Lattice chirality, anomaly matching, and more on the (non)decoupling of mirror fermions

Poppitz, Erich; Shang, Yanwen

doi:10.1088/1126-6708/2009/03/103

Cited by 13 publications

(44 citation statements)

References 69 publications

(165 reference statements)

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“…As reviewed above, in the theory with an anomalous mirror-fermion content studied in [46,47] there were massless mirror-fermion states, as required by 't Hooft anomaly matching. The question we want to address here is whether it is possible that the mirror fermions are lifted by the strong mirror interactions in an anomaly free theory, where the anomaly matching conditions do not require the existence of a massless state?…”

Section: Brief Review Of "Mirror Decoupling" With Ginsparg-wilson Fermentioning

confidence: 98%

“…The precise lattice chiral symmetries allow to formulate precisely on the lattice the 't Hooft anomaly matching conditions. As shown in [46], these should also be obeyed by strong non-gauge mirror dynamics (in the continuum, these are usually discussed in the strong gauge dynamics framework-as it is difficult to make sense of strong four-Fermi or Yukawa interactions in continuum 4d field theory).…”

Section: Brief Review Of "Mirror Decoupling" With Ginsparg-wilson Fermentioning

confidence: 99%

“…The conclusion of that work was that the susceptibilities showed no evidence of a massless state in the mirror sector. However, the subsequent work [46] used the polarization tensor as a probe, and found a directional discontinuity at zero momentum, a clear indication of a massless state. This agreed with the implications of 't Hooft anomaly matching (which was shown [46] to hold for lattice theories with exact chiral symmetries) that in order to reproduce the mirror-sector anomaly a massless state should be present.…”

Section: Brief Review Of "Mirror Decoupling" With Ginsparg-wilson Fermentioning

confidence: 99%

“…However, the subsequent work [46] used the polarization tensor as a probe, and found a directional discontinuity at zero momentum, a clear indication of a massless state. This agreed with the implications of 't Hooft anomaly matching (which was shown [46] to hold for lattice theories with exact chiral symmetries) that in order to reproduce the mirror-sector anomaly a massless state should be present. The interpretation of the two results is that the susceptibilities measured in [47] did not involve operators that coupled to the massless state, whereas the polarization tensor did.…”

Section: Brief Review Of "Mirror Decoupling" With Ginsparg-wilson Fermentioning

confidence: 99%

“…In Section 3, we briefly review some theoretical developments that have appeared previously (for a more thorough discussion we refer the reader to the original references [8,46,[48][49][50]). Various exact (independent of the coupling) identities obeyed by the mirror polarization operator on the lattice were derived there and provide essential consistency checks on our computer code.…”

Section: Outlinementioning

confidence: 99%

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On the decoupling of mirror fermions

Chen

Giedt

Poppitz

2013

J. High Energ. Phys.

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An approach to the formulation of chiral gauge theories on the lattice is to start with a vector-like theory, but decouple one chirality (the "mirror" fermions) using strong Yukawa interactions with a chirally coupled "Higgs" field. While this is an attractive idea, its viability needs to be tested with nonperturbative studies. The model that we study here, the so-called "3-4-5" model, is anomaly free and the presence of massless states in the mirror sector is not required by anomaly matching arguments, in contrast to the "1-0" model that was studied previously. We have computed the polarization tensor in this theory and find a directional discontinuity that appears to be nonzero in the limit of an infinite lattice, which is equivalent to the continuum limit at fixed physical volume. We show that a similar behavior occurs for the free massless Ginsparg-Wilson fermion, where the polarization tensor is known to have a directional discontinuity in the continuum limit. We thus find support for the conclusion that in the continuum limit of the 3-4-5 model, there are massless charged modes in the mirror sector so that it does not decouple from the light sector. The value of the discontinuity we obtain allows for two interpretations: either a chiral gauge theory does not emerge and mirror-sector fermions in a chiral anomaly free representation remain massless, or a massless vectorlike mirror fermion appears. We end by discussing some questions for future study.arXiv:1211.6947v3 [hep-lat]

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Section: Brief Review Of "Mirror Decoupling" With Ginsparg-wilson Fermentioning

confidence: 98%

Section: Brief Review Of "Mirror Decoupling" With Ginsparg-wilson Fermentioning

confidence: 99%

Section: Brief Review Of "Mirror Decoupling" With Ginsparg-wilson Fermentioning

confidence: 99%

Section: Brief Review Of "Mirror Decoupling" With Ginsparg-wilson Fermentioning

confidence: 99%

Section: Outlinementioning

confidence: 99%

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On the decoupling of mirror fermions

Chen

Giedt

Poppitz

2013

J. High Energ. Phys.

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Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories

Kikukawa

2019

Progress of Theoretical and Experimental Physics

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It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg-Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions and therefore having the simpler fermion path-integral measure, it has been argued that the mirror fermions do not decouple: in the 345 model with Dirac-and Majorana-Yukawa couplings to XY-spin field, the twopoint vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the PMS phase. We re-examine why the attempt seems a "Mission: Impossible" in the 345 model. We point out that the effective operators to break the fermion number symmetries ('t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature. We then consider a simpler four-flavor axial gauge model, the 1 4 (-1) 4 model, in which the U(1) A gauge and Spin(6)( ∼ = SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior, and we still argue that all you need is killing the continuous mirror-fermion symmetries with would-be gauge anomalies non-matched. Finally, by gauging a U(1) subgroup of the U(1) A × Spin(6)(SU(4)) of the previous model, we formulate the 21(−1) 3 chiral gauge model and argue that the induced fermion measure term satisfies the required locality property and provides a solution to the reconstruction theorem. This gives us "A New Hope" for the mission to be accomplished.An explicit example of such lattice Dirac operator is given by the overlap Dirac operator [17,19], which was derived by Neuberger from the overlap formalism [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. 2 By the Ginsparg-Wilson relation, it is possible to realize an exact chiral symmetry on the lattice [44] in the manner consistent with the no-go theorem. [45][46][47][48][49] It is also possible to introduce Weyl fermions on the lattice and this opens the possibility to formulate anomaly-free chiral gauge theories on the lattice [50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68]. In the case of U(1) chiral gauge theories, Lüscher[50] proved rigorously that it ...

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On the gauge-invariant path-integral measure for the overlap Weyl fermions in 16 of SO(10)

Kikukawa

2019

Progress of Theoretical and Experimental Physics

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We consider the lattice formulation of SO(10) chiral gauge theory with left-handed Weyl fermions in the 16-dimensional spinor representation ($\underline{16}$) within the framework of the overlap fermion/Ginsparg–Wilson relation. We define a manifestly gauge-invariant path-integral measure for the left-handed Weyl field using all the components of the Dirac field, but the right-handed part of it is just saturated completely by inserting a suitable product of the SO(10)-invariant ’t Hooft vertices in terms of the right-handed field. The definition of the measure applies to all possible topological sectors of admissible link fields. The measure possesses all required transformation properties under lattice symmetries and the induced effective action is CP invariant. The global U(1) symmetry of the left-handed field is anomalous due to the non-trivial transformation of the measure, while that of the right-handed field is explicitly broken by the ’t Hooft vertices. There remains the issue of smoothness and locality in the gauge-field dependence of the Weyl fermion measure, but the question is well defined and the necessary and sufficient condition for this property is formulated in terms of the correlation functions of the right-handed auxiliary fields. In the weak gauge-coupling limit at least, all the auxiliary fields have short-range correlations and the question can be addressed further by Monte Carlo methods without encountering the sign problem. We also discuss the relations of our formulation to other approaches/proposals to decouple the species doubling/mirror degrees of freedom. These include the Eichten–Preskill model, the mirror-fermion model with overlap fermions, the domain-wall fermion model with the boundary Eichten–Preskill term, 4D topological insulator/superconductor with a gapped boundary phase, and the recent studies on the PMS phase/“mass without symmetry breaking”. We clarify the similarities and differences in the technical details and show that our proposal is a unified and well defined testing ground for that basic question.

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Lattice chirality, anomaly matching, and more on the (non)decoupling of mirror fermions

Cited by 13 publications

References 69 publications

On the decoupling of mirror fermions

On the decoupling of mirror fermions

Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories

On the gauge-invariant path-integral measure for the overlap Weyl fermions in 16 of SO(10)

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