15 research outputs found
Analyticity Properties of Graham-Witten Anomalies
Analytic properties of Graham-Witten anomalies are considered. Weyl anomalies
according to their analytic properties are of type A (coming from
-singularities in correlators of several energy-momentum tensors) or of
type B (originating in counterterms which depend logarithmically on a mass
scale). It is argued that all Graham-Witten anomalies can be divided into 2
groups: internal and external, and that all external anomalies are of type B,
whereas among internal anomalies there is one term of type A and all the rest
are of type B. This argument is checked explicitly for the case of a free
scalar field in a 6-dimensional space with a 2-dimensional submanifold.Comment: 2 typos correcte
Dynamical vs. Auxiliary Fields in Gravitational Waves around a Black Hole
The auxiliary/dynamic decoupling method of hep-th/0609001 applies to
perturbations of any co-homogeneity 1 background (such as a spherically
symmetric space-time or a homogeneous cosmology). Here it is applied to compute
the perturbations around a Schwarzschild black hole in an arbitrary dimension.
The method provides a clear insight for the existence of master equations. The
computation is straightforward, coincides with previous results of
Regge-Wheeler, Zerilli and Kodama-Ishibashi but does not require any ingenuity
in either the definition of variables or in fixing the gauge. We note that the
method's emergent master fields are canonically conjugate to the standard ones.
In addition, our action approach yields the auxiliary sectors.Comment: 26 page
Analytic Evidence for Continuous Self Similarity of the Critical Merger Solution
The double cone, a cone over a product of a pair of spheres, is known to play
a role in the black-hole black-string phase diagram, and like all cones it is
continuously self similar (CSS). Its zero modes spectrum (in a certain sector)
is determined in detail, and it implies that the double cone is a co-dimension
1 attractor in the space of those perturbations which are smooth at the tip.
This is interpreted as strong evidence for the double cone being the critical
merger solution. For the non-symmetry-breaking perturbations we proceed to
perform a fully non-linear analysis of the dynamical system. The scaling
symmetry is used to reduce the dynamical system from a 3d phase space to 2d,
and obtain the qualitative form of the phase space, including a
non-perturbative confirmation of the existence of the "smoothed cone".Comment: 25 pages, 4 figure
On rolling, tunneling and decaying in some large N vector models
Various aspects of time-dependent processes are studied within the large N
approximation of O(N) vector models in three dimensions. These include the
rolling of fields, the tunneling and decay of vacua. We present an exact
solution for the quantum conformal case and find a solution for more general
potentials when the total change of the value of the field is small.
Characteristic times are found to be shorter when the time dependence of the
field is taken into account in constructing the exact large N effective
potentials. We show that the different approximations yield the same answers in
the regions of the overlap of the validity. A numerical solution of this
potential reveals a tunneling in which the bubble that separates the true
vacuum from the false one is thick
High and Low Dimensions in The Black Hole Negative Mode
The negative mode of the Schwarzschild black hole is central to Euclidean
quantum gravity around hot flat space and for the Gregory-Laflamme black string
instability. We analyze the eigenvalue as a function of space-time dimension by
constructing two perturbative expansions: one for large d and the other for
small d-3, and determining as many coefficients as we are able to compute
analytically. Joining the two expansions we obtain an interpolating rational
function accurate to better than 2% through the whole range of dimensions
including d=4.Comment: 17 pages, 4 figures. v2: added reference. v3: published versio
On metric geometry of conformal moduli spaces of four-dimensional superconformal theories
Conformal moduli spaces of four-dimensional superconformal theories obtained
by deformations of a superpotential are considered. These spaces possess a
natural metric (a Zamolodchikov metric). This metric is shown to be Kahler. The
proof is based on superconformal Ward identities.Comment: 8 page