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 $\int\sqrt{g}R c_{k}(\Delta)R$, 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

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