Alessandro Codello

Marginally deformed Starobinsky gravity

A bstractWe show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form R2(1−α), with R the Ricci scalar and α a positive parameter smaller than one half, can generate sizable primordial tensor modes. We also suggest natural microscopic sources of these corrections and demonstrate that they generally lead to a nonzero and positive α. Furthermore we argue, that within this framework, the scalar spectral index and tensor modes probe theories of grand unification including theories not testable at the electroweak scale.

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 curvatures. Our method can be generalized easily to the derivation of the non-local heat kernel expansion of a wide class of differential operators.

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.

Leading CFT constraints on multi-critical models in d > 2

A bstractWe consider the family of renormalizable scalar QFTs with self-interacting potentials of highest monomial ϕm below their upper critical dimensions dc=2mm−2

Fluid membranes and2dquantum gravity

{d}_c=\frac{2m}{m-2}

Functional perturbative RG and CFT data in the

, and study them using a combination of CFT constraints, Schwinger-Dyson equation and the free theory behavior at the upper critical dimension. For even integers m ≥ 4 these theories coincide with the Landau-Ginzburg description of multi-critical phenomena and interpolate with the unitary minimal models in d = 2, while for odd m the theories are non-unitary and start at m = 3 with the Lee-Yang universality class. For all the even potentials and for the Lee-Yang universality class, we show how the assumption of conformal invariance is enough to compute the scaling dimensions of the local operators ϕk and of some families of structure constants in either the coupling’s or the ϵ-expansion. For all other odd potentials we express some scaling dimensions and structure constants in the coupling’s expansion.

\epsilon

We construct the covariant eective eld theory of gravity as an expansion in inverse powers of the Planck mass, identifying the leading and next{to{leading quantum corrections. We determine the form of the eective action for the cases of pure gravity with cosmological constant as well as gravity coupled to matter. By means of heat kernel methods we renormalize and compute the leading quantum corrections to quadratic order in a curvature expansion. The nal eective action in our covariant formalism is generally non{local and can be readily used to understand the phenomenology on dierent spacetimes. In particular, we point out that on curved backgrounds the observable leading quantum gravitational eects are less suppressed than on Minkowski spacetime.We construct the covariant effective field theory of gravity as an expansion in inverse powers of the Planck mass, identifying the leading and next-to-leading quantum corrections. We determine the form of the effective action for the cases of pure gravity with cosmological constant as well as gravity coupled to matter. By means of heat kernel methods we renormalize and compute the leading quantum corrections to quadratic order in a curvature expansion. The final effective action in our covariant formalism is generally non-local and can be readily used to understand the phenomenology on different spacetimes. In particular, we point out that on curved backgrounds the observable leading quantum gravitational effects are less suppressed than on Minkowski spacetime.

-expansion

We study the RG flow of two dimensional (fluid) membranes embedded in Euclidean D-dimensional space using functional RG methods based on the effective average action. By considering a truncation ansatz for the effective average action with both extrinsic and intrinsic curvature terms we derive a system of beta functions for the running surface tension, bending rigidity and Gaussian rigidity. We look for non-trivial fixed points but we find no evidence for a crumpling transition at