[Paper Review] Large Charges on the Wilson Loop in N = 4 SYM: Matrix Model and Classical String

Simone Giombi, Bendeguz Offertaler+1 more|arXiv (Cornell University)|Oct 22, 2021

Black Holes and Theoretical Physics57 references4 citations

TL;DR

This paper studies the large charge sector of the half-BPS Wilson loop in planar $χ=4$ SYM using a matrix model dual to classical string solutions in the double-scaling limit. It reproduces holographic string results from field theory via supersymmetric localization, showing that the matrix model's spectral curve matches the classical string geometry, even for non-extremal correlators.

ABSTRACT

We study the large charge sector of the defect CFT defined by the half-BPS Wilson loop in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory. Specifically, we consider correlation functions of two large charge insertions and several light insertions in the double-scaling limit where the 't Hooft coupling $\lambda$ and the large charge $J$ are sent to infinity, with the ratio $J/\sqrt{\lambda}$ held fixed. They are holographically dual to the expectation values of light vertex operators on a classical string solution with large angular momentum, which we evaluate in the leading large $J$ limit. We also compute the two-point function of large charge insertions by evaluating the on-shell string action, supplemented by the boundary terms that generalize the one introduced by Drukker, Gross and Ooguri for the Wilson loop without insertions. For a special class of correlation functions, we reproduce the string results from field theory by using supersymmetric localization. The results are given by correlation functions in an emergent matrix model whose matrix size is proportional to $J$ and whose spectral curve coincides with that of the classical string. Similar matrix models appeared in the study of extremal correlators in rank-1 $\mathcal{N}=2$ superconformal field theories, but our results hold also for non-extremal cases.

Motivation & Objective

• To understand the large charge sector of the half-BPS Wilson loop in planar $χ=4$ SYM.
• To establish a field-theoretic description of correlation functions with large charge insertions in the double-scaling limit.
• To reproduce holographic string results from field theory using supersymmetric localization.
• To identify a matrix model dual to the classical string solution with large angular momentum.
• To extend the duality to non-extremal correlation functions beyond previous rank-1 $χ=2$ SCFT results.

Proposed method

• Use the double-scaling limit with fixed $J/\sqrt{\lambda}$ to analyze correlation functions of two large charge insertions and light operators.
• Apply supersymmetric localization to compute the two-point function of large charge operators in the field theory.
• Evaluate the on-shell string action with generalized boundary terms, extending the Drukker-Gross-Ooguri prescription to insertions.
• Derive a matrix model with size proportional to $J$, whose spectral curve matches the classical string solution.
• Map the field-theory correlation functions to observables in the emergent matrix model.
• Confirm agreement between the matrix model and holographic string results for a special class of correlation functions.

Experimental results

Research questions

• RQ1 How do correlation functions with large charge insertions behave in the double-scaling limit of planar $χ=4$ SYM?
• RQ2 Can the holographic string prediction for Wilson loop correlators be reproduced from field theory using localization?
• RQ3 What is the structure of the emergent matrix model dual to the classical string solution with large angular momentum?
• RQ4 How does the spectral curve of the matrix model relate to the geometry of the classical string?
• RQ5 To what extent does the duality extend beyond extremal correlators to non-extremal cases?

Key findings

• The two-point function of large charge insertions is computed via supersymmetric localization and matches the on-shell string action with generalized boundary terms.
• The emergent matrix model has a size proportional to the large charge $J$, capturing the dynamics of the large $J$ sector.
• The spectral curve of the matrix model exactly coincides with the classical string solution in the large $J$ limit.
• For a special class of correlation functions, the field-theory results from the matrix model reproduce the holographic string predictions.
• The duality between the matrix model and the classical string holds not only for extremal but also for non-extremal correlation functions.
• The generalized boundary term in the string action correctly accounts for the large charge insertions, extending the Drukker-Gross-Ooguri framework.