Large charges on the Wilson loop in $$ \mathcal{N} $$ = 4 SYM. Part II. Quantum fluctuations, OPE, and spectral curve

Abstract

We continue our study of large charge limits of the defect CFT defined by the half-BPS Wilson loop in planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory. In this paper, we compute 1/J corrections to the correlation function of two heavy insertions of charge J and two light insertions, in the double scaling limit where the charge J and the ’t Hooft coupling λ are sent to infinity with the ratio J/$$ \sqrt{\lambda } $$ λ fixed. Holographically, they correspond to quantum fluctuations around a classical string solution with large angular momentum, and can be computed by evaluating Green’s functions on the worldsheet. We derive a representation of the Green’s functions in terms of a sum over residues in the complexified Fourier space, and show that it gives rise to the conformal block expansion in the heavy-light channel. This allows us to extract the scaling dimensions and structure constants for an infinite tower of non-protected dCFT operators. We also find a close connection between our results and the semi-classical integrability of the string sigma model. The series of poles of the Green’s functions in Fourier space corresponds to points on the spectral curve where the so-called quasi-momentum satisfies a quantization condition, and both the scaling dimensions and the structure constants in the heavy-light channel take simple forms when written in terms of the spectral curve. These observations suggest extensions of the results by Gromov, Schafer-Nameki and Vieira on the semiclassical energy of closed strings, and in particular hint at the possibility of determining the structure constants directly from the spectral curve.

Unmixing the Wilson line defect CFT. Part II. Analytic bootstrap

“…At this stage it is not clear what functions should appear at the next order: should we only add L 5 (x) or more general HPLs as well? Our observations also seem to agree with the comments of [105] (see section 5.2), where the Wilson line defect CFT correlators are studied in a large charge expansion. Those results seem to indicate that only products of ordinary logarithms and polylogarithms appear at higher orders, which would indeed suggest a special role played by the functions L n (x) for odd n. It would be interesting to investigate this more in detail in the future.…”

“…In some cases, it is even possible to explicitly write Witten diagrams in terms of ordinary Feynman diagrams, making the analogy between the two even closer [104]. For the Wilson line defect CFT, HPLs were also observed to appear in the large charge expansion of four-point functions between half-BPS operators [105], as well as at weak coupling [14] for the displacement four-point function.…”

“…A possible application of this could be the study of mixing between triple-trace operators in the holographic regime of N = 4 SYM, where in [124] it was suggested that external 1 4 -BPS operators could play a role. 50 Moreover, the study of mixed short-long correlators provides an entirely new class of observables in the study of holographic correlators, providing access 48 An understanding of the structure of four-point functions in this model can also be developed considering the large charge approach of [105], where perturbative results in terms of HPLs are also obtained. 49 See also [123] for an analogous gluon scattering amplitude in AdS5 × S 3 .…”

Stability analysis of a non-unitary CFT

“…Furthermore, the relation between the matrix model (or its Fermi gas picture) and the large charge expansion is already pointed out in the context of N = 2 SQCD in D = 4 [20,100]. A similar phenomenon is also observed in the context of Wilson loops in N = 4 SYM [65,101]. It would be of great use if we can come up with the large charge effective action corresponding to the Fermi gas system, and even better, to the M -theory regime of ABJM theory.…”

“…It would be also interesting to extend this to other models with a possible double-scaling structure, such as various SUSY theories [20,41,43,[51][52][53] or Chern-Simons-matter theories [54,55]. One could also look for other double-scaling limit in systems with boundaries or defects [56][57][58][59][60][61][62][63][64][65], or with non-relativistic conformal symmetry [66][67][68][69][70][71]…”