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.
We study different features of 3D non-relativistic CFT using gravity description. As the corresponding gravity solution can be embedded into the type IIB string theory, we study semi-classical closed/open strings in this background. In particular we consider folded rotating and circular pulsating closed strings where we find the anomalous dimension of the dual operators as a function of their quantum numbers. We also consider moving open strings in this background which can be used to compute the drag force. In particular we find that for slowly moving particles, the energy is lost exponentially and the characteristic time is given in terms of the temperature, while for fast moving particles the energy loss goes as inverse of the time and the characteristic time is independent of the temperature.Dedicated to Reza Mansouri on the occasion of his 60th birthday
We extend the nonrelativistic AdS/CFT correspondence to the fermionic fields. In particular, we study the two point function of a fermionic operator in nonrelativistic CFTs by making use of a massive fermion propagating in geometries with Schrödinger group isometry. Although the boundary of the geometries with Schrödinger group isometry differ from that in AdS geometries where the dictionary of AdS/CFT is established, using the general procedure of AdS/CFT correspondence, we see that the resultant two point function has the expected form for fermionic operators in nonrelativistic CFTs, though a nontrivial regularization may be needed.
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