12,851 research outputs found
Classification of 't Hooft instantons over multi-centered gravitational instantons
This work presents a classification of all smooth 't Hooft-Jackiw-Nohl-Rebbi
instantons over Gibbons-Hawking spaces. That is, we find all smooth SU(2)
Yang-Mills instantons over these spaces which arise by conformal rescalings of
the metric with suitable functions.
Since the Gibbons-Hawking spaces are hyper-Kahler gravitational instantons,
the rescaling functions must be positive harmonic. By using twistor methods we
present integral formulae for the kernel of the Laplacian associated to these
spaces. These integrals are generalizations of the classical Whittaker-Watson
formula. By the aid of these we prove that all 't Hooft instantons have already
been found in a recent paper.
This result also shows that actually all such smooth 't
Hooft-Jackiw-Nohl-Rebbi instantons describe singular magnetic monopoles over
the flat three-space with zero magnetic charge moreover the reducible ones
generate the the full L^2 cohomology of the Gibbons-Hawking spaces.Comment: 18 pages, LaTeX, no figures; journal reference has been include
Holography as a highly efficient RG flow II: An explicit construction
We complete the reformulation of the holographic correspondence as a
\emph{highly efficient RG flow} that can also determine the UV data in the
field theory in the strong coupling and large limit. We introduce a special
way to define operators at any given scale in terms of appropriate
coarse-grained collective variables, without requiring the use of the
elementary fields. The Wilsonian construction is generalised by promoting the
cut-off to a functional of these collective variables. We impose three criteria
to determine the coarse-graining. The first criterion is that the effective
Ward identities for local conservation of energy, momentum, etc. should
preserve their standard forms, but in new scale-dependent background metric and
sources which are functionals of the effective single trace operators. The
second criterion is that the scale-evolution equations of the operators in the
actual background metric should be state-independent, implying that the
collective variables should not explicitly appear in them. The final criterion
is that the endpoint of the scale-evolution of the RG flow can be transformed
to a fixed point corresponding to familiar non-relativistic equations with a
finite number of parameters, such as incompressible non-relativistic
Navier-Stokes, under a certain universal rescaling of the scale and of the time
coordinate. Using previous work, we explicitly show that in the hydrodynamic
limit each such highly efficient RG flow reproduces a unique classical gravity
theory with precise UV data that satisfy our IR criterion. We obtain the
explicit coarse-graining which reproduces Einstein's equations. In a simple
example, we are also able to compute the beta function. Finally, we show how
our construction can be interpolated with the traditional Wilsonian RG flow at
a suitable scale, and can be used to develop new non-perturbative frameworks
for QCD-like theories.Comment: 1+59 pages; Introduction slightly expanded, Section V on beta
function in highly efficient RG flow added, version accepted in PR
-Regularity and Structure of 4-dimensional Shrinking Ricci Solitons
A closed four dimensional manifold cannot possess a non-flat Ricci soliton
metric with arbitrarily small -norm of the curvature. In this paper, we
localize this fact in the case of shrinking Ricci solitons by proving an
-regularity theorem, thus confirming a conjecture of Cheeger-Tian.
As applications, we will also derive structural results concerning the
degeneration of the metrics on a family of complete non-compact four
dimensional shrinking Ricci solitons without a uniform entropy lower bound. In
the appendix, we provide a detailed account of the equivariant good chopping
theorem when collapsing with locally bounded curvature happens
Very Singular Similarity Solutions and Hermitian Spectral Theory for Semilinear Odd-Order PDEs
Very singular self-similar solutions of semilinear odd-order PDEs are studied
on the basis of a Hermitian-type spectral theory for linear rescaled odd-order
operators.Comment: 49 pages, 12 Figure
Einstein-Maxwell gravitational instantons and five dimensional solitonic strings
We study various aspects of four dimensional Einstein-Maxwell multicentred
gravitational instantons. These are half-BPS Riemannian backgrounds of minimal
N=2 supergravity, asymptotic to R^4, R^3 x S^1 or AdS_2 x S^2. Unlike for the
Gibbons-Hawking solutions, the topology is not restricted by boundary
conditions. We discuss the classical metric on the instanton moduli space. One
class of these solutions may be lifted to causal and regular multi `solitonic
strings', without horizons, of 4+1 dimensional N=2 supergravity, carrying null
momentum.Comment: 1+30 page
Quantum critical lines in holographic phases with (un)broken symmetry
All possible scaling IR asymptotics in homogeneous, translation invariant
holographic phases preserving or breaking a U(1) symmetry in the IR are
classified. Scale invariant geometries where the scalar extremizes its
effective potential are distinguished from hyperscaling violating geometries
where the scalar runs logarithmically. It is shown that the general critical
saddle-point solutions are characterized by three critical exponents (). Both exact solutions as well as leading behaviors are exhibited.
Using them, neutral or charged geometries realizing both fractionalized or
cohesive phases are found. The generic global IR picture emerging is that of
quantum critical lines, separated by quantum critical points which correspond
to the scale invariant solutions with a constant scalar.Comment: v3: 32+29 pages, 2 figures. Matches version published in JHEP.
Important addition of an exponent characterizing the IR scaling of the
electric potentia
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