315 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
Q-instantons
We construct the half-supersymmetric instanton solutions that are
electric-magnetically dual to the recently discussed half-supersymmetric
Q7-branes. We call these instantons `Q-instantons'. Whereas the D-instanton is
most conveniently described using the RR axion \chi and the dilaton \phi, the
Q-instanton is most conveniently described using a different set of fields
\chi' and T, where \chi' is an axionic scalar. The real part of the Q-instanton
on-shell action is a function of T and the imaginary part is linear in \chi'.
Discrete shifts of the axion \chi' correspond to PSL(2,Z) transformations that
are of finite order. These are e.g. pure S-duality transformations relating
weak and strongly coupled regimes. We argue that near each orbifold point of
the quantum axion-dilaton moduli space PSL(2,Z)\PSL(2,R)/SO(2) the higher order
R^4 terms in the string effective action contain contributions from an infinite
sum of single multiply-charged instantons with the Q-instantons corresponding
to the orbifold points \tau=i,\rho where \tau is the complex axion-dilaton
field.Comment: 29 pages, 1 figur
Scaling solutions and geodesics in moduli space
In this paper we consider cosmological scaling solutions in general
relativity coupled to scalar fields with a non-trivial moduli space metric. We
discover that the scaling property of the cosmology is synonymous with the
scalar fields tracing out a particular class of geodesics in moduli space -
those which are constructed as integral curves of the gradient of the log of
the potential. Given a generic scalar potential we explicitly construct a
moduli metric that allows scaling solutions, and we show the converse - how one
can construct a potential that allows scaling once the moduli metric is known.Comment: 10 pages, 3 figure
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Limits of JT gravity
We construct various limits of JT gravity, including Newton-Cartan and
Carrollian versions of dilaton gravity in two dimensions as well as a theory on
the three-dimensional light cone. In the BF formulation our boundary conditions
relate boundary connection with boundary scalar, yielding as boundary action
the particle action on a group manifold or some Hamiltonian reduction thereof.
After recovering in our formulation the Schwarzian for JT, we show that
AdS-Carroll gravity yields a twisted warped boundary action. We comment on
numerous applications and generalizations.Comment: 41 pages, 3 figures, 1 table; v2: Matches published version +
Footnote 11; v3: Corrected typo in Carrollian/Galilean generalized dilaton
potentia
Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure
We continue our study of the global properties of the z=2 Schroedinger
space-time. In particular, we provide a codimension 2 isometric embedding which
naturally gives rise to the previously introduced global coordinates.
Furthermore, we study the causal structure by probing the space-time with point
particles as well as with scalar fields. We show that, even though there is no
global time function in the technical sense (Schroedinger space-time being
non-distinguishing), the time coordinate of the global Schroedinger coordinate
system is, in a precise way, the closest one can get to having such a time
function. In spite of this and the corresponding strongly Galilean and almost
pathological causal structure of this space-time, it is nevertheless possible
to define a Hilbert space of normalisable scalar modes with a well-defined
time-evolution. We also discuss how the Galilean causal structure is reflected
and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.Comment: 32 page
Schr\"odinger Manifolds
This article propounds, in the wake of influential work of Fefferman and
Graham about Poincar\'e extensions of conformal structures, a definition of a
(Poincar\'e-)Schr\"odinger manifold whose boundary is endowed with a conformal
Bargmann structure above a non-relativistic Newton-Cartan spacetime. Examples
of such manifolds are worked out in terms of homogeneous spaces of the
Schr\"odinger group in any spatial dimension, and their global topology is
carefully analyzed. These archetypes of Schr\"odinger manifolds carry a Lorentz
structure together with a preferred null Killing vector field; they are shown
to admit the Schr\"odinger group as their maximal group of isometries. The
relationship to similar objects arising in the non-relativisitc AdS/CFT
correspondence is discussed and clarified.Comment: 42 pages, 1 figure, published version: J. Phys. A: Math. Theor. 45
(2012) 395203 (24pp
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