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Irreversibility and higher-spin conformal field theory

I discuss the idea that quantum irreversibility is a general principle of nature and a related "conformal hypothesis", stating that all fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points. In particu...

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Autor principal: Anselmi, Damiano
Lenguaje:eng
Publicado: 1999
Materias:
Acceso en línea:https://dx.doi.org/10.1088/0264-9381/17/15/301
http://cds.cern.ch/record/412141
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author Anselmi, Damiano
author_facet Anselmi, Damiano
author_sort Anselmi, Damiano
collection CERN
description I discuss the idea that quantum irreversibility is a general principle of nature and a related "conformal hypothesis", stating that all fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points. In particular, the Newton constant should be viewed as a low-energy effect of the RG scale. This approach leads naturally to consider higher-spin conformal field theories, which are here classified, as candidate high-energy theories. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. The central charges c and a are well defined and positive. I calculate their values and study the operator-product structure. Fermionic theories have no gauge invariance and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. The propagation of the ghost degrees of freedom is visible through the existence of composite operators of high spin and low dimension, violating the Ferrara-Gatto-Grillo theorem. Other theories, such as conformal antisymmetric tensors and higher-derivative theories, are shown to be less promising, because of more severe internal problems.
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spelling cern-4121412023-03-14T19:55:23Zdoi:10.1088/0264-9381/17/15/301http://cds.cern.ch/record/412141engAnselmi, DamianoIrreversibility and higher-spin conformal field theoryParticle Physics - TheoryI discuss the idea that quantum irreversibility is a general principle of nature and a related "conformal hypothesis", stating that all fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points. In particular, the Newton constant should be viewed as a low-energy effect of the RG scale. This approach leads naturally to consider higher-spin conformal field theories, which are here classified, as candidate high-energy theories. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. The central charges c and a are well defined and positive. I calculate their values and study the operator-product structure. Fermionic theories have no gauge invariance and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. The propagation of the ghost degrees of freedom is visible through the existence of composite operators of high spin and low dimension, violating the Ferrara-Gatto-Grillo theorem. Other theories, such as conformal antisymmetric tensors and higher-derivative theories, are shown to be less promising, because of more severe internal problems.I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.hep-th/9912122CERN-TH-99-383CERN-TH-99-383oai:cds.cern.ch:4121411999-12-15
spellingShingle Particle Physics - Theory
Anselmi, Damiano
Irreversibility and higher-spin conformal field theory
title Irreversibility and higher-spin conformal field theory
title_full Irreversibility and higher-spin conformal field theory
title_fullStr Irreversibility and higher-spin conformal field theory
title_full_unstemmed Irreversibility and higher-spin conformal field theory
title_short Irreversibility and higher-spin conformal field theory
title_sort irreversibility and higher-spin conformal field theory
topic Particle Physics - Theory
url https://dx.doi.org/10.1088/0264-9381/17/15/301
http://cds.cern.ch/record/412141
work_keys_str_mv AT anselmidamiano irreversibilityandhigherspinconformalfieldtheory