Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Wilson Loops of Anti-symmetric Representation and D5-branes

Satoshi Yamaguchi

TL;DR

The paper identifies the AdS/CFT dual of circular Wilson loops in the rank-$k$ antisymmetric representation by constructing an AdS$_2\times$S$^4$ D5-brane with electric flux in AdS$_5\times$S$^5$. The holographic calculation of the on-shell action, including careful boundary terms, yields $S_{\rm tot}=-\sqrt{\lambda}\frac{2N}{3\pi}\sin^3\theta_k$ with $k=\frac{2N}{\pi}\left(\tfrac{1}{2}\theta_k-\tfrac{1}{4}\sin 2\theta_k\right)$, matching the semiclassical limit of the Gaussian matrix model for the antisymmetric representation. The analysis shows that the AdS$_2\times$S$^4$ D5-brane preserves the same half of supersymmetry as the AdS$_2\times$S$^2$ D3-brane, supporting the proposed operator-brane correspondence. Together, these results reinforce the brane realization of Wilson loops in higher representations and connect to bubbling geometries in the AdS/CFT framework.

Abstract

We use a D5-brane with electric flux in AdS_5 x S^5 background to calculate the circular Wilson loop of anti-symmetric representation in N=4 super Yang-Mills theory in 4 dimensions. The result agrees with the Gaussian matrix model calculation.

Wilson Loops of Anti-symmetric Representation and D5-branes

TL;DR

The paper identifies the AdS/CFT dual of circular Wilson loops in the rank- antisymmetric representation by constructing an AdSS D5-brane with electric flux in AdSS. The holographic calculation of the on-shell action, including careful boundary terms, yields with , matching the semiclassical limit of the Gaussian matrix model for the antisymmetric representation. The analysis shows that the AdSS D5-brane preserves the same half of supersymmetry as the AdSS D3-brane, supporting the proposed operator-brane correspondence. Together, these results reinforce the brane realization of Wilson loops in higher representations and connect to bubbling geometries in the AdS/CFT framework.

Abstract

We use a D5-brane with electric flux in AdS_5 x S^5 background to calculate the circular Wilson loop of anti-symmetric representation in N=4 super Yang-Mills theory in 4 dimensions. The result agrees with the Gaussian matrix model calculation.

Paper Structure

This paper contains 10 sections, 62 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction and summary
  2. Supersymmetry of AdS D-branes
  3. Supersymmetry of $AdS_5\times S^5$ spacetime
  4. Supersymmetry of the $AdS_2\times S^2$ D3-branes
  5. Supersymmetry of the $AdS_2\times S^4$ D5-branes
  6. String charges of AdS D-branes
  7. $AdS_2\times S^4$ D5-brane solution and the circular Wilson loop
  8. Wick rotation of the solution and the on-shell action
  9. Gaussian matrix model calculation
  10. Spinors in $AdS_2\times S^2 \times S^4$ fibration

Figures (3)

  • Figure 1: The eigenvalue distribution with a hole or $AdS_5\times S^5$ geometry with an $AdS_2\times S^4$ D5-brane.
  • Figure 2: The picture of eigenvalue distribution and external force. The upper figure expresses the eigenvalue distribution of the vacuum. When we add small external constant force to the first $k$ eigenvalues, these eigenvalues move a little to the right and there appears a "hole" next to the $k$-th eigenvalue.
  • Figure 3: The picture of the branes. There are $N$ D3-branes, one D5-brane and $k$ fundamental strings stretched between the D3-branes and the D5-brane.