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We study 2-dimensional Logarithmic Galilean Conformal Algebra (LGCA) by mak-
ing use of a contraction of Topologically Massive Gravity at critical point. We observe
that using a naive contraction at the critical point fails to give a well defined theory,
though contracting the theory while we are approaching the critical point leads to a
well behaved expression for two point functions of the energy-momentum tensors of
LGCA.
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