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

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

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

Quantum corrections in Galileon theories

We calculate the one-loop quantum corrections in the cubic Galileon theory, using cutoff regularization. We confirm the expected form of the one-loop effective action and that the couplings of the Galileon theory do not get renormalized. However, new terms, not included in the tree-level action, are induced by quantum corrections. We also consider the one-loop corrections in an effective brane theory, which belongs to the Horndeski or generalized Galileon class. We find that new terms are generated by quantum corrections, while the tree-level couplings are also renormalized. We conclude that the structure of the generalized Galileon theories is altered by quantum corrections more radically than that of the Galileon theory.Comment: 8 pages; v2 minor typos corrected, references added; v3 minor clarifications; v4 version published in PR

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

A proper fixed functional for four-dimensional Quantum Einstein Gravity

Abstract: Realizing a quantum theory for gravity based on Asymptotic Safety hinges on the existence of a non-Gaussian fixed point of the theory’s renormalization group flow. In this work, we use the functional renormalization group equation for the effective average action to study the fixed point underlying Quantum Einstein Gravity at the functional level including an infinite number of scale-dependent coupling constants. We formulate a list of guiding principles underlying the construction of a partial differential equation encoding the scale-dependence of f(R)-gravity. We show that this equation admits a unique, globally well-defined fixed functional describing the non-Gaussian fixed point at the level of functions of the scalar curvature. This solution is constructed explicitly via a numerical double-shooting method. In the UV, this solution is in good agreement with results from polynomial expansions including a finite number of coupling constants, while it scales proportional to R2, dressed up with non-analytic terms, in the IR. We demonstrate that its structure is mainly governed by the conformal sector of the flow equation. The relation of our work to previous, partial constructions of similar scaling solutions is discussed

Fractal Geometry of Higher Derivative Gravity

We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal dimensions of such hypersurfaces embedded in a quantum spacetime at very small distances

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