scholarly journals Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of theSU(Nc)conformal anomaly and studies of the conformal symmetry limit

2016 ◽  
Vol 94 (1) ◽  
Author(s):  
Gorazd Cvetič ◽  
A. L. Kataev
Keyword(s):  
Conformal Symmetry ◽  
Conformal Anomaly ◽  
Symmetry Limit ◽  
Perturbation Expansions ◽  
Sum Rule ◽  
Adler Function

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 WEYL ANOMALY FROM WEYL GRAVITY

2000 ◽  
Vol 15 (16) ◽  
pp. 1043-1049 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV
Keyword(s):  
Field Theory ◽  
Conformal Symmetry ◽  
Conformal Anomaly ◽  
Superconformal Field Theory ◽  
Weyl Gravity

We calculate the conformal anomaly from 5-D Weyl gravity (with broken conformal symmetry) which is conjectured to be supergravity dual to [Formula: see text] superconformal field theory via AdS/CFT correspondence. Its comparison with [Formula: see text] SCFT conformal anomaly (uv calculation) suggests that such duality may exist subject to the presence of subleading 1/N corrections to cosmological and gravitational constants.

scholarly journals QCD Evolution Equations from Conformal Symmetry

2015 ◽  
Vol 37 ◽  
pp. 1560048
Author(s):  
V. M. Braun ◽  
A. N. Manashov
Keyword(s):  
Perturbation Theory ◽  
Conformal Invariance ◽  
Evolution Equations ◽  
Conformal Symmetry ◽  
Scale Dependence ◽  
Conformal Anomaly ◽  
Parton Distributions ◽  
Anomalous Dimensions ◽  
The Given ◽  
Modified Theory

QCD evolution equations in MS-like schemes can be recovered from the same equations in a modified theory, QCD in non-integer d = 4 - 2ϵ dimensions, which enjoys exact scale and conformal invariance at the critical point. Restrictions imposed by the conformal symmetry of the modified theory allow one to obtain complete evolution kernels in integer (physical) dimensions at the given order of perturbation theory from the spectrum of anomalous dimensions added by the calculation of the special conformal anomaly at one order less. We use this technique to derive two-loop evolution equations for flavor-nonsinglet quark-antiquark light-ray operators that encode the scale dependence of generalized hadron parton distributions.

scholarly journals SYMMETRIES, HORIZONS AND BLACK HOLE ENTROPY

2008 ◽  
Vol 17 (03n04) ◽  
pp. 659-664 ◽  
Author(s):  
S. CARLIP
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Degrees Of Freedom ◽  
Conformal Symmetry ◽  
Goldstone Boson ◽  
Thermal Characteristics ◽  
Black Hole Entropy ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Statistical Mechanical

Black holes behave as thermodynamic systems, and a central task of any quantum theory of gravity is to explain these thermal properties. A statistical-mechanical description of black hole entropy once seemed remote, but today we suffer an embarrassment of riches: despite counting very different states, many inequivalent approaches to quantum gravity obtain identical results. Such "universality" may reflect an underlying two-dimensional conformal symmetry near the horizon, which can be powerful enough to control the thermal characteristics independent of other details of the theory. This picture suggests an elegant description of the relevant degrees of freedom as Goldstone-boson-like excitations arising from symmetry breaking by the conformal anomaly.

scholarly journals CURRENT ALGEBRA AND CONFORMAL FIELD THEORY ON A FIGURE EIGHT

1993 ◽  
Vol 08 (32) ◽  
pp. 5641-5671 ◽  
Author(s):  
A.P. BALACHANDRAN ◽  
G. BIMONTE ◽  
K.S. GUPTA ◽  
G. MARMO ◽  
P. SALOMONSON ◽  
...  
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Current Algebra ◽  
Central Charge ◽  
Conformal Symmetry ◽  
Conformal Anomaly ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Left And Right ◽  
Kirchhoff's Law

We examine the dynamics of a free massless scalar field on a figure eight network. Upon requiring the scalar field to have a well-defined value at the junction of the network, it is seen that the conserved currents of the theory satisfy Kirchhoff’s law, that is that the current flowing into the junction equals the current flowing out. We obtain the corresponding current algebra and show that, unlike on a circle, the left- and right-moving currents on the figure eight do not in general commute in quantum theory. Since a free scalar field theory on a one-dimensional spatial manifold exhibits conformal symmetry, it is natural to ask whether an analogous symmetry can be defined for the figure eight. We find that, unlike in the case of a manifold, the action plus boundary conditions for the network are not invariant under separate conformal transformations associated with left- and right-movers. Instead, the system is, at best, invariant under only a single set of transformations. Its conserved current is also found to satisfy Kirchhoff’s law at the junction. We obtain the associated conserved charges, and show that they generate a Virasoro algebra. Its conformal anomaly (central charge) is computed for special values of the parameters characterizing the network.

Conformal Symmetry in Statistical Mechanics

2019 ◽  
pp. 188-240
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Statistical Mechanics ◽  
Central Charge ◽  
Conformal Symmetry ◽  
Finite Size ◽  
Virasoro Algebra ◽  
Momentum Tensor ◽  
Critical Parameters ◽  
Operator Product ◽  
Conformal Anomaly ◽  
Conformal Transformations

The core of the exposition of the theory of conformal symmetry in statistical mechanics are the concepts of correlation functions of order parameter fields, whose behaviour under conformal transformations are the defining characteristic of conformal field theories. Chapter 7 discusses the transformation properties of the energy-momentum tensor, the conformal Ward identities, and the operator product expansion lead to the loop or Witt algebra with central extension, the Virasoro algebra, allowing the characterization of the possible universality classes, in particular through the conformal anomaly or central charge. It discusses how the finite-size corrections to thermodynamic quantities, obtained from conformal transformations to finite geometries, can be used to determine critical parameters, especially the central charge.

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