20 research outputs found
Holographic Renormalization for z=2 Lifshitz Space-Times from AdS
Lifshitz space-times with critical exponent z=2 can be obtained by
dimensional reduction of Schroedinger space-times with critical exponent z=0.
The latter space-times are asymptotically AdS solutions of AdS gravity coupled
to an axion-dilaton system and can be uplifted to solutions of type IIB
supergravity. This basic observation is used to perform holographic
renormalization for 4-dimensional asymptotically z=2 locally Lifshitz
space-times by Scherk-Schwarz dimensional reduction of the corresponding
problem of holographic renormalization for 5-dimensional asymptotically locally
AdS space-times coupled to an axion-dilaton system. We can thus define and
characterize a 4-dimensional asymptotically locally z=2 Lifshitz space-time in
terms of 5-dimensional AdS boundary data. In this setup the 4-dimensional
structure of the Fefferman-Graham expansion and the structure of the
counterterm action, including the scale anomaly, will be discussed. We find
that for asymptotically locally z=2 Lifshitz space-times obtained in this way
there are two anomalies each with their own associated nonzero central charge.
Both anomalies follow from the Scherk--Schwarz dimensional reduction of the
5-dimensional conformal anomaly of AdS gravity coupled to an axion-dilaton
system. Together they make up an action that is of the Horava-Lifshitz type
with nonzero potential term for z=2 conformal gravity.Comment: 32 pages, v2: modified discussion of the central charge
Scaling Cosmologies from Duality Twisted Compactifications
Oscillating moduli fields can support a cosmological scaling solution in the
presence of a perfect fluid when the scalar field potential satisfies
appropriate conditions. We examine when such conditions arise in
higher-dimensional, non-linear sigma-models that are reduced to four dimensions
under a generalized Scherk-Schwarz compactification. We show explicitly that
scaling behaviour is possible when the higher-dimensional action exhibits a
global SL(n,R) or O(2,2) symmetry. These underlying symmetries can be exploited
to generate non-trivial scaling solutions when the moduli fields have
non-canonical kinetic energy. We also consider the compactification of
eleven-dimensional vacuum Einstein gravity on an elliptic twisted torus.Comment: 21 pages, 3 figure
Pseudo-supersymmetry and a Tale of Alternate Realities
We discuss how all variant 10d and 11d maximal supergravities, including star
supergravities and supergravities in different signatures, can be obtained as
different real slices of three complex actions. As an application we study the
recently introduced domain-wall/cosmology correspondence in this approach. We
give an example in 9d and 10d where the domain-wall and corresponding cosmology
can be viewed as different real slices of the same complex solution. We argue
how in this case the pseudo-supersymmetry of the cosmological solutions can be
understood as the invariance under supersymmetry of a variant supergravity.Comment: 32 page
String theory duals of Lifshitz-Chern-Simons gauge theories
We propose candidate gravity duals for a class of non-Abelian z=2 Lifshitz
Chern-Simons (LCS) gauge theories studied by Mulligan, Kachru and Nayak. These
are nonrelativistic gauge theories in 2+1 dimensions in which parity and
time-reversal symmetries are explicitly broken by the presence of a
Chern-Simons term. We show that these field theories can be realized as
deformations of DLCQ N=4 super Yang-Mills theory. Using the holographic
dictionary, we identify the bulk fields that are dual to these deformations.
The geometries describing the groundstates of the non-Abelian LCS gauge
theories realized here exhibit a mass gap.Comment: 25+14 pages, 3 figures; v2: significant corrections regarding IR
geometry, resulting in new section 5; journal versio
Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography
For a specific action supporting z = 2 Lifshitz geometries we identify the Lifshitz UV completion by solving for the most general solution near the Lifshitz boundary. We identify all the sources as leading components of bulk fields which requires a vielbein formalism. This includes two linear combinations of the bulk gauge field and timelike vielbein where one asymptotes to the boundary timelike vielbein and the other to the boundary gauge field. The geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry that we call torsional Newton-Cartan (TNC) geometry. There is a constraint on the sources but its pairing with a Ward identity allows one to reduce the variation of the on-shell action to unconstrained sources. We compute all the vevs along with their Ward identities and derive conditions for the boundary theory to admit conserved currents obtained by contracting the boundary stress-energy tensor with a TNC analogue of a conformal Killing vector. We also obtain the anisotropic Weyl anomaly that takes the form of a Hořava-Lifshitz action defined on a TNC geometry. The Fefferman-Graham expansion contains a free function that does not appear in the variation of the on-shell action. We show that this is related to an irrelevant deformation that selects between two different UV completions