[Paper Review] CPT violation: mechanism and phenomenology

F. R. Klinkhamer|ArXiv.org|Oct 15, 2001

Noncommutative and Quantum Gravity Theories5 references3 citations

TL;DR

This paper proposes a mechanism for CPT violation in chiral gauge theories on spacetimes with nontrivial topology, such as ℝ³×S¹, where quantum effects induce a CPT-odd modification of Maxwell theory via a Chern-Simons-like term. The key result is that CPT violation arises from the interplay of chiral fermions, gauge interactions, and compactified spatial dimensions, leading to observable effects in cosmology, such as birefringence in the cosmic microwave background.

ABSTRACT

A new mechanism for T and CPT violation is reviewed, which relies on chiral fermions, gauge interactions and nontrivial spacetime topology. Also discussed are the possible effects on the propagation of electromagnetic waves in vacuo, in particular for the cosmic microwave background radiation.

Motivation & Objective

• To investigate whether CPT invariance can be violated in local relativistic quantum field theories under specific conditions.
• To explore the role of nontrivial spacetime topology and chiral gauge theories in generating CPT violation.
• To examine the phenomenological consequences of CPT-violating modifications to Maxwell theory, particularly for long-baseline electromagnetic wave propagation.
• To establish the consistency of the CPT-violating mechanism with microcausality and unitarity in quantum field theory.
• To provide a mechanism for CPT violation that is not tied to quantum gravity or string theory, but arises from topological and fermionic effects.

Proposed method

• Analyzes a 4D chiral gauge theory with SO(10) gauge group and three generations of left-handed 16-plet fermions on a spacetime with one compactified spatial dimension (ℝ³×S¹).
• Derives the effective action using perturbative methods in quantum field theory, showing the emergence of a CPT-odd Chern-Simons-like term in the effective Maxwell theory.
• Uses two-dimensional Abelian chiral gauge theories on a torus (T²) as exactly solvable models to demonstrate the CPT anomaly, with periodic boundary conditions on fermions.
• Computes the effective action up to order h⁶, showing a nonvanishing CPT-odd term that changes sign under CPT transformation.
• Applies the Coulomb gauge to the Maxwell–Chern–Simons theory and computes commutators of electric and magnetic fields to assess microcausality.
• Analyzes the behavior of the commutator function D_MCS(x) for spacelike separations, confirming microcausal structure despite Lorentz violation.

Experimental results

Research questions

• RQ1 Can CPT invariance be violated in a local relativistic quantum field theory without invoking quantum gravity or string theory?
• RQ2 What is the role of spacetime topology and chiral fermions in generating CPT violation?
• RQ3 How does the CPT-odd modification of Maxwell theory affect the propagation of electromagnetic waves over cosmological distances?
• RQ4 Is the CPT-violating theory microcausal and unitary, particularly in the presence of a Chern-Simons term?
• RQ5 Can the CPT anomaly be observed indirectly through cosmological signals such as the cosmic microwave background radiation?

Key findings

• CPT violation arises in chiral gauge theories on spacetimes with nontrivial topology, such as ℝ³×S¹, due to quantum effects involving chiral fermions and gauge interactions.
• The effective theory develops a CPT-odd Chern-Simons-like term with a mass scale m_G ≈ 10⁻³⁵ eV/c², dependent on the compactification size L and the gauge coupling α_G.
• The CPT anomaly does not occur in simply connected spaces like ℝ×S³ or in vector-like theories such as QED on ℝ³×S¹, highlighting the necessity of both chirality and nontrivial topology.
• The modified Maxwell theory leads to birefringence in vacuum, which could be detected in the cosmic microwave background radiation via polarization changes over large distances.
• Microcausality is preserved for the physical electric and magnetic fields in the spacelike Chern–Simons term, despite Lorentz violation, due to the absence of pathological poles in the field commutators.
• The CPT-odd term is generated perturbatively in 4D chiral gauge theories and confirmed in exactly solvable 2D models, with a nonvanishing complex coefficient that changes sign under CPT, confirming CPT violation.