Lattice chirality and the decoupling of mirror fermions
arXiv:0706.1043 · doi:10.1088/1126-6708/2007/08/081
Abstract
We show, using exact lattice chirality, that partition functions of lattice gauge theories with vectorlike fermion representations can be split into "light" and "mirror" parts, such that the "light" and "mirror" representations are chiral. The splitting of the full partition function into "light" and "mirror" is well defined only if the two sectors are separately anomaly free. We show that only then is the generating functional, and hence the spectrum, of the mirror theory a smooth function of the gauge field background. This explains how ideas to use additional non-gauge, high-scale mirror-sector dynamics to decouple the mirror fermions without breaking the gauge symmetry--for example, in symmetric phases at strong mirror Yukawa coupling--are forced to respect the anomaly-free condition when combined with the exact lattice chiral symmetry. Our results also explain a paradox posed by a recent numerical study of the mirror-fermion spectrum in a toy would-be-anomalous two-dimensional theory. In passing, we prove some general properties of the partition functions of arbitrary chiral theories on the lattice that should be of interest for further studies in this field.
arXiv comment29 pages, 2 figures; published version, new addendum
References in corpus (36)
- Exactly massless quarks on the lattice
- A Method for Simulating Chiral Fermions on the Lattice
- Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
- A construction of lattice chiral gauge theories
- The index theorem in QCD with a finite cut-off
- Locality properties of Neuberger's lattice Dirac operator
- Chiral Fermions on the Lattice
- Abelian chiral gauge theories on the lattice with exact gauge invariance
- A continuum limit of the chiral Jacobian in lattice gauge theory
- Bounds on the Wilson Dirac Operator
- Weyl fermions on the lattice and the non-abelian gauge anomaly
- Axial anomaly and topological charge in lattice gauge theory with Overlap Dirac operator
- Geometrical aspects of chiral anomalies in the overlap
- Absence of Chiral Fermions in the Eichten--Preskill Model
- A Lattice Construction of Chiral Gauge Theories
- Lattice regularization of chiral gauge theories to all orders of perturbation theory
- Lattice Chiral Gauge Theories
- Investigation of the Domain Wall Fermion Approach to Chiral Gauge Theories on the Lattice
- Domain wall fermions in a waveguide: the phase diagram at large Yukawa coupling
- Lattice Formulation of the Standard Model
- Finite size corrections in two dimensional gauge theories and a quantitative chiral test of the overlap
- Exact Chiral Symmetry on the Lattice
- SU(N) chiral gauge theories on the lattice
- Monte Carlo evaluation of a fermion number violating observable in 2D
- Noncompact chiral U(1) gauge theories on the lattice
- Chiral Lattice Gauge Theories from Warped Domain Walls and Ginsparg-Wilson Fermions
- Global obstructions to gauge-invariance in chiral gauge theory on the lattice
- Index of a family of lattice Dirac operators and its relation to the non-abelian anomaly on the lattice
- Gauge fixing, families index theory, and topological features of the space of lattice gauge fields
- Fermion-Higgs model with strong Wilson-Yukawa coupling in two dimensions
- Warped Domain Wall Fermions
- Fermion-number violation in regularizations that preserve fermion-number symmetry
- Translational Anomaly in Chiral Gauge Theories on a Torus and the Overlap Formalism
- Families index theory for Overlap lattice Dirac operator. I
- A Wilson-Yukawa model with undoubled chiral fermions in 2D
- Anomalous gauge theories revisited
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- Nonperturbative Regulator for Chiral Gauge Theories?
- On Yang-Mills Theories with Chiral Matter at Strong Coupling
- Chiral Lattice Gauge Theories and The Strong Coupling Dynamics of a Yukawa-Higgs Model with Ginsparg-Wilson Fermions
- On the decoupling of mirror fermions
- Constraining a fourth generation of quarks: non-perturbative Higgs boson mass bounds
- Higgs-Yukawa model in chirally-invariant lattice field theory
- Higgs boson mass bounds in the presence of a very heavy fourth quark generation
- On the gauge invariant path-integral measure for the overlap Weyl fermions in of SO(10)
- Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
- A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance
- Lattice chirality, anomaly matching, and more on the (non)decoupling of mirror fermions
- Upper Higgs boson mass bounds from a chirally invariant lattice Higgs-Yukawa model