Symmetric mass generation of Kähler-Dirac fermions from the perspective of symmetry-protected topological phases

Guo, Yuxuan; You, Yi-Zhuang

doi:10.1103/physrevb.108.115139

Cited by 3 publications

(1 citation statement)

References 79 publications

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“…This agrees with the critical numbers of Weyl fermions needed to cancel the spin-Z 4 anomaly in flat space and also the number of boundary chiral fermions that can be gapped in five dimensional topological superconductors [27,28]. Indeed this condition, combined with the dimension dependent counting implied by the decomposition of a Kähler-Dirac field into spinors, is capable of predicting the numbers of fermions needed to cancel a variety of discrete 't Hooft anomaly for free Majorana fermions in any dimension [29][30][31][32][33].…”

Section: The Minimal Anomaly Free Mirror Modelsupporting

confidence: 65%

Lattice regularization of reduced Kähler-Dirac fermions and connections to chiral fermions

Catterall

2024

SciPost Phys.

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We show how a path integral for reduced Kähler-Dirac fermions suffers from a phase ambiguity associated with the fermion measure that is an analog of the measure problem seen for chiral fermions. However, unlike the case of chiral symmetry, a doubler free lattice action exists which is invariant under the corresponding onsite symmetry. This allows for a clear diagnosis and solution to the problem using mirror fermions resulting in a unique gauge invariant measure. By introducing an appropriate set of Yukawa interactions which are consistent with ’t Hooft anomaly cancellation we conjecture the mirrors can be decoupled from low energy physics. Moreover, the minimal such Kähler-Dirac mirror model yields a light sector which corresponds, in the flat space continuum limit, to the Pati-Salam GUT model.

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Section: The Minimal Anomaly Free Mirror Modelsupporting

confidence: 65%

Lattice regularization of reduced Kähler-Dirac fermions and connections to chiral fermions

Catterall

2024

SciPost Phys.

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A Lattice Formulation of Weyl Fermions on a Single Curved Surface

Aoki,

Fukaya,

Kan

2024

Progress of Theoretical and Experimental Physics

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In the standard lattice domain-wall fermion formulation, one needs two flat domain-walls where both of the left- and right-handed massless modes appear. In this work we investigate a single domain-wall system with a nontrivial curved background. Specifically we consider a massive fermion on a three-dimensional square lattice, whose domain-wall is a two-dimensional sphere. In the free theory, we find that a single Weyl fermion is localized at the wall and it feels gravity through the induced spin connection. With a topologically nontrivial U(1) link gauge field, however, we find a zero mode with the opposite chirality localized at the center where the gauge field is singular. In the latter case, the low-energy effective theory is not chiral but vectorlike. We discuss how to circumvent this obstacle in formulating lattice chiral gauge theory in the single domain-wall fermion system.

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Fermion mass generation without symmetry breaking

Cresswell-Hogg,

Litim

2024

Phys. Rev. D

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We study the generation of fermion mass in a context where interactions break a discrete chiral symmetry. Then, fermion mass is not protected by a symmetry, no symmetry is broken by the generation of mass, and a vanishing mass no longer enhances a symmetry. We elaborate these scenarios for template fermionic and Yukawa theories in three dimensions where mass can be generated either by fluctuations, strong dynamics, or the vacuum expectation value of a scalar field. We find that fluctuation-induced contributions to fermion mass are parametrically suppressed in the number of fermion flavors N. The generation of fermion mass then takes the form of a rapid crossover which turns into a second order quantum phase transition for large N, much like in settings with fundamental chiral symmetry. We further discuss theories where fermion mass can be generated spontaneously without breaking any symmetry other than scale symmetry. Implications of our findings are discussed. Published by the American Physical Society 2024

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Symmetric mass generation of Kähler-Dirac fermions from the perspective of symmetry-protected topological phases

Cited by 3 publications

References 79 publications

Lattice regularization of reduced Kähler-Dirac fermions and connections to chiral fermions

Lattice regularization of reduced Kähler-Dirac fermions and connections to chiral fermions

A Lattice Formulation of Weyl Fermions on a Single Curved Surface

Fermion mass generation without symmetry breaking

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