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Symmetric Mass Generation (2204.14271v1)

Published 29 Apr 2022 in cond-mat.str-el, hep-lat, hep-ph, hep-th, and quant-ph

Abstract: The most well-known mechanism for fermions to acquire a mass is the Nambu-Goldstone-Anderson-Higgs mechanism, i.e. after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group. This new mechanism is generally referred to as the "Symmetric Mass Generation (SMG)." It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes current numerical results, introduces a novel unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and overviews various features and applications of SMG.

Citations (55)

Summary

  • The paper introduces a novel mechanism where fermions acquire mass without breaking symmetry, challenging traditional Higgs approaches.
  • It employs numerical methods like DMRG and Monte Carlo simulations to confirm the SMG phase across various spacetime dimensions.
  • The study outlines unconventional quantum phase transitions with implications for lattice regularization in chiral gauge theories.

An Overview of Symmetric Mass Generation

The paper "Symmetric Mass Generation" by Juven Wang and Yi-Zhuang You provides a comprehensive exploration of a novel mechanism for fermions to acquire mass without involving symmetry breaking, termed Symmetric Mass Generation (SMG). Unlike the well-known Higgs mechanism, which relies on spontaneous symmetry breaking, SMG offers a pathway where fermions can obtain mass while preserving the symmetry structure.

Core Concepts and Connections

SMG connects deeply with modern theoretical constructs in condensed matter and high-energy physics, including topological insulators and superconductors, symmetry-protected topological (SPT) states, and quantum anomalies. It provides insights into the lattice regularization of chiral gauge theories, an enduring problem in gauge theory discretization.

Anomaly-Free Mass Generation

Central to the SMG is the recognition that fermions can be massed without breaking symmetries as long as the symmetry group is anomaly free. An anomaly-free symmetry group permits the construction of an interacting fermion system that respects the symmetry, even as it opens an excitation gap.

Numerical Evidences and Methods

The discussion includes substantial numerical evidence supporting the existence of SMG phases across diverse spacetime dimensions. Methods such as density matrix renormalization group (DMRG) and Monte Carlo simulations have played vital roles in verifying the SMG phase's realizability. The persistence of a fermionic excitation gap without long-range fermion bilinear order substantiate the SMG mechanism.

Symmetric Mass Generation Transitions

Crucially, the SMG transition can be direct and continuous, implying an unconventional quantum phase transition. This transition defies the Landau-Ginzburg-Wilson paradigm, exhibiting characteristics of a deconfined quantum critical point. At this juncture, fermionic matter appears to undergo fractionalization, where gapless partons emerge transiently.

Theoretical Frameworks

The paper outlines theoretical advancements in understanding SMG, highlighting frameworks such as parton-Higgs and s-confinement mechanisms. It emphasizes the importance of Yukawa-like couplings and symmetry extension constructions in describing the symmetry-preserving gap generation.

The Future and Implications

The notion of SMG expands potential applications beyond condensed matter systems, suggesting implications in regularizing the lattice Standard Model. The paper discusses possible SMG utilization in eliminating fermion doublers in chiral gauge theories, an endeavor to supersede traditional mirror fermion models.

Conclusion

Overall, the exploration of SMG offers a groundbreaking perspective on mass generation, challenging conventional paradigms and opening new theoretical and numerical avenues. As SMG stands at the intersection of condensed matter and particle physics, further advancements in this domain may shed light on fundamental physics' longstanding conundrums, possibly influencing future model-building in both fields.

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