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arXiv · 1311.3457

Logarithmic Exotic Conformal Galilean Algebras

Malte Henkel·Ali Hosseiny·Shahin Rouhani
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Abstract

Logarithmic representations of the conformal Galilean algebra (CGA) and the Exotic Conformal Galilean algebra ({\sc ecga}) are constructed. This can be achieved by non-decomposable representations of the scaling dimensions or the rapidity indices, specific to conformal galilean algebras. Logarithmic representations of the non-exotic CGA lead to the expected constraints on scaling dimensions and rapidities and also on the logarithmic contributions in the co-variant two-point functions. On the other hand, the {\sc ecga} admits several distinct situations which are distinguished by different sets of constraints and distinct scaling forms of the two-point functions. Two distinct realisations for the spatial rotations are identified as well. The first example of a reducible, but non-decomposable representation, without logarithmic terms in the two-point function is given.

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Malte Henkel, Ali Hosseiny, Shahin Rouhani. 2013-11-14. Logarithmic Exotic Conformal Galilean Algebras. https://doi.org/10.1016/j.nuclphysb.2013.12.009

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