One-loop Effective Action of the Holographic Antisymmetric Wilson Loop

TL;DR

This paper calculates the spectrum and one-loop effective action of holographic antisymmetric Wilson loops in N=4 SYM, using D5-brane configurations and heat kernel methods, revealing supersymmetry and quantum corrections.

Contribution

It provides a detailed derivation of the excitation spectrum and one-loop determinant for antisymmetric Wilson loops via D5-brane holography, including supersymmetry verification.

Findings

Spectrum of excitations explicitly derived.

Confirmed supersymmetry of the configuration.

One-loop effective action computed using heat kernel techniques.

Abstract

We systematically study the spectrum of excitations and the one-loop determinant of holographic Wilson loop operators in antisymmetric representations of $\mathcal{N}=4$ supersymmetric Yang-Mills theory. Holographically, these operators are described by D5-branes carrying electric flux and wrapping an $S^4 \subset S^5$ in the $AdS_5\times S^5$ bulk background. We derive the dynamics of both bosonic and fermionic excitations for such D5-branes. A particularly important configuration in this class is the D5-brane with $AdS_2\times S^4$ worldvolume and $k$ units of electric flux, which is dual to the circular Wilson loop in the totally antisymmetric representation of rank $k$. For this Wilson loop, we obtain the spectrum, show explicitly that it is supersymmetric and calculate the one-loop effective action using heat kernel techniques.