Branes from Light: Embeddings and Energetics for Symmetric $k$-Quarks in $\mathcal{N}=4$ SYM

TL;DR

This paper constructs D3-brane duals for symmetric $k$-quarks in $ ext{AdS}_5$ and computes their energy and radiation, extending previous methods and confirming known results in $ ext{AdS/CFT}$ correspondence.

Contribution

It introduces a novel light-ray shooting method for embedding D3-branes dual to symmetric $k$-quarks, generalizing prior work and validating it against known antisymmetric cases.

Findings

Successfully reproduces known D5-brane embeddings for antisymmetric $k$-quarks.

Calculates the energy and radiation rate of symmetric $k$-quarks from D3-brane embeddings.

Matches the Bremsstrahlung function for the fundamental representation.

Abstract

We construct the D3-brane dual to a $k$-quark of $\mathcal{N}=4$ super-Yang-Mills theory in the totally symmetric representation of $SU(N)$, undergoing arbitrary motion. Our method of construction generalizes previous work by Mikhailov, and proceeds by shooting light rays inward from the anti-de Sitter boundary, to trace out the brane embedding. We expect this method to have wider relevance, and provide evidence for this by showing that it correctly reproduces the known D5-brane embeddings dual to totally antisymmetric $k$-quarks. As an application of our solutions, we compute the energy of the D3-brane and extract from it the $k$-quark's intrinsic energy and rate of radiation. The result matches expectations based on previous calculations, and makes contact with the exact Bremsstrahlung function for the fundamental representation.