In theoretical physics, a central charge is an operator Z that commutes with all the other symmetry operators. The adjective "central" refers to the center of the symmetry group -- the subgroup of elements that commute with all other elements of the original group—or to the center of a Lie algebra. In some cases, such as two-dimensional conformal field theory, a central charge may also commute with all of the other operators, including operators which are not symmetry generators.
More precisely, the central charge is the charge that corresponds, by Noether's theorem, to the center of the central extension of the symmetry group.
In theories with supersymmetry, this definition can be generalized to include supergroups and Lie superalgebras. A central charge is any operator which commutes with all the other supersymmetry generators. Theories with extended supersymmetry typically have many operators of this kind. In string theory, in the first quantized formalism, these operators also have the interpretation of winding numbers (topological quantum numbers) of various strings and branes.
In conformal field theory, the central charge is a c-number (commutes with every other operator) term that appears in the commutator of two components of the stress energy tensor.
Famous quotes containing the words central and/or charge:
“The best laws cannot make a constitution work in spite of morals; morals can turn the worst laws to advantage. That is a commonplace truth, but one to which my studies are always bringing me back. It is the central point in my conception. I see it at the end of all my reflections.”
—Alexis de Tocqueville (1805–1859)
“I do the wrong, and first begin to brawl.
The secret mischiefs that I set abroach
I lay unto the grievous charge of others.”
—William Shakespeare (1564–1616)