Trace anomaly and massless scalar degrees of freedom in gravity

Journal Article · Sun Feb 15 04:00:00 EST 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.79.045014· OSTI ID:21260028

Giannotti, Maurizio; Mottola, Emil ^[1]

---

1. Theoretical Division, T-2, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

The trace anomaly of quantum fields in electromagnetic or gravitational backgrounds implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. Considering first the axial anomaly and using QED as an example, we compute the full one-loop triangle amplitude of the fermionic stress tensor with two current vertices, <T{sup {mu}}{sup {nu}}J{sup {alpha}}J{sup {beta}}>, and exhibit the scalar pole in this amplitude associated with the trace anomaly, in the limit of zero electron mass m{yields}0. To emphasize the infrared aspect of the anomaly, we use a dispersive approach and show that this amplitude and the existence of the massless scalar pole is determined completely by its ultraviolet finite terms, together with the requirements of Poincare invariance of the vacuum, Bose symmetry under interchange of J{sup {alpha}} and J{sup {beta}}, and vector current and stress-tensor conservation. We derive a sum rule for the appropriate positive spectral function corresponding to the discontinuity of the triangle amplitude, showing that it becomes proportional to {delta}(k{sup 2}) and therefore contains a massless scalar intermediate state in the conformal limit of zero electron mass. The effective action corresponding to the trace of the triangle amplitude can be expressed in local form by the introduction of two scalar auxiliary fields which satisfy massless wave equations. These massless scalar degrees of freedom couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects.

• OSTI ID: 21260028
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 79; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
DEGREES OF FREEDOM
ELECTRONS
GRAVITATION
GRAVITATIONAL FIELDS
INTERMEDIATE STATE
MASS
MASSLESS PARTICLES
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
SCATTERING
SPECTRAL FUNCTIONS
STRESSES
SUM RULES
SYMMETRY
ULTRAVIOLET RADIATION
VECTOR CURRENTS
WAVE EQUATIONS