C-P-T Fractionalization

Wang, Juven

doi:10.48550/arxiv.2109.15320

Cited by 3 publications

(7 citation statements)

References 45 publications

(74 reference statements)

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“…Here, a (0 + 1)D theory has no parity P but only at most time-reversal T, and Majorana fermion has no charge conjugation C symmetry; so only the T fractionalization is found. In higher dimensions, the common theme along the direction of this phenomenon is the C-P-T fractionalization [182].…”

Section: Symmetry Extensionmentioning

confidence: 99%

Symmetric Mass Generation

Wang

You

2022

Symmetry

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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, also applicable to chiral fermions with anomaly-free chiral symmetries. 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 the current numerical results, introduces an unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and presents an overview of various features and applications of SMG.

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Section: Symmetry Extensionmentioning

confidence: 99%

Symmetric Mass Generation

Wang

You

2022

Symmetry

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“…3. Discrete R, C, P = PR and T = TR symmetry transformations: Here we follow the systematic analysis on the C-P-T symmetries together with the fermion parity Z F 2 in [24]. In particular, we generalize the previous C-P-T transformation in (2) to include the full theory with two domain walls.…”

Section: Fermion Doubling -Chiral Fermion and Mirror Fermion Spectramentioning

confidence: 99%

“…Notice that the full parent theory has the generalized P and T symmetries that contain not merely the ordinary P and T symmetries but also the R symmetry. Namely, we have already defined the ordinary PR ≡ P as the generalized P in (24), and the ordinary TR ≡ T as the generalized T in (25).…”

Section:   mentioning

confidence: 99%

“…II, we define the analogous problem called CT or P problem in this 1+1d toy model with chiral fermions and with a seemly generic nonzero θ term, written as θ 2π F for some abelian field strength F . Under the standard unitary C, P, and anti-unitary T active transformations on the fields (e.g., [24]), the two components of 1+1d abelian gauge field A = (A 0 , A 1 ) and its field strength F 01 at the spacetime coordinates x µ = (x 0 , x 1 ) = (t, x) are transformed as Z C 2 : A 0 (t, x) → −A 0 (t, x), A 1 (t, x) → −A 1 (t, x), F 01 (t, x) → −F 01 (t, x). Z P 2 : A 0 (t, x) → +A 0 (t, −x), A 1 (t, x) → −A 1 (t, −x), F 01 (t, x) → −F 01 (t, −x).…”

Section: Introduction and The Problemmentioning

confidence: 99%

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CT or P Problem and Symmetric Gapped Fermion Solution

Wang¹

2022

Preprint

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An analogous "Strong CP problem" is identified in a toy model in two dimensional spacetime: a general 1+1d abelian U(1) anomaly-free chiral fermion and chiral gauge theory with a generic theta instanton term θ 2π 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 θ angle (including the effect of θ 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 contents, confinement, and Anderson-Higgs mass by Yukawa-Higgs term. One solution enriches this toy model by introducing several new physics beyond the Standard Model: a parity-reflection PR discrete symmetry mapping between the chiral and mirror fermions as fermion doubling localized on two domain walls at a 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 in at a lower energy. Another solution no longer requires the mirror fermion sector, but directly replaces the chiral fermion's Higgs mass to the SMG mass. Without loss of generality, an arguably simplest 1+1d U(1) symmetric 3L-4L-5R-0R anomaly-free chiral fermion and chiral gauge theory is demonstrated in detail.

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“…Here a (0+1)D theory has no parity P but only at most time-reversal T , and Majorana fermion has no charge conjugation C symmetry; so only the T fractionalization is found. In higher dimensions, the common theme along the direction of this phenomenon is the C-P -T fractionalization [171].…”

Section: No Table VIII Summary Of the Symmetry-extension Construction...mentioning

confidence: 99%

Symmetric Mass Generation

Wang,

You

2022

Preprint

Self Cite

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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.

show abstract

C-P-T Fractionalization

Cited by 3 publications

References 45 publications

Symmetric Mass Generation

Symmetric Mass Generation

CT or P Problem and Symmetric Gapped Fermion Solution

Symmetric Mass Generation

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