774 research outputs found
Effective models of membranes from symmetry breaking
We show how to obtain all the models of the continuous description of
membranes by constructing the appropriate non-linear realizations of the
Euclidean symmetries of the embedding. The procedure has the advantage of
giving a unified formalism with which the models are generated and highlights
the relevant order parameters in each phase. We use our findings to investigate
a fluid description of both tethered and hexatic membranes, showing that both
the melting and the loss of local order induce long range interactions in the
high temperature fluid phase. The results can be used to understand the
appearance of intrinsic ripples in crystalline membranes in a thermal bath.Comment: 8 pages, 4 figures; to appear in PR
Renormalization of multicritical scalar models in curved space
We consider the leading order perturbative renormalization of the
multicritical models and some generalizations in curved space. We
pay particular attention to the nonminimal interaction with the scalar
curvature and discuss the emergence of the conformal
value of the coupling as the renormalization group fixed point of its
beta function at and below the upper critical dimension as a function of .
We also examine our results in relation with Kawai and Ninomiya's formulation
of two dimensional gravity.Comment: 13 pages, 3 figures; v3: matches the published versio
One loop beta functions and fixed points in Higher Derivative Sigma Models
We calculate the one loop beta functions for nonlinear sigma models in four
dimensions containing general two and four derivative terms. In the O(N) model
there are four such terms and nontrivial fixed points exist for all N \geq 4.
In the chiral SU(N) models there are in general six couplings, but only five
for N=3 and four for N=2; we find fixed points only for N=2,3. In the
approximation considered, the four derivative couplings are asymptotically free
but the coupling in the two derivative term has a nonzero limit. These results
support the hypothesis that certain sigma models may be asymptotically safe.Comment: 26 page
On the non-local heat kernel expansion
We propose a novel derivation of the non-local heat kernel expansion, first
studied by Barvinsky, Vilkovisky and Avramidi, based on simple diagrammatic
equations satisfied by the heat kernel. For Laplace-type differential operators
we obtain the explicit form of the non-local heat kernel form factors to second
order in the curvature. Our method can be generalized easily to the derivation
of the non-local heat kernel expansion of a wide class of differential
operators.Comment: 23 pages, 1 figure, 31 diagrams; references added; to appear in JM
RG flows of Quantum Einstein Gravity on maximally symmetric spaces
We use the Wetterich-equation to study the renormalization group flow of
-gravity in a three-dimensional, conformally reduced setting. Building on
the exact heat kernel for maximally symmetric spaces, we obtain a partial
differential equation which captures the scale-dependence of for
positive and, for the first time, negative scalar curvature. The effects of
different background topologies are studied in detail and it is shown that they
affect the gravitational RG flow in a way that is not visible in
finite-dimensional truncations. Thus, while featuring local background
independence, the functional renormalization group equation is sensitive to the
topological properties of the background. The detailed analytical and numerical
analysis of the partial differential equation reveals two globally well-defined
fixed functionals with at most a finite number of relevant deformations. Their
properties are remarkably similar to two of the fixed points identified within
the -truncation of full Quantum Einstein Gravity. As a byproduct, we
obtain a nice illustration of how the functional renormalization group realizes
the "integrating out" of fluctuation modes on the three-sphere.Comment: 35 pages, 6 figure
The renormalization of fluctuating branes, the Galileon and asymptotic safety
We consider the renormalization of d-dimensional hypersurfaces (branes)
embedded in flat (d+1)-dimensional space. We parametrize the truncated
effective action in terms of geometric invariants built from the extrinsic and
intrinsic curvatures. We study the renormalization-group running of the
couplings and explore the fixed-point structure. We find evidence for an
ultraviolet fixed point similar to the one underlying the asymptotic-safety
scenario of gravity. We also examine whether the structure of the Galileon
theory, which can be reproduced in the nonrelativistic limit, is preserved at
the quantum level.Comment: 15 pages, 1 figure; v3: equation 4.2 and consequent equations
correcte
Fixed-Functionals of three-dimensional Quantum Einstein Gravity
We study the non-perturbative renormalization group flow of f(R)-gravity in
three-dimensional Asymptotically Safe Quantum Einstein Gravity. Within the
conformally reduced approximation, we derive an exact partial differential
equation governing the RG-scale dependence of the function f(R). This equation
is shown to possess two isolated and one continuous one-parameter family of
scale-independent, regular solutions which constitute the natural
generalization of RG fixed points to the realm of infinite-dimensional theory
spaces. All solutions are bounded from below and give rise to positive definite
kinetic terms. Moreover, they admit either one or two UV-relevant deformations,
indicating that the corresponding UV-critical hypersurfaces remain finite
dimensional despite the inclusion of an infinite number of coupling constants.
The impact of our findings on the gravitational Asymptotic Safety program and
its connection to new massive gravity is briefly discussed.Comment: 34 pages, 14 figure
Scheme dependence and universality in the functional renormalization group
We prove that the functional renormalization group flow equation admits a
perturbative solution and show explicitly the scheme transformation that
relates it to the standard schemes of perturbation theory. We then define a
universal scheme within the functional renormalization group.Comment: 5 pages, improved version; v2: published version; v3 and v4: fixed
various typos (final result is unaffected
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