Analytical approach to the D3-brane gravity dual for 3d Yang-Mills theory

TL;DR

This paper introduces an analytical method for approximating normalizable string modes in top-down gravity duals, enabling precise calculations of glueball properties in 3d Yang-Mills theory.

Contribution

It develops a controlled approximation technique for string modes in gravity duals, improving analytical tractability of strongly-coupled gauge theories.

Findings

Accurate analytical approximations for bulk modes in 3d Yang-Mills duals.

Derived masses, sizes, and correlation functions of glueball excitations.

Method can be systematically refined and applied to other gravity duals.

Abstract

The complexity of "top-down" string-dual candidates for strongly-coupled Yang-Mills theories and in particular for QCD almost always prohibits their exact analytical or even comprehensive numerical treatment. This impedes both a thorough quantitative analysis and the development of more realistic gravity duals. To mitigate these impediments, we devise an analytical approach to top-down duals on the basis of controlled, uniformly converging high-accuracy approximations for the normalizable string modes corresponding to gauge-theory states. We demonstrate the potential of this approach in Witten's dual for $3d$ Yang-Mills theory, i.e. in the near-horizon limit of non-extremal $D\text{3}$-branes, compactified on $S^{1}$. We obtain accurate analytical approximations to the bulk modes which satisfy the boundary conditions exactly. On their basis, analytical results for masses, sizes, pole residues and correlation functions of glueball excitations are derived by spectral methods. These approximations can be systematically improved and rather universally adapted to more complex gravity duals.