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Domain wall fermions for planar physics / Simon Hands

Journal of High Energy Physics, Volume: 09, Issue: 047

Swansea University Author: Simon, Hands

DOI (Published version): 10.1007/JHEP09(2015)047

Abstract

In 2+1 dimensions, Dirac fermions in reducible, i.e. four-component representations of the spinor algebra form the basis of many interesting model field theories and effective descriptions of condensed matter phenomena. This paper explores lattice formulations which preserve the global U(2N) symmetr...

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Published in: Journal of High Energy Physics
Published: 2015
URI: https://cronfa.swan.ac.uk/Record/cronfa23345
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Abstract: In 2+1 dimensions, Dirac fermions in reducible, i.e. four-component representations of the spinor algebra form the basis of many interesting model field theories and effective descriptions of condensed matter phenomena. This paper explores lattice formulations which preserve the global U(2N) symmetry present in the massless limit, and its breakdown to U(N)xU(N) implemented by three independent and parity-invariant fermion mass terms. I set out generalisations of the Ginsparg-Wilson relation, leading to a formulation of an overlap operator, and explore the remnants of the global symmetries which depart from the continuum form by terms of order of the lattice spacing. I also define a domain wall formulation in 2+1+1d, and present numerical evidence, in the form of bilinear condensate and meson correlator calculations in quenched non-compact QED using reformulations of all three mass terms, to show that U(2N) symmetry is recovered in the limit that the domain-wall separation L tends to infinity. The possibility that overlap and domain wall formulations of reducible fermions may coincide only in the continuum limit is discussed.
Item Description: arXiv:1507.07717
Keywords: Lattice Quantum Field Theory, Field Theories in Lower Dimensions, Global Symmetries
College: College of Science
Issue: 047