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On the D3-brane description of some 1/4 BPS Wilson loops

Nadav Drukker, Simone Giombi, Riccardo Ricci, Diego Trancanelli

TL;DR

This work extends the holographic description of Wilson loops in ${\cal N}=4$ SYM by constructing D3-brane solutions in ${\rm AdS}_5\times S^5$ that describe certain $1/4$ BPS loops. It presents two independent setups: a Wilson loop with insertions and a circle-wrapping loop on $S^5$, both preserving eight supercharges; the D3-brane configurations reproduce the strong-coupling observables and capture all $1/N$ corrections in the large $N$, large $\lambda$ limit, with a stable and an unstable branch mirroring nonperturbative contributions. The stable D3-brane actions agree with matrix-model predictions for the $1/4$ BPS loops and quantify non-planar corrections, while the unstable branches correspond to exponentially small corrections akin to worldsheet instantons. The results strengthen the dictionary between high-rank Wilson loops and giant gravitons, reveal intriguing links to surface operators, and point to rich future directions for exploring backreaction, more general $1/4$ or lower-BPS loops, and BMN-type limits in holography.

Abstract

Recently it has been proposed that Wilson loops in high-dimensional representations in N=4 supersymmetric Yang-Mills theory (or multiply wrapped loops) are described by D-branes in AdS_5 x S^5, rather than by fundamental strings. Thus far explicit D3-brane solutions have been only found in the case of the half-BPS circle or line. Here we present D3-brane solutions describing some 1/4 BPS loops. In one case, where the loop is conjectured to be given by a Gaussian matrix model, the action of the brane correctly reproduces the expectation value of the Wilson loop including all 1/N corrections at large λ. As in the corresponding string solution, here too we find two classical solutions, one stable and one not. The unstable one contributes exponentially small corrections that agree with the matrix model calculation.

On the D3-brane description of some 1/4 BPS Wilson loops

TL;DR

This work extends the holographic description of Wilson loops in SYM by constructing D3-brane solutions in that describe certain BPS loops. It presents two independent setups: a Wilson loop with insertions and a circle-wrapping loop on , both preserving eight supercharges; the D3-brane configurations reproduce the strong-coupling observables and capture all corrections in the large , large limit, with a stable and an unstable branch mirroring nonperturbative contributions. The stable D3-brane actions agree with matrix-model predictions for the BPS loops and quantify non-planar corrections, while the unstable branches correspond to exponentially small corrections akin to worldsheet instantons. The results strengthen the dictionary between high-rank Wilson loops and giant gravitons, reveal intriguing links to surface operators, and point to rich future directions for exploring backreaction, more general or lower-BPS loops, and BMN-type limits in holography.

Abstract

Recently it has been proposed that Wilson loops in high-dimensional representations in N=4 supersymmetric Yang-Mills theory (or multiply wrapped loops) are described by D-branes in AdS_5 x S^5, rather than by fundamental strings. Thus far explicit D3-brane solutions have been only found in the case of the half-BPS circle or line. Here we present D3-brane solutions describing some 1/4 BPS loops. In one case, where the loop is conjectured to be given by a Gaussian matrix model, the action of the brane correctly reproduces the expectation value of the Wilson loop including all 1/N corrections at large λ. As in the corresponding string solution, here too we find two classical solutions, one stable and one not. The unstable one contributes exponentially small corrections that agree with the matrix model calculation.

Paper Structure

This paper contains 12 sections, 93 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Wilson loop with insertions
  3. Setup
  4. String solution
  5. Supersymmetry analysis
  6. D3-brane solution
  7. Conserved charges
  8. Wilson loop wrapping a circle on $S^5$
  9. Setup
  10. String solution
  11. D3-brane solution
  12. Discussion

Figures (1)

  • Figure 1: A depiction of string and D3-brane solutions. The solid line gives $\rho$ as a function of $\theta$ for the string with boundary value of $\theta=\pi/3$. The D3-brane solution is represented by the dashed and dotted lines which are respectively $\rho$ and $u$ as functions of $\theta$ (for $\kappa=1$). In both cases there are two solutions, a stable one with $0\leq\theta\leq\theta_0$ (where $\rho$ for the string and D3-brane are nearly indistinguishable) and an unstable one, with $\theta\leq\theta_0\leq\pi$. The unstable D3-brane solution reaches the boundary of $AdS$ not only at $\theta_0$, but also at $\theta=\pi/2$, where $u$ diverges, but then it turns back and closes smoothly on itself.