Asymptotic Freedom and Infrared Behavior in the Type 0 String Approach to Gauge Theory

TL;DR

This paper explores the duality between type 0 string theory backgrounds and four-dimensional SU(N) gauge theories, analyzing their asymptotic freedom, infrared behavior, and fixed points through renormalization group equations.

Contribution

It provides a detailed analysis of the RG flow in type 0 string backgrounds, identifying fixed points and the effects of the 2-loop beta function on the dual gauge theory.

Findings

Confirmed the logarithmic coupling flow consistent with asymptotic freedom.

Identified a fixed point at infinite coupling with an AdS_5×S^5 metric.

Demonstrated a continuous RG trajectory from UV to IR fixed points.

Abstract

In a recent paper we considered the type 0 string theories, obtained from the ten-dimensional closed NSR string by a GSO projection which excludes space-time fermions, and studied the low-energy dynamics of N coincident D-branes. This led us to conjecture that the four-dimensional SU(N) gauge theory coupled to 6 adjoint massless scalars is dual to a background of type 0 theory carrying N units of R-R 5-form flux and involving a tachyon condensate. The tachyon background leads to a ``soft breaking'' of conformal invariance, and we derived the corresponding renormalization group equation. Minahan has subsequently found its asymptotic solution for weak coupling and showed that the coupling exhibits logarithmic flow, as expected from the asymptotic freedom of the dual gauge theory. We study this solution in more detail and identify the effect of the 2-loop beta function. We also demonstrate the existence of a fixed point at infinite coupling. Just like the fixed point at zero coupling, it is characterized by the AdS_5\times S^5 Einstein frame metric. We argue that there is a RG trajectory extending all the way from the zero coupling fixed point in the UV to the infinite coupling fixed point in the IR.