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We study a new contraction of a $d+1$ dimensional relativistic
conformal algebra where $n+1$ directions remain unchanged. For
$n=0,1$ the resultant algebras admit infinite dimensional extension
containing one and two copies of Virasoro algebra, respectively. For
$n> 1$ the obtained algebra is finite dimensional containing an
$so(2,n+1)$ subalgebra. The gravity dual is provided by taking a
Newton-Cartan like limit of the Einstein's equations of AdS space
which singles out an $AdS_{n+2}$ spacetime. The infinite dimensional
extension of $n=0,1$ cases may be understood from the fact that the
dual gravities contain $AdS_2$ and $AdS_3$ factor, respectively. We
also explore how the AdS/CFT correspondence works for this case
where we see that the main role is playing by $AdS_{n+2}$ base
geometry.
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