Conformal anomaly is an anomaly i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory. In physics, the word anomaly is used to describe a classical symmetry—i. ... In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a Euclidean-like space with a point added at infinity, or a Minkowski-like space with a couple of points added at infinity. That is, the setting is a compactification of a familiar space... In physics, a classical theory usually refers to a theory that does not obey the principles of quantum mechanics (classical theory vs. ...

In string theory, conformal symmetry on the worldsheet is a local Weyl symmetry and 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. String theory is a physical model whose fundamental building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles) that were the basis of most earlier physics. ... A world line of an object or person is the sequence of events labeled with time and place, that marks the history of the object or person. ... In theoretical physics, the Weyl transformation is a local rescaling of the metric tensor: The invariance of a theory or an expression under this transformation is called the Weyl symmetry. ... World line of the orbit of the Earth depicted as a circle in two spatial dimensions X and Y (the plane of the Earth orbit) and a time dimension, Z, making the circle appear as a helix. ... There is an ontological procession of dimensionality. ... Critical dimension is the dimensionality of spacetime in which string theory is consistent assuming a constant dilaton background. ... Bosonic string theory is the original version of string theory, developed in the late 1960s. ... Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. ...

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 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 quark masses, so it has a much greater effect on the masses of hadrons.) Quantum chromodynamics (QCD) is the physical theory describing one of the fundamental forces, the strong interaction. ... Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. ... This article refers to a particle physics phenomenon. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... Properties In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... Properties In physics, the neutron is a subatomic particle with no net electric charge and a mass of 939. ... Matter is anything that has mass and occupies space. ... 1974 discovery photograph of a possible charmed baryon, now identified as the Σc++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ...