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

Multi-critical multi-field models: a CFT approach to the leading order

We present some general results for the multi-critical multi-field models in d>2 recently obtained using CFT and Schwinger-Dyson methods at perturbative level without assuming any symmetry. Results in the leading non trivial order are derived consistently for several conformal data in full agreement with functional perturbative RG methods. Mechanisms like emergent (possibly approximate) symmetries can be naturally investigated in this framework.Comment: 12 pages, 1 figure, Contribution to the Conference QFT2018, Quantum Fields From Fundamental Concepts to Phenomenological Questions, Mainz 26-28 September 201

Molecular pathogenesis of prion diseases

Introduction: Prion diseases or transmissible spongiform encephalopathies (TSEs) are rare, fatal and incurable neurodegenerative disorders of humans and animals (Prusiner, 1998). In humans, prion diseases occur with unique aetiology as sporadic, genetic or infectious disorders. Sporadic cases of prion diseases, which account for the majority of casualties (up to 85% of all cases), are of unknown origin; the genetic forms are less frequent (up to 15%), while the infectious cases are extremely rare with an incidence of less than 1% (Prusiner, 2001). Creutzfeldt-Jakob disease (CJD), Gerstmann-Str\ue4ussler-Scheinker (GSS) syndrome, Fatal Familial Insomnia (FFI) are examples of human prion diseases. In animals the disease is mostly infectious and the mode of transmission is horizontal. Prion diseases include scrapie in sheep and goats, bovine spongiform encephalopathy (BSE) in cattle, and chronic wasting disease of deer, elk, and moose (Williams, 2005). The agents responsible for prion diseases are infectious proteins named prions. The term \u2018prion\u2019 was coined when Stanley B. Prusiner introduced the concept of proteinaceous infectious particles (Prusiner, 1982). Since the introduction of this once heretical notion, mounting evidence has strengthened its validity. In the next sections of this chapter we present and discuss the peculiar complexity of the molecular pathogenesis of prion diseases in humans and animals

Asymptotic safety in einstein gravity and scalar-fermion matter

Within the functional renormalization group approach we study the effective quantum field theory of Einstein gravity and one self-interacting scalar coupled to Nf Dirac fermions. We include in our analysis the matter anomalous dimensions induced by all the interactions and analyze the highly nonlinear beta functions determining the renormalization flow. We find the existence of a nontrivial fixed point structure both for the gravity and the matter sector, besides the usual Gaussian matter one. This suggests that asymptotic safety could be realized in the gravitational sector and in the standard model. Nontriviality in the Higgs sector might involve gravitational interactions. © 2010 The American Physical Society

Gravitational form factors and decoupling in 2D

We calculate and analyse non-local gravitational form factors induced by quantum matter fields in curved two-dimensional space. The calculations are performed for scalars, spinors and massive vectors by means of the covariant heat kernel method up to the second order in the curvature and confirmed using Feynman diagrams. The analysis of the ultraviolet (UV) limit reveals a generalized "running" form of the Polyakov action for a nonminimal scalar field and the usual Polyakov action in the conformally invariant cases. In the infrared (IR) we establish the gravitational decoupling theorem, which can be seen directly from the form factors or from the physical beta function for fields of any spin.Comment: 19 pages, v2: fixed corrupted label

Gravitational form factors and decoupling in 2D

We calculate and analyse non-local gravitational form factors induced by quantum matter fields in curved two-dimensional space. The calculations are performed for scalars, spinors and massive vectors by means of the covariant heat kernel method up to the second order in the curvature and confirmed using Feynman diagrams. The analysis of the ultraviolet (UV) limit reveals a generalized “running” form of the Polyakov action for a nonminimal scalar field and the usual Polyakov action in the conformally invariant cases. In the infrared (IR) we establish the gravitational decoupling theorem, which can be seen directly from the form factors or from the physical beta function for fields of any spin

Symmetry and universality of multifield interactions in 6-ϵ dimensions

We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in d=6-ϵ dimensions. As expected by the paradigm of universality, each class is uniquely characterized by its symmetry group and by a set of its scaling properties, neither of which are built-in by the formalism but instead emerge nontrivially as outputs of our computations. For three fields, we find several solutions mostly with discrete symmetries. These are nontrivial conformal field theory candidates in less than six dimensions, one of which is a new perturbatively unitary critical model

Critical models with N≤4 scalars in d=4-ϵ

We adopt a combination of analytical and numerical methods to study the renormalization group flow of the most general field theory with quartic interaction in d=4-ϵ with N=3 and N=4 scalars. For N=3, we find that it admits only three nondecomposable critical points: The Wilson-Fisher with O(3) symmetry, the cubic with H3=(Z2)3â ŠS3 symmetry, and the biconical with O(2)×Z2. For N=4, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions

A multicritical Landau-Potts field theory

We investigate a perturbatively renormalizable Sq invariant model with N = q − 1 scalar field components below the upper critical dimension dc = 10/3. Our results hint at the existence of multicritical generalizations of the critical models of spanning random clusters and percolations in three dimensions. We also discuss the role of our multicritical model in a conjecture that involves the separation of first and second order phases in the (d, q) diagram of the Potts model