CT or P Problem and Symmetric Gapped Fermion Solution

• URL: http://arxiv.org/abs/2207.14813v3
• Date: Sat, 14 Jan 2023 02:02:02 GMT
• Title: CT or P Problem and Symmetric Gapped Fermion Solution
• Authors: Juven Wang
• Abstract summary: We show that a 1+1d abelian U(1) anomaly-free chiral fermion/gauge theory can be solved by a Symmetric Mass Generation mechanism. One solution replaces some chiral fermion's Higgs-induced mean-field mass with SMG-induced non-mean-field mass. Another solution enriches this toy model by introducing several new physics beyond the Standard Model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: An analogous "Strong CP problem" is identified in a toy model in 2-dimensional spacetime: a general 1+1d abelian U(1) anomaly-free chiral fermion and chiral gauge theory with a generic theta instanton term $\frac{\theta}{2 \pi} \int F$. The theta term alone violates the charge-conjugation-time-reversal CT and the parity P discrete symmetries. The analogous puzzle here is the CT or P problem in 1+1d: Why can the $\bar{\theta}$ angle (including the effect of $\theta$ and the complex phase of a mass matrix) be zero or small for a natural reason? We show that this CT or P problem can be solved by a Symmetric Mass Generation mechanism (SMG, namely generating a mass or energy gap while preserving an anomaly-free symmetry). This 1+1d toy model mimics several features of the 3+1d Standard Model: chiral matter content, confinement, and Anderson-Higgs-induced mass by Yukawa-Higgs term. One solution replaces some chiral fermion's Higgs-induced mean-field mass with SMG-induced non-mean-field mass. Another solution enriches this toy model by introducing several new physics beyond the Standard Model: a parity-reflection PR discrete symmetry maps between the chiral and mirror fermions as fermion doubling localized on two domain walls at high energy, and SMG dynamically generates mass to the mirror fermion while still preserving the anomaly-free chiral symmetry at an intermediate energy scale, much before the Higgs mechanism generates mass to the chiral fermion at lower energy. Without loss of generality, an arguably simplest 1+1d U(1) symmetric anomaly-free chiral fermion/gauge theory (e.g., Weyl fermions with $3_L$-$4_L$-$5_R$-$0_R$ U(1) charges) is demonstrated. As an analogy to the superfluid-insulator or order-disorder quantum phase transition, in contrast to the Peccei-Quinn solution sitting in the (quasi-long-range-order) superfluid phase, our solution is in the SMG insulator disordered phase.

Related papers

• A tractable model of monitored fermions with conserved $\mathrm{U}(1)$ charge [0.0]
  We study measurement-induced phases of free fermion systems with U(1) symmetry. We derive a field theory description for the purity and bipartite entanglement at large space and time scales.
  arXiv  Detail & Related papers  (2024-07-10T20:53:47Z)
• Interacting chiral fermions on the lattice with matrix product operator norms [37.69303106863453]
  We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice. The fermion doubling problem is circumvented by constructing a Fock space endowed with a semi-definite norm. We demonstrate that the scaling limit of the free model recovers the chiral fermion field.
  arXiv  Detail & Related papers  (2024-05-16T17:46:12Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Spectral properties of critical 1+1D Abelian-Higgs model [0.0]
  The presence of gauge symmetry in 1+1D is known to be redundant, since it does not imply the existence of dynamical gauge bosons. Recent research has revealed an unexpected phase transition when the system is discretized on the lattice.
  arXiv  Detail & Related papers  (2023-04-03T14:29:58Z)
• Strong CP Problem and Symmetric Mass Solution [0.0]
  We propose a novel solution to the Strong CP problem -- to explain why SU(3) strong force has a nearly zero theta angle $bartheta_3 simeq 0$ for the 4d Standard Model (SM) The new ingredient is Symmetric Mass Generation (SMG): symmetry-preserving mass or energy gap can be generated without breaking any symmetry $G$. The predictive signature of both SMG-based models is that some SM fermions or mirror fermions are highly interacting.
  arXiv  Detail & Related papers  (2022-12-28T18:59:51Z)
• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D [0.0]
  In (1)D topological phases, unpaired Majorana zero modes (MZMs) can arise only if the internal symmetry group $G_f$ of the ground state splits as $G_f = G_b times mathbbZf$. In contrast, (2+1)D topological superconductors (TSC) can host unpaired MZMs at defects even when $G_f$ is not of the form $G_b times mathbbZf$.
  arXiv  Detail & Related papers  (2022-10-05T18:00:00Z)
• Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model [11.191494874283313]
  We show the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless (BKT) class. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless.
  arXiv  Detail & Related papers  (2022-02-24T20:33:48Z)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)
• Non-Hermitian extension of the Nambu--Jona-Lasinio model in 3+1 and 1+1 dimensions [68.8204255655161]
  We present a non-Hermitian PT-symmetric extension of the Nambu--Jona-Lasinio model of quantum chromodynamics in 3+1 and 1+1 dimensions. We find that in both cases, in 3+1 and in 1+1 dimensions, the inclusion of a non-Hermitian bilinear term can contribute to the generated mass.
  arXiv  Detail & Related papers  (2020-04-08T14:29:36Z)
• Quantum Simulation of 2D Quantum Chemistry in Optical Lattices [59.89454513692418]
  We propose an analog simulator for discrete 2D quantum chemistry models based on cold atoms in optical lattices. We first analyze how to simulate simple models, like the discrete versions of H and H$+$, using a single fermionic atom. We then show that a single bosonic atom can mediate an effective Coulomb repulsion between two fermions, leading to the analog of molecular Hydrogen in two dimensions.
  arXiv  Detail & Related papers  (2020-02-21T16:00:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.