Scale invariance with fundamental matters and anomaly: A holographic description

TL;DR

This paper explores a holographic model of quantum field theories with scale invariance but without conformal invariance, revealing diverse geometries and symmetry-breaking phenomena relevant to strongly coupled systems like QCD.

Contribution

It introduces a simple holographic model demonstrating the existence of scale-invariant, non-conformal field theories with novel geometries and symmetry-breaking features.

Findings

Discovery of scale-invariant, non-conformal geometries including Schrödinger and warped AdS_3.

Identification of spontaneous translational symmetry breaking at low temperatures.

Insights into the holographic duals of complex quantum field theories with anomalies.

Abstract

Generally, quantum field theories can be thought as deformations away from conformal field theories. In this article, with a simple bottom up model assumed to possess a holographic description, we study a putative large N quantum field theory with large and arbitrary number of adjoint and fundamental degrees of freedom and a non-vanishing chiral anomaly, in the presence of an external magnetic field and with a non-vanishing density. Motivated by the richness of quantum chromodynamics under similar condition, we explore the solution space to find an infinite class of scale-invariant, but not conformal, field theories that may play a pivotal role in defining the corresponding physics. In particular, we find two classes of geometries: Schrodinger isometric and warped AdS_3 geometries with an SL(2,R) X U(1) isometry. We find hints of spontaneous breaking of translational symmetry, at low temperatures, around the warped backgrounds.