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The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern–Simons Theory

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Abstract

In the context of Chern–Simons (CS) Theory, a subspace separation method for the Lagrangian is proposed. The method is based on the iterative use of the Extended Cartan Homotopy Formula, and allows one to (1) separate the action in bulk and boundary contributions, and (2) systematically split the Lagrangian in appropriate reflection of the subspace structure of the gauge algebra. In order to apply the method, one must regard CS forms as a particular case of more general objects known as transgression forms. Five-dimensional CS Supergravity is used as an example to illustrate the method.

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Authors and Affiliations

  1. Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333, Munich, Germany

    Fernando Izaurieta & Eduardo Rodríguez

  2. Departament de Física Teòrica, Universitat de València, 46100, Burjassot, València, Spain

    Fernando Izaurieta, Eduardo Rodríguez & Patricio Salgado

  3. Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Fernando Izaurieta, Eduardo Rodríguez & Patricio Salgado

Authors
  1. Fernando Izaurieta
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  2. Eduardo Rodríguez
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  3. Patricio Salgado
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Correspondence to Fernando Izaurieta.

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Izaurieta, F., Rodríguez, E. & Salgado, P. The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern–Simons Theory. Lett Math Phys 80, 127–138 (2007). https://doi.org/10.1007/s11005-007-0148-0

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  • DOI: https://doi.org/10.1007/s11005-007-0148-0

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