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• W4311990274 abstract "An analogous ``strong $CP$ problem'' is identified in a toy model in two-dimensional spacetime: a general $1+1mathrm{d}$ Abelian U(1) anomaly free chiral fermion and chiral gauge theory with a generic theta instanton term $frac{ensuremath{theta}}{2ensuremath{pi}}ensuremath{int}F$. 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 $1+1mathrm{d}$: Why can the $overline{ensuremath{theta}}$ angle (including the effect of $ensuremath{theta}$ 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 $1+1mathrm{d}$ toy model mimics several features of the $3+1mathrm{d}$ Standard Model: chiral matter content, confinement, and Anderson-Higgs 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 $1+1mathrm{d}$ U(1) symmetric anomaly free chiral fermion/gauge theory (e.g., Weyl fermions with ${3}_{L}text{ensuremath{-}}{4}_{L}text{ensuremath{-}}{5}_{R}text{ensuremath{-}}{0}_{R}$ U(1) charges) is demonstrated in detail. As an analogy to the superfluid-insulator or order-disorder quantum phase transition, in contrast to the conventional Peccei-Quinn solution sitting in the (quasi-long-range-order)-superfluid ordered phase, our solution is in the SMG insulator disordered phase." @default.
• W4311990274 created "2023-01-03" @default.
• W4311990274 creator A5088718265 @default.
• W4311990274 date "2022-12-16" @default.
• W4311990274 modified "2023-09-30" @default.
• W4311990274 title "<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>C</mml:mi><mml:mi>T</mml:mi></mml:math> or <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>P</mml:mi></mml:math> problem and symmetric gapped fermion solution" @default.
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• W4311990274 doi "https://doi.org/10.1103/physrevd.106.125007" @default.
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