Dilaton-Maxwell gravity with matter near two dimensions

TL;DR

This paper investigates the renormalization group properties of dilaton-Maxwell gravity with matter near two dimensions, revealing a non-trivial ultraviolet fixed point and extending results to dilatonic-Yang-Mills theories with matter.

Contribution

It demonstrates the existence of a non-trivial, ultraviolet stable fixed point in dilaton-Maxwell gravity with matter and extends this analysis to dilatonic-Yang-Mills theories with multiple matter fields.

Findings

Existence of a non-trivial ultraviolet fixed point for the gravitational coupling G.

Dilatonic coupling functions also exhibit a real, non-trivial fixed point.

The properties hold in dilatonic-Yang-Mills theories with matter, with a specific fixed point for G.

Abstract

Unlike Einstein gravity, dilaton-Maxwell gravity with matter is renormalizable in $2+\epsilon$ dimensions and has a smooth $\epsilon\to 0$ limit.By performing a renormalization- group study of this last theory we show that the gravitational coupling constant $G$ has a non-trivial,ultraviolet stable fixed point (asymptotic freedom) and that the dilatonic coupling functions (including the dilatonic potential) exhibit also a real, non-trivial fixed point. At such point the theory represents a standard charged string-inspired model.Stability and the gauge dependence of the fixed-point solution is discussed.It is shown that all these properties remain valid in a dilatonic-Yang-Mills theory with $n$ scalars and $m$ spinors, that has the UF stable fixed point $G^* = 3\epsilon (48+12N-m-2n)^{-1}$.In addition, it is seen that by increasing $N$ (number of gauge fields) the matter central charge $C=n+m/2$ ($0<C<24+6N$) can be increased correspondingly (in pure dilatonic gravity $0<C<24$).