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This is a review of the status and outstanding issues in attempts to construct chiral lattice gauge theories by decoupling the mirror fermions from a vectorlike theory.
E. H. Fradkin and S. H. Shenker, “Phase diagrams of lattice gauge theories with Higgs fields,” Phys. Rev. D 19
1979
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1980
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G.’t Hooft, In: G.’t Hooft, Editor, Recent developments in gauge theories, Plenum, N.Y. (1980)
1980
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S. Raby, S. Dimopoulos, and L. Susskind, “Tumbling gauge theories,” Nucl. Phys. B 169
1980
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K. Fujikawa, “Path integral for gauge theories with fermions,” Phys. Rev. D 21
1980
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D. Foerster, H. B. Nielsen and M. Ninomiya, “Dynamical stability of local gauge symmetry: creation of light from chaos,” Phys. Lett. B 94
1980
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Y. Frishman, A. Schwimmer, T. Banks and S. Yankielowicz, “The axial anomaly and the bound state spectrum in confining theories,” Nucl. Phys. B 177
1981
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L. H. Karsten and J. Smit, “Lattice fermions: species doubling, chiral invariance, and the triangle anomaly,” Nucl. Phys. B 183
1981
Earlier work this paper cites.
C. B. Lang, C. Rebbi and M. Virasoro, “The phase structure of a nonabelian gauge-higgs field system,” Phys. Lett. B 104
1981
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S. R. Coleman and B. Grossman, “’t Hooft’s consistency condition as a consequence of analyticity and unitarity,” Nucl. Phys. B 203
1982
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P. H. Ginsparg and K. G. Wilson, “A remnant of chiral symmetry on the lattice,” Phys. Rev. D 25
1982
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E. Witten, “Global gravitational anomalies,” Commun. Math. Phys. 100
1985
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R. Jackiw and R. Rajaraman, “Vector meson mass generation through chiral anomalies,” Phys. Rev. Lett. 54
1985
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E. Eichten, R. D. Peccei, J. Preskill and D. Zeppenfeld, “Chiral gauge theories in the 1/N expansion,” Nucl. Phys. B 268
1986
Earlier work this paper cites.
L. Alvarez-Gaume, S. Della Pietra and V. Della Pietra, “The effective action for chiral fermions,” Phys. Lett. B 166
1986
Earlier work this paper cites.
I. G. Halliday, E. Rabinovici, A. Schwimmer and M. S. Chanowitz, “Quantization of anomalous two-dimensional models,” Nucl. Phys. B 268
1986
Earlier work this paper cites.
E. Eichten and J. Preskill, “Chiral gauge theories on the lattice,” Nucl. Phys. B 268
1986
Earlier work this paper cites.
J. Smit, “Fermions on a lattice,” Lectures given at the 25th Cracow International School of Theoretical Physics, Zakopane, Poland, Jun 2-14, 1985, Acta Phys. Polon. B 17
1986
Earlier work this paper cites.
S. Della Pietra, V. Della Pietra and L. Alvarez-Gaume, “The chiral determinant and the eta-invariant,” Commun. Math. Phys. 109
1987
Earlier work this paper cites.
I. H. Lee and R. E. Shrock, “Chiral symmetry breaking phase transition in lattice gauge-higgs theories with fermions,” Phys. Rev. Lett. 59
1987
Earlier work this paper cites.
C. Rebbi, “Chiral invariant regularization of fermions on the lattice,” Phys. Lett. B 186
1987
Earlier work this paper cites.
G. T. Bodwin and E. V. Kovacs, “Perturbative analysis of Rebbi’s lattice fermion proposal,” Phys. Lett. B 193
1987
Earlier work this paper cites.
A. Pelissetto, “Lattice nonlocal chiral fermions,” Annals Phys. 182
1988
Earlier work this paper cites.
A. Hasenfratz and T. Neuhaus, “Nonperturbative study of the strongly coupled scalar fermion model,” Phys. Lett. B 220
1989
Earlier work this paper cites.
I. H. Lee, J. Shigemitsu and R. E. Shrock, “Study of different lattice formulations of a Yukawa model with a real scalar field,” Nucl. Phys. B 334
1990
Earlier work this paper cites.
I. H. Lee, J. Shigemitsu and R. E. Shrock, “Lattice study of a Yukawa theory with a real scalar field,” Nucl. Phys. B 330
1990
Earlier work this paper cites.
S. Aoki, I. H. Lee, D. Mustaki, J. Shigemitsu and R. E. Shrock, “Study of nonperturbative continuum limits in a lattice Yukawa model,” Phys. Lett. B 244
1990
Earlier work this paper cites.
M. A. Stephanov and M. M. Tsypin, “The phase structure of the U ( 1 ) U(1) Higgs-fermion lattice theory,” Phys. Lett. B 242
1990
Earlier work this paper cites.
M. Golterman and D. N. Petcher, “The 1/d expansion for lattice theories of chiral fermions with Yukawa couplings,” Nucl. Phys. B 359
1991
Earlier work this paper cites.
D. B. Kaplan, “A method for simulating chiral fermions on the lattice,” Phys. Lett. B 288
1992
Earlier work this paper cites.
T. Banks and A. Dabholkar, “Decoupling a fermion whose mass comes from a Yukawa coupling: Nonperturbative considerations,” Phys. Rev. D 46
1992
Earlier work this paper cites.
M. Golterman, D. N. Petcher and J. Smit, “Fermion interactions in models with strong Wilson-Yukawa couplings,” Nucl. Phys. B 370
1992
Cited alongside, same era.
W. Bock, A. K. De, and J. Smit, “Fermion masses at strong Wilson-Yukawa coupling in the symmetric phase,” Nucl. Phys. B 388
1992
Cited alongside, same era.
S. Aoki, I. H. Lee and R. E. Shrock, “Decoupling of doubler modes and tuning of fermion masses in the S U ( 2 ) × U ( 1 ) Y SU(2)\times U(1)_{Y} lattice electroweak theory,” Phys. Rev. D 45
1992
Cited alongside, same era.
D. B. Kaplan, “Chiral fermions on the lattice,” Nucl. Phys. Proc. Suppl. 30
1993
Cited alongside, same era.
R. Narayanan and H. Neuberger, “Chiral fermions on the lattice,” Phys. Rev. Lett. 71
1993
Cited alongside, same era.
H. Neuberger, “Bounds on the Wilson Dirac operator,” Phys. Rev. D 61
2000
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M. Golterman, “Lattice chiral gauge theories,” Nucl. Phys. Proc. Suppl. 94
2001
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H. Neuberger, “Exact chiral symmetry on the lattice,” Ann. Rev. Nucl. Part. Sci. 51
2001
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D. H. Adams, “Axial anomaly and topological charge in lattice gauge theory with overlap-Dirac operator,” Annals Phys. 296
2002
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D. H. Adams, “Families index theory for overlap lattice Dirac operator. I,” Nucl. Phys. B 624
2002
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P. Hasenfratz, “Lattice 2001: Reflections,” Nucl. Phys. Proc. Suppl. 106
2002
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M. F. L. Golterman, D. N. Petcher and E. Rivas, “Absence of chiral fermions in the Eichten-Preskill model,” Nucl. Phys. B 395
1993
Cited alongside, same era.
W. Bock, A. K. De, E. Focht and J. Smit, “Fermion Higgs model with strong Wilson-Yukawa coupling in two dimensions,” Nucl. Phys. B 401
1993
Cited alongside, same era.
M. Golterman, K. Jansen, D. N. Petcher and J. C. Vink, “Investigation of the domain wall fermion approach to chiral gauge theories on the lattice,” Phys. Rev. D 49
1994
Cited alongside, same era.
J. Terning, “Chiral technicolor and precision electroweak measurements,” Phys. Lett. B 344
1995
Cited alongside, same era.
P. C. Argyres and M. R. Douglas, “New phenomena in SU(3) supersymmetric gauge theory,” Nucl. Phys. B 448
1995
Cited alongside, same era.
D. Kutasov and A. Schwimmer, “Universality in two-dimensional gauge theory,” Nucl. Phys. B 442
1995
Cited alongside, same era.
R. Narayanan and H. Neuberger, “A construction of lattice chiral gauge theories,” Nucl. Phys. B 443
1995
Cited alongside, same era.
Later among the works it cites.
K. Fujikawa, M. Ishibashi and H. Suzuki, “Ginsparg-Wilson operators and a no-go theorem,” Phys. Lett. B 538
2002
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K. Fujikawa, M. Ishibashi and H. Suzuki, “CP breaking in lattice chiral gauge theories,” JHEP 0204
2002
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T. Appelquist and R. Shrock, “Dynamical symmetry breaking of extended gauge symmetries,” Phys. Rev. Lett. 90
2003
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K. A. Intriligator, “IR free or interacting? A proposed diagnostic,” Nucl. Phys. B 730
2005
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T. Bhattacharya, C. Csaki, M. R. Martin, Y. Shirman and J. Terning, “Warped domain wall fermions,” JHEP 0508
2005
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T. Bhattacharya, M. R. Martin and E. Poppitz, “Chiral lattice gauge theories from warped domain walls and Ginsparg-Wilson fermions,” Phys. Rev. D 74
2006
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K. A. Intriligator and N. Seiberg, “Lectures on supersymmetry breaking,” Class. Quant. Grav. 24
2007
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J. Giedt and E. Poppitz, “Chiral lattice gauge theories and the strong coupling dynamics of a Yukawa-Higgs model with Ginsparg-Wilson fermions,” JHEP 0710
2007
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2007
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2007
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E. Poppitz and Y. Shang, “Lattice chirality and the decoupling of mirror fermions,” JHEP 0708
2007
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C. Amsler et al
2008
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2008
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2008
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P. Hasenfratz and R. von Allmen, “Towards Weyl fermions on the lattice without artefacts,” JHEP 0802
2008
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E. Poppitz and Y. Shang, “’Light from chaos’ in two dimensions,” Int. J. Mod. Phys. A 23
2008
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2009
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E. Poppitz and M. Ünsal, “Chiral gauge dynamics and dynamical supersymmetry breaking,” JHEP 0907
2009
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2009
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S. Catterall, D. B. Kaplan and M. Ünsal, “Exact lattice supersymmetry,” Phys. Rept. 484
2009
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J. Giedt, “Progress in four-dimensional lattice supersymmetry,” Int. J. Mod. Phys. A 24
2009
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2009
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2009
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B. Holdom, “Approaching a strong fourth family,” Phys. Lett. B 686
2010
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