Fundamental Flavours, Fields and Fixed Points: A Brief Account

TL;DR

This paper uses holography to explore infrared fixed points in a strongly coupled SU(N) gauge theory with fundamental matter, revealing exact solutions with different geometric structures and numerical flows to IR fixed points.

Contribution

It provides a simple Einstein-DBI holographic model with exact solutions and numerical flows illustrating various IR fixed points in a strongly coupled gauge theory.

Findings

Exact solutions of AdS$_m \times \mathbb{R}^n$ and AdS$_m \times$EAdS$_n$ types.

Identification of non-perturbative IR fixed points.

Numerical flows from AdS$_5$ UV to AdS$_2$ and AdS$_3$ IR.

Abstract

In this article we report on a preliminary study, {\it via} Holography, of infrared fixed points in a putative strongly coupled SU$(N_c)$ gauge theory, with $N_f$ fundamental matter, in the presence of additional fields in the fundamental sector, e.g. density or a magnetic field. In an inherently {\it effective} or a {\it bottom up} approach, we work with a simple system: Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld (DBI) matter. We obtain a class of exact solutions, dual to candidate grounds states in the infrared (IR), with a scaling ansatz for various fields. These solutions are of two kinds: AdS$_m \times {\mathbb R}^n$--type, and AdS$_m \times$EAdS$_n$--type, where $m$ and $n$ are suitable integers. Both these classes of solutions are {\it non-perturbative} in back-reaction. The AdS$_m \times$EAdS$_n$--type contains examples of Bianchi type-V solutions. We also construct explicit numerical flows from an AdS$_5$ ultraviolet to both an AdS$_2$ and an AdS$_3$ IR.