The conformal anomaly and anomaly-induced action

2021 ◽  
pp. 414-424
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Effective Action ◽  
Black Hole Physics ◽  
Dimensional Regularization ◽  
Form Factors ◽  
Simple Calculation ◽  
Conformal Anomaly ◽  
Local Form ◽  
Conformal Transformations ◽  
Transformation Rules ◽  
Non Local

This chapter describes in detail basic results concerning the conformal (trace) anomaly and anomaly-induced action in four spacetime dimensions. It is shown how the anomaly appears from the non-local form factors discussed in chapter 16. Starting from the conformal transformations, the necessary invariants and transformation rules are obtained. The simplest derivation of the anomaly in dimensional regularization is explained, followed by the equally simple calculation of the anomaly-induced effective action of gravity. The chapter also briefly discusses applications of the induced effective action in cosmology and black hole physics.

scholarly journals Vacuum Effective Actions and Mass-Dependent Renormalization in Curved Space

2019 ◽  
Author(s):  
Omar Zanusso ◽  
Sebastián A. Franchino-Viñas ◽  
Tibério de Paula Netto
Keyword(s):  
Heat Kernel ◽  
Effective Action ◽  
Form Factors ◽  
The Other ◽  
Local Form ◽  
Curved Space ◽  
Four Dimensions ◽  
Semiclassical Gravity ◽  
Non Local ◽  
Mass Dependent

We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton's constant and the other gravitational couplings.

scholarly journals Vacuum Effective Actions and Mass-Dependent Renormalization in Curved Space

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 67 ◽  
Author(s):  
Sebastián Franchino-Viñas ◽  
Tibério de Paula Netto ◽  
Omar Zanusso
Keyword(s):  
Heat Kernel ◽  
Effective Action ◽  
Form Factors ◽  
The Other ◽  
Local Form ◽  
Curved Space ◽  
Four Dimensions ◽  
Semiclassical Gravity ◽  
Non Local ◽  
Mass Dependent

We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton’s constant and the other gravitational couplings.

scholarly journals Conformal Symmetry in Field Theory and in Quantum Gravity

Universe ◽  
2018 ◽  
Vol 4 (11) ◽  
pp. 125 ◽  
Author(s):  
Lesław Rachwał
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
Effective Action ◽  
Conformal Symmetry ◽  
Gravitational Theory ◽  
Fine Tuning ◽  
Conformal Anomaly ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Non Local

Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum effective action. First, the long and complicated story of UV-divergences is recalled. With the development of UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities and spacetime singularities might be completely solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory should be safe. After the construction of UV-finite theory, we focused on making it manifestly conformally invariant using the dilaton trick. We also argue that in this class of theories conformal anomaly can be taken to vanish by fine-tuning the couplings. As applications of this theory, the constraints of the conformal symmetry on the form of the effective action and on the scattering amplitudes are shown. We also remark about the preservation of the unitarity bound for scattering. Finally, the old model of conformal supergravity by Fradkin and Tseytlin is briefly presented.

scholarly journals The conformal anomaly action to fourth order (4T) in $$d=4$$ in momentum space

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Claudio Corianò ◽  
Matteo Maria Maglio ◽  
Dimosthenis Theofilopoulos
Keyword(s):  
Momentum Space ◽  
Form Factors ◽  
Conformal Anomaly ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Independent Form ◽  
Stress Energy ◽  
Complete Determination ◽  
Non Local

AbstractWe elaborate on the structure of the conformal anomaly effective action up to 4-th order, in an expansion in the gravitational fluctuations (h) of the background metric, in the flat spacetime limit. For this purpose we discuss the renormalization of 4-point functions containing insertions of stress-energy tensors (4T), in conformal field theories in four spacetime dimensions with the goal of identifying the structure of the anomaly action. We focus on a separation of the correlator into its transverse/traceless and longitudinal components, applied to the trace and conservation Ward identities (WI) in momentum space. These are sufficient to identify, from their hierarchical structure, the anomaly contribution, without the need to proceed with a complete determination of all of its independent form factors. Renormalization induces sequential bilinear graviton-scalar mixings on single, double and multiple trace terms, corresponding to $$R\square ^{-1}$$ R □ - 1 interactions of the scalar curvature, with intermediate virtual massless exchanges. These dilaton-like terms couple to the conformal anomaly, as for the chiral anomalous WIs. We show that at 4T level a new traceless component appears after renormalization. We comment on future extensions of this result to more general backgrounds, with possible applications to non local cosmologies.

Non-local form factors in flat and curved spacetime

2021 ◽  
pp. 397-413
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Form Factors ◽  
Local Form ◽  
Quantum Field ◽  
Direct Relation ◽  
Curved Space ◽  
Flat Spacetime ◽  
Infrared Limit ◽  
Non Local ◽  
Generally Covariant ◽  
The Relationship

This chapter is devoted to the direct explicit calculations of non-local form factors in two-point functions in real scalar field theory. Two simple examples in flat spacetime demonstrate the relationship between logarithmic ultraviolet (UV) divergences in the cut-off and dimensional regularizations, which is used for deriving the form factors. The chapter then shows how one can establish the direct relation between logarithmic UV divergences and the logarithmic behavior of the momentum-dependent non-local form factors in the UV. In the low-energy (infrared) limit, it is possible to observe quadratic decoupling with respect to the mass of the quantum field. In curved space, analogous results are reproduced using the generally covariant heat-kernel solution. Calculations are given in full details.

On non-local form factors

1955 ◽  
Vol 1 (6) ◽  
pp. 1113-1119 ◽  
Author(s):  
R. J. Finkelstein
Keyword(s):  
Form Factors ◽  
Local Form ◽  
Non Local

scholarly journals De Sitter and power-law solutions in non-local Gauss–Bonnet gravity

2018 ◽  
Vol 15 (11) ◽  
pp. 1850188 ◽  
Author(s):  
E. Elizalde ◽  
S. D. Odintsov ◽  
E. O. Pozdeeva ◽  
S. Yu. Vernov
Keyword(s):  
Power Law ◽  
Sufficient Conditions ◽  
Model Parameters ◽  
Local Form ◽  
De Sitter ◽  
Dynamical Equations ◽  
Non Local ◽  
Necessary And Sufficient ◽  
The Universe ◽  
Universe Evolution

The cosmological dynamics of a non-locally corrected gravity theory, involving a power of the inverse d’Alembertian, is investigated. Casting the dynamical equations into local form, the fixed points of the models are derived, as well as corresponding de Sitter and power-law solutions. Necessary and sufficient conditions on the model parameters for the existence of de Sitter solutions are obtained. The possible existence of power-law solutions is investigated, and it is proven that models with de Sitter solutions have no power-law solutions. A model is found, which allows to describe the matter-dominated phase of the Universe evolution.

From BRST symmetry to the Zinn-Justin equation

2019 ◽  
pp. 237-252
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Quadratic Equation ◽  
Local Action ◽  
Local Form ◽  
Abelian Gauge ◽  
Brst Cohomology ◽  
Gauge Fixing ◽  
Non Local ◽  
Popov Ghost

Chapter 14 contains a general discussion of the quantization and renormalization of non–Abelian gauge theories. The quantization necessitates gauge fixing and introduces the Faddeev–Popov determinant. Slavnov–Taylor identities for vertex (one–particle–irreducible (1PI)) functions, the basis of a first proof of renormalizability, follow. The Faddeev–Popov determinant leads to a non–local action. A local form is generated by introducing Faddeev–Popov ghost fields. The new local action has an important new symmetry, the BRST symmetry. However, the explicit realization of the symmetry is not stable under renormalization. By contrast, a quadratic equation that is satisfied by the action and generating functional of 1PI functions, the Zinn–Justin equation, is stable and at the basis of a general proof of the renormalizability of non–Abelian gauge theories. The proof involves some simple elements of BRST cohomology. The renormalized form of BRST symmetry then makes it possible to prove gauge independence and unitarity.

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