On the decoupling of mirror fermions

Chen, Chen; Giedt, Joel; Poppitz, Erich

doi:10.1007/jhep04(2013)131

Cited by 25 publications

(31 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…14 To define the actual operators, one needs the point-splitting procedure because of the fermi statistics. A possible choice is the following: In [73][74][75][76][77][78][79][80], the 345 model is formulated by introducing all possible Dirac-and Majoranatype Yukawa couplings to the XY spin field in order to break the global continuous symmetries of the mirror sector.…”

Section: )mentioning

confidence: 99%

“…However, in the related formulation by Poppitz and his collaborators [73][74][75][76][77][78][79][80] which includes the mirror degrees of freedom [81][82][83][84][85][86][87][88][89][90][91] in terms of Ginsparg-Wilson fermions and therefore has the simpler fermion path-integral measure, it was argued that the mirror fermions do not decouple: in the two-dimensional 345 model with Dirac-and Majorana-Yukawa couplings to XY-spin field, the two-point vertex function of the (external) U (1) gauge field in the mirror sector shows a singular non-local behavior in the paramagnetic strong-coupling phase(PMS) [74,92,93]. 6 The singular non-local term turns out to be same as the contribution of the massless Weyl fermions of the target sector.…”

Section: Introductionmentioning

confidence: 99%

“…49) Indeed, this type of the Majorana-Yukawa couplings are used in the formulation of the 345 model by Bhattacharya, Chen, Giedt, Poppitz and Shang in consideration [73][74][75][76][77][78][79][80]. However, again, the limit of the large Majorana mass parameter M is singular.…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

View full text Add to dashboard Cite

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 ...

show abstract

Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

View full text Add to dashboard Cite

show abstract

“…In [13] the gauge fields were given space-dependent couplings, but it is thought that the construction is unlikely to have a continuum limit [14]. Certain other cases of exotic interactions have been closely examined and do not appear to possess the expected mass gap [15][16][17]. In the third category, where mirror fermions are projected out, one must show that the resulting fermion contribution to the gauge measure is analytic in the gauge fields and can be derived from a local fermion action.…”

Section: Introductionmentioning

confidence: 99%

Nonperturbative Regulator for Chiral Gauge Theories?

Grabowska¹,

Kaplan²

2016

Phys. Rev. Lett.

View full text Add to dashboard Cite

We propose a nonperturbative gauge invariant regulator for d-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d + 1 dimensions with quantum gauge fields that reside on one d-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local d-dimensional interpretation only if the chiral fermion representation is anomaly free. A physical realization of this construction would imply the existence of mirror fermions in the standard model that are invisible except for interactions induced by vacuum topology, and which could gravitate differently than conventional matter.

show abstract

“…The mirror fermion approach enjoys on-site fermions and gauge symmetry, as well as a physically transparent, fi-nite dimensional Hilbert space for each site. Previous attempts at gapping out only anomaly-free mirror fermions without breaking the gauge symmetry have been unsuccessful [17][18][19][20], which led to speculation that it is impossible to do so [20]. On the other hand, recently discovered connections [21,22] between entangled-or topologicalstates and quantum anomalies suggest that we should be able to gap out only the mirror theory without breaking any gauge symmetry if the chiral theory is free of all anomalies.…”

mentioning

confidence: 99%

A Novel Non-Perturbative Lattice Regularization of an Anomaly-Free $1 + 1d$ Chiral $SU(2)$ Gauge Theory

DeMarco,

Wen

2017

Preprint

View full text Add to dashboard Cite

We present a numerical treatment of a novel non-perturbative lattice regularization of a 1 + 1d SU (2) Chiral Gauge Theory. Our approach follows recent proposals that exploit the newly discovered connection between anomalies and topological (or entangled) states to show how to create a lattice regularization of any anomaly-free chiral gauge theory. In comparison to other methods, our regularization enjoys on-site fermions and gauge action, as well as a physically transparent fermion Hilbert space. We follow the 'mirror fermion' approach, in which we first create a lattice regularization of both the chiral theory and its mirror conjugate and then introduce interactions that gap out only the mirror theory. The connection between topological states and anomalies shows that such interactions exist if the chiral theory is free of all quantum anomalies. Instead of numerically intractable fermion-fermion interactions, we couple the mirror theory to a Higgs field driven into a symmetry-preserving, disordered, gapped phase.

show abstract

On the decoupling of mirror fermions

Cited by 25 publications

References 52 publications

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

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

Nonperturbative Regulator for Chiral Gauge Theories?

A Novel Non-Perturbative Lattice Regularization of an Anomaly-Free $1 + 1d$ Chiral $SU(2)$ Gauge Theory

Contact Info

Product

Resources

About