On AdS/CFT of Galilean Conformal Field Theories

Abstract

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.

Flat-space energy-momentum tensor from BMS/GCA correspondence

“…However, the combinations similar to (2.18), i.e. 11) are finite in the flat limit. We define the energy-momentum tensor of flat-space ,T ij , by 12) JHEP03 (2014)005 where light-cone coordinates for flat spacetime,x ± , are given byx ± = u/G±φ.…”

“…Thus one can write an expansion for them in terms of positive powers of G/ℓ. If we demand that 11) are well-defined, the coefficients of (G/ℓ) 0 in f n andf −n must be the same. Then, it is not difficult to check that 12) where θ and χ are arbitrary functions.…”

“…If one considers a two dimensional CFT and takes its non-relativistic limit by contracting one of the coordinates, the contracted algebra is exactly (2.17) [10][11][12][13]. In this context the algebra (2.17) is called Galilean conformal algebra due to appearance of Galilean subalgebra.…”

“…The observation of [1,2] was that BMS algebra is isomorphic Galilean conformal algebra (GCA) which is a result of contraction of conformal algebra [10][11][12][13]. This connection dubbed the BMS/GCA correspondence was studied carefully in [3] where it was shown that in order to have a well-defined correspondence at the level of centrally extended algebras, at the level of spacetime, the time direction must be contracted in the CFT and the resultant theory is an ultra-relativistic field theory.…”

Aspects of infinite dimensional ℓ-super Galilean conformal algebra

“…The same algebra appears in non-relativistic analogue of AdS/CFT correspondence and called infinite dimensional Galilean conformal algebra (GCA) [10,11,12,13,14,15] (see also [16,17,18,19,20,21] for some varieties of the algebra). The same algebra also appears in cosmological topologically massive gravity [22,2] and bosonic string theory [23,24].…”