Wilson loops at large $N$ and the quantum M2 brane

Abstract

The Wilson loop operator in the $U(N{)}_k\times U(N{)}_{-k}$ ABJM theory at large $N$ and fixed level $k$ has a dual description in terms of a wrapped M2 brane in the M-theory background AdS${}_4\times S^7/{\mathbb{Z}}_k$. We consider the localization result for the $\frac{1}{2}$-BPS circular Wilson loop expectation value $W$ in this regime, and compare it to the prediction of the M2 brane theory. The leading large $N$ exponential factor is matched as expected by the classical action of the M2 brane solution with AdS${}_2\times S^1$ geometry. We show that the subleading $k$-dependent prefactor in $W$ is also exactly reproduced by the one-loop term in the partition function of the wrapped M2 brane (with all Kaluza-Klein modes included). This appears to be the first case of an exact matching of the overall numerical prefactor in the Wilson loop expectation value against the dual holographic result. It provides an example of a consistent quantum M2 brane computation, suggesting various generalizations.

13 pages. v2: few footnotes and references added

References in corpus (9)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
• Strong-coupling expansion of cusp anomaly from quantum superstring
• The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling
• Two-loop cusp anomaly in ABJM at strong coupling
• ABJ Wilson loops and Seiberg Duality
• Semiclassical Analysis of M2-brane in AdS_4 x S^7 / Z_k

Cited by in corpus (1)

• Comments on ABJM free energy on $S^3$ at large $N$ and perturbative expansions in M-theory and string theory