# Fermion masses without symmetry breaking in two spacetime dimensions

@article{BenTov2014FermionMW, title={Fermion masses without symmetry breaking in two spacetime dimensions}, author={Yoni BenTov}, journal={Journal of High Energy Physics}, year={2014}, volume={2015}, pages={1-41} }

A bstractI study the prospect of generating mass for symmetry-protected fermions without breaking the symmetry that forbids quadratic mass terms in the Lagrangian. I focus on 1+1 spacetime dimensions in the hope that this can provide guidance for interacting fermions in 3+1 dimensions. I first review the SO(8) Gross-Neveu model and emphasize a subtlety in the triality transformation. Then I focus on the “m = 0” manifold of the SO(7) Kitaev-Fidkowski model. I argue that this theory exhibits a…

## 18 Citations

Symmetric Fermion Mass Generation as Deconfined Quantum Criticality

- Physics
- 2017

Author(s): You, YZ; He, YC; Xu, C; Vishwanath, A | Abstract: © 2018 authors. Published by the American Physical Society. Massless (2+1)D Dirac fermions arise in a variety of systems from graphene to…

Confinement transition of ℤ2 gauge theories coupled to massless fermions: Emergent quantum chromodynamics and SO(5) symmetry

- Physics, MedicineProceedings of the National Academy of Sciences
- 2018

This work develops a field theory description of the direct transition involving an emergent nonabelian [SU(2)] gauge theory and a matrix Higgs field and finds numerical evidence for an enlarged SO(5) symmetry rotating between antiferromagnetism and valence bond solid orders proximate to criticality.

Origin of families and $SO(18)$ grand unification

- Physics
- 2016

We exploit a recent advance in the study of interacting topological superconductors to propose a solution to the family puzzle of particle physics in the context of SO(18) [or more correctly,…

From bosonic topological transition to symmetric fermion mass generation

- Physics
- 2018

The bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry protected topological phase and the trivial phase. In this work, we derive a description of this…

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

- PhysicsProgress of Theoretical and Experimental Physics
- 2019

It is 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…

Anomalies and Bosonization

- Physics
- 2018

Recently, general methods of bosonization beyond 1+1 dimensions have been developed. In this article, we review these bosonizations and extend them to the case with boundary conditions. In…

Notes on 8 Majorana Fermions

- Physics
- 2019

Eight Majorana fermions in $d=1+1$ dimensions enjoy a triality that permutes the representation of the $SO(8)$ global symmetry in which the fermions transform. This triality plays an important role…

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

- PhysicsProgress of Theoretical and Experimental Physics
- 2019

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…

UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases

- PhysicsPhysical Review B
- 2019

Symmetry-protected phases are gapped phases of matter which are distinguished only in the presence of a global symmetry G. These quantum phases lack any symmetry-breaking or topological order, and…

Fermionic SPT phases in higher dimensions and bosonization

- Physics
- 2017

A bstractWe discuss bosonization and Fermionic Short-Range-Entangled (FSRE) phases of matter in one, two, and three spatial dimensions, emphasizing the physical meaning of the cohomological…

## References

SHOWING 1-10 OF 98 REFERENCES

Massive fermions without fermion bilinear condensates

- Physics
- 2015

We study a lattice field theory model containing two flavors of massless staggered fermions with an onsite four-fermion interaction. The model contains a $SU(4)$ symmetry which forbids non-zero…

ANOMALIES AND FERMION ZERO MODES ON STRINGS AND DOMAIN WALLS

- Physics
- 1985

the parity anomaly in 2n + 1 dimensions, and the Dirac index density in 2n + 2 dimensions can be understood in terms of the physics of fermion zero modes on strings and domain walls. We show that the…

Dynamical symmetry breaking in asymptotically free field theories

- Physics
- 1974

Two-dimensional massless fermion field theories with quartic interactions are analyzed. These models are asymptotically free. The models are expanded in powers of $\frac{1}{N,}$ where $N$ is the…

Adler-Bell-Jackiw Anomaly and Fermion Number Breaking in the Presence of a Magnetic Monopole

- Physics
- 1982

Abstract In (V - A) theories, fermion number is broken in the presence of the 't Hooft-Polyakov magnetic monopole through the Adler-Bell-Jackiw anomaly. An exactly solvable zeroth-order approximation…

Interacting Topological Superconductors and possible Origin of $16n$ Chiral Fermions in the Standard Model

- Physics
- 2014

Motivated by the observation that the Standard Model of particle physics (plus a right-handed neutrino) has precisely 16 Weyl fermions per generation, we search for $(3+1)$-dimensional chiral…

Symmetries and Strings in Field Theory and Gravity

- Physics
- 2011

We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of Zp gauge theories shows…

Majorana fermions, exact mapping between quantum impurity fixed points with four bulk fermion species, and solution of the “unitarity puzzle”

- Physics
- 1997

Abstract Several quantum impurity problems with four flavors of bulk fermions have zero temperature fixed points that exhibit non-Fermi liquid behavior. These include the two-channel Kondo effect,…

REFLECTIONS ON MIRROR FERMIONS

- Physics
- 1984

Abstract The survival principle is modified in a manner suggested by unified theories, which generally leave relic discrete symmetries, in addition to the SU(3) × SU(2) × U(1) gauge symmetry,…

BPS kinks in the Gross-Neveu model

- Physics
- 2001

We find the exact spectrum and degeneracies for the Gross-Neveu model in two dimensions. This model describes N interacting Majorana fermions; it is asymptotically free, and has dynamical mass…

Parity doubling among the baryons

- Physics
- 2006

Abstract We study the evidence for and possible origins of parity doubling among the baryons. First we explore the experimental evidence, finding a significant signal for parity doubling in the…