Conformal Windows of SU(N) Gauge Theories, Higher Dimensional Representations and The Size of The Unparticle World

TL;DR

This paper analyzes the conformal windows of SU(N) gauge theories with higher representations, determining the fraction of theories that develop infrared fixed points and sizing the unparticle physics landscape.

Contribution

It provides exact results for supersymmetric theories and approximate results for nonsupersymmetric ones regarding the conformal windows and unparticle world size.

Findings

50% of supersymmetric theories can develop an infrared fixed point

Circa 25% of nonsupersymmetric theories can develop an infrared fixed point

Conformal regions dominate in nonsupersymmetric theories with multiple representations

Abstract

We present the conformal windows of SU(N) supersymmetric and nonsupersymmetric gauge theories with vector-like matter transforming according to higher irreducible representations of the gauge group. We determine the fraction of asymptotically free theories expected to develop an infrared fixed point and find that it does not depend on the specific choice of the representation. This result is exact in supersymmetric theories while it is an approximate one in the nonsupersymmetric case. The analysis allows us to size the unparticle world related to the existence of underlying gauge theories developing an infrared stable fixed point. We find that exactly 50 % of the asymptotically free theories can develop an infrared fixed point while for the nonsupersymmetric theories it is circa 25 %. When considering multiple representations, only for the nonsupersymmetric case, the conformal regions quickly dominate over the nonconformal ones. For four representations, 70 % of the asymptotically free space is filled by the conformal region. According to our theoretical landscape survey the unparticle physics world occupies a sizable amount of the particle world, at least in theory space, and before mixing it (at the operator level) with the nonconformal one.