[Paper Review] Massive torsion modes from Adler-Bell-Jackiw and scaling anomalies

Lay Nam Chang, Chopin Soo|ArXiv.org|May 1, 1999

Quantum, superfluid, helium dynamics1 references3 citations

TL;DR

This paper demonstrates that axial torsion and torsion trace modes acquire mass due to quantum anomalies—specifically the Adler-Bell-Jackiw (ABJ) and scaling anomalies—when regularization introduces a mass scale. The non-transverse vacuum polarization tensors of these modes lead to mass generation at the regulator scale, explaining their absence in experiments and offering a mechanism for CPT violation in chiral gravity models.

ABSTRACT

Regularization of quantum field theories introduces a mass scale which breaks axial rotational and scaling invariances. We demonstrate from first principles that axial torsion and torsion trace modes have non-transverse vacuum polarization tensors, and become massive as a result. The underlying reasons are similar to those responsible for the Adler-Bell-Jackiw (ABJ) and scaling anomalies. Since these are the only torsion components that can couple minimally to spin 1/2 particles, the anomalous generation of masses for these modes, naturally of the order of the regulator scale, may help to explain why torsion and its associated effects, including CPT violation in chiral gravity, have so far escaped detection. As a simpler manifestation of the reasons underpinning the ABJ anomaly than triangle diagrams, the vacuum polarization demonstration is also pedagogically useful.

Motivation & Objective

• To explain why torsion modes, particularly axial and trace components, remain undetected despite their theoretical presence in chiral gravity.
• To identify the quantum anomaly mechanisms responsible for the spontaneous mass generation of torsion modes.
• To establish a connection between the ABJ anomaly and the emergence of massive torsion modes through vacuum polarization.
• To provide a pedagogical alternative to triangle diagram methods for understanding anomalies in quantum field theory.
• To clarify the role of regularization-induced mass scales in breaking axial and scaling symmetries, leading to massive torsion modes.

Proposed method

• Analyzes vacuum polarization tensors of torsion fields in the presence of regularization, which explicitly breaks axial and scaling symmetries.
• Applies the framework of the Adler-Bell-Jackiw anomaly to torsion fields, showing that non-transverse components lead to mass generation.
• Uses the scaling anomaly as a complementary mechanism to explain mass generation for torsion trace modes.
• Derives the structure of the vacuum polarization tensor for axial and trace torsion components, showing their non-transverse nature.
• Establishes that the mass scale of the generated modes is naturally of the order of the regularization scale.
• Compares the mechanism to the standard ABJ anomaly, using vacuum polarization instead of triangle diagrams for conceptual clarity.

Experimental results

Research questions

• RQ1 Why do axial torsion and torsion trace modes remain undetected in experiments despite their theoretical existence?
• RQ2 What quantum anomaly mechanism leads to the mass generation of torsion modes in chiral gravity?
• RQ3 How does the regularization scale influence the mass of torsion modes through symmetry breaking?
• RQ4 In what way is the vacuum polarization tensor of torsion fields responsible for non-transverse contributions and mass generation?
• RQ5 Can the ABJ and scaling anomalies be extended to explain mass generation in torsion fields, analogous to their role in gauge theories?

Key findings

• Axial torsion and torsion trace modes acquire mass due to non-transverse vacuum polarization tensors induced by quantum anomalies.
• The mass generation mechanism is rooted in the Adler-Bell-Jackiw and scaling anomalies, which arise from regularization breaking axial and scaling symmetries.
• The generated masses are naturally of the order of the regularization scale, consistent with quantum field theory expectations.
• These modes are the only torsion components that can couple minimally to spin-1/2 fermions, explaining their potential role in CPT violation.
• The mechanism provides a simpler, vacuum polarization-based explanation of anomalies than traditional triangle diagrams.
• The results offer a natural explanation for the non-observation of torsion effects in current experiments, as the modes are massive and suppressed at low energies.