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arXiv · 1411.2042

Renormalization-Group Evolution of Chiral Gauge Theories

Yan-Liang Shi·Robert Shrock
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Abstract

We calculate the ultraviolet to infrared evolution and analyze possible types of infrared behavior for several asymptotically free chiral gauge theories with gauge group SU($N$) and massless chiral fermions transforming according to a symmetric rank-2 tensor representation $S$ and $N+4$ copies (flavors) of a conjugate fundamental representation $\bar F$, together with a vectorlike subsector with chiral fermions in higher-dimensional representation(s). We construct and study three such chiral gauge theories. These have respective vectorlike subsectors comprised of (a) $p$ copies of fermions in the adjoint representation, (b) $N = 2k$ even and $p$ copies of fermions in the antisymmetric rank-$k$ tensor representation, and (c) $p$ copies of $\{S + \bar S\}$ fermions. Results are presented for beta functions, their infrared zeros, and predictions from the most-attractive-channel approach for the formation of bilinear fermion condensates. Importantly, we show that for these theories, the expected ultraviolet to infrared evolution obeys a conjectured inequality concerning the field degrees of freedom for all values of the parameters $N$ and $p$ characterizing each theory.

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Yan-Liang Shi, Robert Shrock. 2014-11-07. Renormalization-Group Evolution of Chiral Gauge Theories. https://doi.org/10.1103/physrevd.91.045004

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