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- Conformal_anomaly abstract "A conformal anomaly, scale anomaly, or Weyl anomaly is an anomaly, i.e., a quantum phenomenon that breaks the conformal symmetry of the classical theory.A classically conformal theory is a theory which, when placed on a surface with arbitrary background metric, has an action that is invariant under rescalings of the background metric (Weyl transformations), combined with corresponding transformations of the other fields in the theory.A conformal quantum theory is one whose partition function is unchanged by rescaling the metric.The variation of the partition function with respect to the background metric is proportional to the stress tensor, and therefore the variation with respect to a conformal rescaling is proportional to the trace of the stress tensor.Therefore in the presence of a conformal anomaly the trace of the stress tensor has a non-vanishing expectation.In string theory, conformal symmetry on the worldsheet is a local Weyl symmetry and the anomaly must therefore cancel if the theory is to be consistent. The required cancellation implies that the spacetime dimensionality must be equal to the critical dimension which is either 26 in the case of bosonic string theory or 10 in the case of superstring theory. This case is called critical string theory. There are alternative approaches known as non-critical string theory in which the space-time dimensions can be less than 26 for the bosonic theory or less 10 for the superstring i.e. the four-dimensional case is plausible within this context.In quantum chromodynamics in the chiral limit, the classical theory has no mass scale so there is a conformal symmetry, but this is broken by a conformal anomaly. This introduces a scale, which is the scale at which colour confinement occurs. This determines the sizes and masses of hadrons, including protons and neutrons. Hence this effect is responsible for most of the mass of ordinary matter. (In fact the quarks have non-zero masses, so the classical theory does have a mass scale. However, the masses are small so it is still nearly conformal, so there is still a conformal anomaly. The mass due to the conformal anomaly is much greater than the up, down and strange quark masses, so it has a much greater effect on the masses of hadrons.)".
- Conformal_anomaly wikiPageExternalLink 1201.6073.
- Conformal_anomaly wikiPageID "1931704".
- Conformal_anomaly wikiPageRevisionID "604731113".
- Conformal_anomaly hasPhotoCollection Conformal_anomaly.
- Conformal_anomaly subject Category:Anomalies_in_physics.
- Conformal_anomaly subject Category:Conformal_field_theory.
- Conformal_anomaly subject Category:Quantum_chromodynamics.
- Conformal_anomaly subject Category:Renormalization_group.
- Conformal_anomaly subject Category:String_theory.
- Conformal_anomaly type Abnormality114501726.
- Conformal_anomaly type Abstraction100002137.
- Conformal_anomaly type AnomaliesInPhysics.
- Conformal_anomaly type Anomaly114505821.
- Conformal_anomaly type Attribute100024264.
- Conformal_anomaly type Condition113920835.
- Conformal_anomaly type PhysicalCondition114034177.
- Conformal_anomaly type State100024720.
- Conformal_anomaly comment "A conformal anomaly, scale anomaly, or Weyl anomaly is an anomaly, i.e., a quantum phenomenon that breaks the conformal symmetry of the classical theory.A classically conformal theory is a theory which, when placed on a surface with arbitrary background metric, has an action that is invariant under rescalings of the background metric (Weyl transformations), combined with corresponding transformations of the other fields in the theory.A conformal quantum theory is one whose partition function is unchanged by rescaling the metric.The variation of the partition function with respect to the background metric is proportional to the stress tensor, and therefore the variation with respect to a conformal rescaling is proportional to the trace of the stress tensor.Therefore in the presence of a conformal anomaly the trace of the stress tensor has a non-vanishing expectation.In string theory, conformal symmetry on the worldsheet is a local Weyl symmetry and the anomaly must therefore cancel if the theory is to be consistent. ".
- Conformal_anomaly label "Anomalia conforme".
- Conformal_anomaly label "Conformal anomaly".
- Conformal_anomaly sameAs Anomalia_conforme.
- Conformal_anomaly sameAs m.06710j.
- Conformal_anomaly sameAs Q5160243.
- Conformal_anomaly sameAs Q5160243.
- Conformal_anomaly sameAs Conformal_anomaly.
- Conformal_anomaly wasDerivedFrom Conformal_anomaly?oldid=604731113.
- Conformal_anomaly isPrimaryTopicOf Conformal_anomaly.