curve are given for 3-cusped fundamental Wilson loops in the ladders limit of N = 4 Super Yang-Mills with additional scalars inserted at a cusp between uncoupled arcs. This gives some further credence to the already natural and evidenced view that the Quantum Spectral Curve in fact pertains to a wide class of observables beyond the spectrum, as well as providing additional nonperturbative ladders limit results.

Colour-twist operators. Part I. Spectrum and wave functions

“…Equally, in the fishnet theory, or N = 4 SYM theory, we expect the twist to play an essential role for a possible SoV construction for the correlation functions. An example of SoV structures was recently found in [9][10][11][12] for correlation functions of cusp operators, and following this paper for single trace operators [15].…”

“…However, in some special cases they turn out to be the same[8] 3. This expectation was partly confirmed for the case of the cusp correlation function in the ladders limit[9,10] and in the near-BPS limit[11,12].…”

“…Finally, the case of correlation function of cusp operators on a piecewise circular Wilson loop that was recently studied in [9][10][11][12] has an equivalent description in terms of a circular Wilson loop without the cusps. In this description, the effect of the cusp angles is accounted for by including colour-twist operators inserted along the loop, see figure 5.…”

“…One arc (say, the arc connecting z 0 and x 0 ) can be chosen to be a part of the initial circle, the other two are obtained as a result of the action of R(z 0 , z0, θ 1 ) and R(z 0 , z0, θ 1 ).R(y 0 , y0, θ 2 ) on arcs of the initial circle (the ones connecting x 0 with y 0 and y 0 with z 0 , respectively). The set-up on the figure (b) was studied in [9,10] in the ladders limit.…”

“…Essentially, it becomes periodic with period given by the twist transformation, so that both coordinates and all derivatives are matched by the twist transformation, see figure 6. 10 For example, for the γ-deformation, we end up with a string that is extended along the equator of As we go around the worldsheet, we end at two different points in spacetime that are related to each other by the twist isometry transformation.…”