53 research outputs found
Polyakov Effective Action from Functional Renormalization Group Equation
We discuss the Polyakov effective action for a minimally coupled scalar field
on a two dimensional curved space by considering a non-local covariant
truncation of the effective average action. We derive the flow equation for the
form factor in , and we show how the standard
result is obtained when we integrate the flow from the ultraviolet to the
infrared.Comment: 19 pages, 5 figure
Leading Gravitational Corrections and a Unified Universe
Leading order gravitational corrections to the Einstein-Hilbert action can
lead to a consistent picture of the universe by unifying the epochs of
inflation and dark energy in a single framework. While the leading local
correction induces an inflationary phase in the early universe, the leading
non-local term leads to an accelerated expansion of the universe at the present
epoch. We argue that both the leading UV and IR terms can be obtained within
the framework of a covariant effective field theory of gravity. The
perturbative gravitational corrections therefore provide a fundamental basis
for understanding a possible connection between the two epochs.Comment: 5 pages, 2 figures. This essay received "Honorable Mention" in the
2016 Gravity Research Foundation Awards for Essays on Gravitation. arXiv
admin note: substantial text overlap with arXiv:1603.0002
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
A functional RG equation for the c-function
After showing how to prove the integrated c-theorem within the functional RG
framework based on the effective average action, we derive an exact RG flow
equation for Zamolodchikov's c-function in two dimensions by relating it to the
flow of the effective average action. In order to obtain a non-trivial flow for
the c-function, we will need to understand the general form of the effective
average action away from criticality, where nonlocal invariants, with beta
functions as coefficients, must be included in the ansatz to be consistent. We
then apply our construction to several examples: exact results, local potential
approximation and loop expansion. In each case we construct the relative
approximate c-function and find it to be consistent with Zamolodchikov's
c-theorem. Finally, we present a relation between the c-function and the
(matter induced) beta function of Newton's constant, allowing us to use heat
kernel techniques to compute the RG running of the c-function.Comment: 41 pages, 17 figures; v2: some minor correction
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
Functional and Local Renormalization Groups
We discuss the relation between functional renormalization group (FRG) and
local renormalization group (LRG), focussing on the two dimensional case as an
example. We show that away from criticality the Wess-Zumino action is described
by a derivative expansion with coefficients naturally related to RG quantities.
We then demonstrate that the Weyl consistency conditions derived in the LRG
approach are equivalent to the RG equation for the -function available in
the FRG scheme. This allows us to give an explicit FRG representation of the
Zamolodchikov-Osborn metric, which in principle can be used for computations.Comment: 19 pages, 1 figur
Leading order CFT analysis of multi-scalar theories in d>2
We investigate multi-field multicritical scalar theories using CFT
constraints on two- and three-point functions combined with the Schwinger-Dyson
equation. This is done in general and without assuming any symmetry for the
models, which we just define to admit a Landau-Ginzburg description that
includes the most general critical interactions built from monomials of the
form . For all such models we analyze to the
leading order of the -expansion the anomalous dimensions of the
fields and those of the composite quadratic operators. For models with even
we extend the analysis to an infinite tower of composite operators of arbitrary
order. The results are supplemented by the computation of some families of
structure constants. We also find the equations which constrain the nontrivial
critical theories at leading order and show that they coincide with the ones
obtained with functional perturbative RG methods. This is done for the case
as well as for all the even models. We ultimately specialize to
symmetric models, which are related to the -state Potts universality class,
and focus on three realizations appearing below the upper critical dimensions
, and , which can thus be nontrivial CFTs in three
dimensions.Comment: 58 pages; v2: minor clarifications added, to appear in EPJ
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