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  Gauging nonpolynomial algebras

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Some nonlinear theories, such as W-gravity, have lead to interest in gauging nonlinear but polynomial algebras of the form $$[t_a,t_b]=c_{ab}+f^c_{ab}t_c+V^{cd}_{ab}t_c t_d+\ldots$$
At each order of nonlinearity, a new field is associated to the generator and the algebra may be gauged in the usual fashion (see, for example https://journals.aps.org/prd/abstract/10.1103/PhysRevD.48.1768)

The quantum deformations of algebras that appear in understanding the low energy limit of quantum gravity theories, such as the kappa-Poincaré algebra $U_\kappa (\mathfrak{iso}(3,1))$, exhibit nonpolynomial nonlinearities in their commutation relations, on the other hand.

If a QFT on curved spacetime is a first approximation, and that on noncommutative spacetime a second, an interest would be in studying the resulting gauge theory as a "third" or higher approximation to quantum gravity, but how can such an algebra be gauged?

One possibility would be to simply Taylor expand the nonlinearities and gauge the resulting theory, if the intoduction of infinitely many new fields and potential issues with nonanalytic functions is acceptable, but is this the only known method?

asked Jul 2, 2022 in Mathematics by Quantumnessie (90 points) [ revision history ]

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