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arXiv · 2201.12629

Galilean Gauge Theories from Null Reductions

Arjun Bagchi·Rudranil Basu·Minhajul Islam·Kedar S. Kolekar·Aditya Mehra
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Abstract

The procedure of null reduction provides a concrete way of constructing field theories with Galilean invariance. We use this to examine Galilean gauge theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime dimensions 3 and 4. Different non-relativistic conformal symmetries arise in these contexts: Schr{\"o}dinger symmetry in $d=3$ and Galilean conformal symmetry in $d=4$. A canonical analysis further reveals that the symmetries enhance to their infinite dimensional versions in phase space and pick up central extensions. In addition, for the Abelian theory, we discuss non-relativistic electro-magnetic duality in $d=3$ and its difference with the $d=4$ version. We also mention some quantum aspects for both Abelian and non-Abelian theories.

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Arjun Bagchi, Rudranil Basu, Minhajul Islam, Kedar S. Kolekar, Aditya Mehra. 2022-01-29. Galilean Gauge Theories from Null Reductions. https://doi.org/10.1007/jhep04(2022)176

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