Renormalization-Group Evolution of Chiral Gauge Theories

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.

arXiv comment28 pages, latex

References in corpus (31)

• A New Constraint on Strongly Coupled Field Theories
• Fermion Masses and Mixing in Extended Technicolor Models
• UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond
• Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions
• Neutrino Masses in Theories with Dynamical Electroweak Symmetry Breaking
• Dynamical Symmetry Breaking of Extended Gauge Symmetries
• Large N flavor beta-functions: a recap
• Determining the conformal window: SU(2) gauge theory with N_f = 4, 6 and 10 fermion flavours
• The conformal window in QCD and supersymmetric QCD
• Phases of Chiral Gauge Theories
• An Extended Technicolor Model
• Relations between Observables and the Infrared Fixed-Point in QCD
• Mass anomalous dimension in SU(2) with six fundamental fermions
• Study of Possible Ultraviolet Zero of the Beta Function in Gauge Theories with Many Fermions
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• New Constraints on Chiral Gauge Theories
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Higher-Loop Structural Properties of the $\beta$ Function in Asymptotically Free Vectorial Gauge Theories
• Conformal Behavior at Four Loops and Scheme (In)Dependence
• Study of Scheme Transformations to Remove Higher-Loop Terms in the $\beta$ Function of a Gauge Theory
• Higher-Loop Calculations of the Ultraviolet to Infrared Evolution of a Vectorial Gauge Theory in the Limit $N_c\to \infty$, $N_f\to \infty$ with $N_f/N_c$ Fixed
• Implications of Dynamical Generation of Standard-Model Fermion Masses
• Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory
• Two-Color Theory with Novel Infrared Behavior
• Higher Loop Corrections to the Infrared Evolution of Fermionic Gauge Theories in the RI' Scheme
• Infrared Fixed Points in the minimal MOM Scheme
• On the Unification of Gauge Symmetries in Theories with Dynamical Symmetry Breaking
• Lattice Study on quantum-mechanical dynamics of two-color QCD with six light flavors
• On the Ultraviolet to Infrared Evolution of Chiral Gauge Theories
• Generational Structure of Models with Dynamical Symmetry Breaking
• Patterns of Dynamical Gauge Symmetry Breaking

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• $A_k\bar{F}$ Chiral Gauge Theories
• Scheme-Independent Calculations of Anomalous Dimensions of Baryon Operators in Conformal Field Theories
• Determination of SU(4)${}_{TC}$ Technicolor Gauge Group from Embedding in Extended Technicolor
• If the Weak Were Strong and the Strong Were Weak
• Conformal Phase Diagram of Complete Asymptotically Free Theories
• ${\beta }_{IR}^{\prime }$ at an Infrared Fixed Point in Chiral Gauge Theories
• Dynamical Symmetry Breaking in Chiral Gauge Theories with Direct-Product Gauge Groups
• Ultraviolet to Infrared Evolution and Nonperturbative Behavior of $\mathrm{SU}(N)\otimes \mathrm{SU}(N-4)\otimes \mathrm{U}(1)$ Chiral Gauge Theories