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Anomalies, Anomalous U(1)'s and generalized Chern-Simons terms

P. Anastasopoulos, M. Bianchi, E. Dudas, E. Kiritsis

TL;DR

The paper develops a comprehensive framework for anomalous U(1) factors in 4D field theory and string orientifolds, focusing on generalized anomaly cancellation through axions, Stückelberg masses, and generalized Chern-Simons terms. It derives the most general low-energy effective action, computes disk-induced axion and GCS couplings in orientifold models, and performs explicit string-theory and field-theory analyses of three-gauge-boson amplitudes, including the decoupling of heavy fermions. A key finding is that gauge-invariant GCS terms are generically nonzero and scheme-dependent, while axionic couplings remain UV-finite and observable combinations are scheme-independent. The work also explores collider-relevant signatures such as rare decays of TeV-scale Z' bosons and concludes that, at low energy, stringy anomalous U(1)s and purely field-theoretic anomalous U(1)s are not qualitatively distinguished, motivating further investigation into additional discriminants.

Abstract

A detailed analysis of anomalous U(1)'s and their effective couplings is performed both in field theory and string theory. It is motivated by the possible relevance of such couplings in particle physics, as well as a potential signal distinguishing string theory from other UV options. The most general anomaly related effective action is analyzed and parameterized. It contains Stuckelberg, axionic and Chern-Simons-like couplings. It is shown that such couplings are generically non-trivial in orientifold string vacua and are not in general fixed by anomalies. A similar analysis in quantum field theories provides similar couplings. The trilinear gauge boson couplings are also calculated and their phenomenological relevance is advocated. We do not find qualitative differences between string and field theory in this sector.

Anomalies, Anomalous U(1)'s and generalized Chern-Simons terms

TL;DR

The paper develops a comprehensive framework for anomalous U(1) factors in 4D field theory and string orientifolds, focusing on generalized anomaly cancellation through axions, Stückelberg masses, and generalized Chern-Simons terms. It derives the most general low-energy effective action, computes disk-induced axion and GCS couplings in orientifold models, and performs explicit string-theory and field-theory analyses of three-gauge-boson amplitudes, including the decoupling of heavy fermions. A key finding is that gauge-invariant GCS terms are generically nonzero and scheme-dependent, while axionic couplings remain UV-finite and observable combinations are scheme-independent. The work also explores collider-relevant signatures such as rare decays of TeV-scale Z' bosons and concludes that, at low energy, stringy anomalous U(1)s and purely field-theoretic anomalous U(1)s are not qualitatively distinguished, motivating further investigation into additional discriminants.

Abstract

A detailed analysis of anomalous U(1)'s and their effective couplings is performed both in field theory and string theory. It is motivated by the possible relevance of such couplings in particle physics, as well as a potential signal distinguishing string theory from other UV options. The most general anomaly related effective action is analyzed and parameterized. It contains Stuckelberg, axionic and Chern-Simons-like couplings. It is shown that such couplings are generically non-trivial in orientifold string vacua and are not in general fixed by anomalies. A similar analysis in quantum field theories provides similar couplings. The trilinear gauge boson couplings are also calculated and their phenomenological relevance is advocated. We do not find qualitative differences between string and field theory in this sector.

Paper Structure

This paper contains 16 sections, 226 equations, 3 figures.

Table of Contents

  1. Introduction and conclusions
  2. The general low-energy anomaly-related effective action
  3. Anomalies and anomalous U(1)'s in orientifold models
  4. General formulae for the disk couplings of axions to gauge bosons
  5. String derivation of anomalous couplings
  6. Direct computation
  7. The susy analog: $\gamma\to 2\tilde{\gamma}$
  8. Heavy fermions and low-energy effective actions
  9. Three gauge boson amplitudes
  10. Triangle anomalies and regularization dependence
  11. Basis changes
  12. Explicit Orientifold Examples
  13. $Z_6$ orbifold
  14. $Z_6'$ orbifold
  15. Computation of anomaly diagrams
  16. ...and 1 more sections

Figures (3)

  • Figure 1: The first diagram is one of the twelve diagrams which contribute to the GCS terms. The second is one of the six diagrams which contribute to the axionic couplings. Both are obtained by integrating out heavy fermions.
  • Figure 2: We denote by $\blacklozenge$/$\lozenge$ the fixed points on each torus, which are invariant/related to others by the $Z_6$ action.
  • Figure 3: We denote by $\blacklozenge$/$\lozenge$ the fixed points on each torus, which are invariant/related to others by the $Z_6'$ action.