# Conformal Symmetry as a Template for QCD

## Abstract

Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero {beta} function as well as higher-twist effects. For example, commensurate scale relations which relate QCD observables to each other, such as the generalized Crewther relation, have no renormalization scale or scheme ambiguity and retain a convergent perturbative structure which reflects the underlying conformal symmetry of the classical theory. The ''conformal correspondence principle'' also dictates the form of the expansion basis for hadronic distribution amplitudes. The AdS/CFT correspondence connecting superstring theory to superconformal gauge theory has important implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for hard exclusive processes as well as determining essential aspects of hadronic light-front wavefunctions. Theoretical and phenomenological evidence is now accumulating that QCD couplings based on physical observables such as {tau} decay become constant at small virtuality; i.e., effective charges develop an infrared fixed point in contradiction to the usual assumption of singular growth in the infrared. The near-constant behavior of effective couplings also suggests that QCD can be approximated as a conformal theory even at relatively small momentum transfer. The importance of using an analytic effective chargemore »

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center, Menlo Park, CA (US)

- Sponsoring Org.:
- USDOE Office of Science (US)

- OSTI Identifier:
- 829728

- Report Number(s):
- SLAC-PUB-10576

TRN: US0405831

- DOE Contract Number:
- AC03-76SF00515

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 4 Aug 2004

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; DECAY; DISTRIBUTION; EFFECTIVE CHARGE; HADRONS; MOMENTUM TRANSFER; QUANTUM CHROMODYNAMICS; RENORMALIZATION; SYMMETRY

### Citation Formats

```
Brodsky, S.
```*Conformal Symmetry as a Template for QCD*. United States: N. p., 2004.
Web. doi:10.2172/829728.

```
Brodsky, S.
```*Conformal Symmetry as a Template for QCD*. United States. doi:10.2172/829728.

```
Brodsky, S. Wed .
"Conformal Symmetry as a Template for QCD". United States. doi:10.2172/829728. https://www.osti.gov/servlets/purl/829728.
```

```
@article{osti_829728,
```

title = {Conformal Symmetry as a Template for QCD},

author = {Brodsky, S},

abstractNote = {Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero {beta} function as well as higher-twist effects. For example, commensurate scale relations which relate QCD observables to each other, such as the generalized Crewther relation, have no renormalization scale or scheme ambiguity and retain a convergent perturbative structure which reflects the underlying conformal symmetry of the classical theory. The ''conformal correspondence principle'' also dictates the form of the expansion basis for hadronic distribution amplitudes. The AdS/CFT correspondence connecting superstring theory to superconformal gauge theory has important implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for hard exclusive processes as well as determining essential aspects of hadronic light-front wavefunctions. Theoretical and phenomenological evidence is now accumulating that QCD couplings based on physical observables such as {tau} decay become constant at small virtuality; i.e., effective charges develop an infrared fixed point in contradiction to the usual assumption of singular growth in the infrared. The near-constant behavior of effective couplings also suggests that QCD can be approximated as a conformal theory even at relatively small momentum transfer. The importance of using an analytic effective charge such as the pinch scheme for unifying the electroweak and strong couplings and forces is also emphasized.},

doi = {10.2172/829728},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2004},

month = {8}

}