Abstract
We construct a free field realization of an extension of the BMS algebra in 2+1 dimensional space-time. Besides the supertranslations and superrotations, the extension contains an infinite set of superdilatations. We also comment the difficulties that appear when trying to extend the algebra to that of the full conformal group.
Highlights
There is a renewed interest in the BMS group [1, 2]
When this paper was being completed a paper [17] has appeared that constructs a generalization of the BMS symmetry by studying asymptotic symmetries of a gravitational theory
See for example [13, 19, 20], one can construct the generators of the conformal algebra (Poincaré, dilatations and special conformal transformations) as integrals over the space of local densities depending on the field and their space-time derivatives
Summary
There is a renewed interest in the BMS group [1, 2]. One of the interest is to deduce Weinberg’s soft graviton theorems [3] as the Ward identities of BMS supertranslations [4, 5, 6, 7]. In the case of three dimensions the BMS algebra has been studied [9, 10] with supertranslations and superrotations [11]. A canonical realization of the bms algebra with supertranslations and superrotations associated to a free Klein-Gordon (KG) field in 2 + 1 dimensions, for both massive and massless fields, was studied in [12]. When this paper was being completed a paper [17] has appeared that constructs a generalization of the BMS symmetry by studying asymptotic symmetries of a gravitational theory. Their algebra, that includes superdilatations, agrees with our canonical results.
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