Abstract
In this work, we propose a four-dimensional gauged Wess-Zumino-Witten model, obtained as a dimensional reduction from a transgression field theory invariant under the \( \mathcal{N} \) = 1 Poincaré supergroup. For this purpose, we consider that the two gauge connections on which the transgression action principle depends are given by linear and non-linear realizations of the gauge group respectively. The field content of the resulting four-dimensional theory is given by the gauge fields of the linear connection, in addition to a set of scalar and spinor multiplets in the same representation of the gauge supergroup, which in turn, correspond to the coordinates of the coset space between the gauge group and the five-dimensional Lorentz group. We then decompose the action in terms of four-dimensional quantities and derive the corresponding equations of motion. We extend our analysis to the non- and ultra- relativistic regimes.
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Acknowledgments
The authors would like to thank P. Salgado for enlightening discussions. P.C. acknowledges financial support from the National Agency for Research and Development (ANID) through Fondecyt grants No. 1211077 and 11220328. F.I. acknowledges financial support from ANID through Fondecyt grant 1211219. E.R. acknowledges financial support from ANID through SIA grant No. SA77210097 and Fondecyt grant No. 11220486 and 1231133. P.C. and E.R. would like to thank to the Dirección de Investigación and Vicerectoría de Investigación of the Universidad Católica de la Santísima Concepción, Chile, for their constant support. S.S. acknowledges financial support from Universidad de Tarapacá, Chile.
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Concha, P., Izaurieta, F., Rodríguez, E. et al. Four dimensional topological supergravities from transgression field theory. J. High Energ. Phys. 2024, 248 (2024). https://doi.org/10.1007/JHEP05(2024)248
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DOI: https://doi.org/10.1007/JHEP05(2024)248