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Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing$
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Laurent Lellouch, Rainer Sommer, Benjamin Svetitsky, Anastassios Vladikas, and Leticia F. Cugliandolo

Print publication date: 2011

Print ISBN-13: 9780199691609

Published to Oxford Scholarship Online: January 2012

DOI: 10.1093/acprof:oso/9780199691609.001.0001

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Lattice gauge theory beyond the Standard Model

(p.699) 12 Lattice gauge theory beyond the Standard Model
Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing

Thomas Appelquist

Ethan T. Neil

Oxford University Press

This chapter gives an overview of methods and recent studies in the application of lattice gauge theory to physics beyond the standard model. It focuses on theories in which electroweak symmetry is broken spontaneously by new strong interactions. An introduction is given to some common features of such theories, described in terms of the chiral Lagrangian. Apparent difficulties in reconciling QCD-based models with precision experimental results provide the motivation for study of more general Yang-Mills theories. They are examined using the running coupling, which exhibits a perturbative infrared fixed point when enough light fermions are included, defining a "conformal window" in which confinement is lost and chiral symmetry is restored. Some analytic approaches to studying the conformal window are discussed, but the lack of an adequate method in the presence of a strongly-coupled fixed point leads to the consideration of non-perturbative lattice methods. Direct determination of the running coupling and its evolution is discussed, as well as the use of thermal phase transitions to distinguish confining from infrared-conformal theories. Finally, the direct simulation of the spectrum and other properties for theories outside the conformal window is described.

Keywords:   Lattice gauge theory, beyond the standard model, electroweak, chiral Lagrangian, Yang-Mills, running coupling, conformal window, thermal phase transition

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