Abstract

We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory. This is illustrated for Yang-Mills theory, gravity on flat and cosmological backgrounds and for the massless sector of closed string theory. The perturbation lemma yields an algorithmic procedure to determine the higher corrections of the gauge invariant variables and the action in terms of these.

Highlights

  • Philosophically this seems to be quite different from fixing a gauge, our results establish an operational equivalence with gauge fixing

  • In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory

  • While a loss of manifest Lorentz invariance may be too much to ask for in particle physics applications, in cosmology the situation is different: there is a preferred time, so that the space/time split needed for the definition of Bardeen variables respects the symmetries of the FLRW backgrounds, making these variables ideally suited for cosmological perturbation theory

Read more

Summary

Gauge invariant spin-1 and spin-2 theory

We illustrate the general approach for two simple theories: Maxwell’s theory and gravity linearized about flat space. We explain the formulation of these theories in terms of chain complexes, introduce gauge invariant variables and establish the notion of homotopy transfer

Maxwell’s theory
Gravity on flat space
Homotopy interpretation of linearized gravity
Gauge invariant closed string theory
Linearized double field theory on flat backgrounds
Chain complex of double field theory
Homotopy interpretation
Homotopy transfer
General theory
Homotopy transfer and the homological perturbation lemma
Yang-Mills theory
Cosmological perturbation theory
Gravity around FLRW
Quadratic action in terms of Bardeen variables
Findings
Discussion and outlook

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.