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:
“Et in Arcadia ego.
[I too am in Arcadia.]”
—Anonymous, Anonymous.
Tomb inscription, appearing in classical paintings by Guercino and Poussin, among others. The words probably mean that even the most ideal earthly lives are mortal. Arcadia, a mountainous region in the central Peloponnese, Greece, was the rustic abode of Pan, depicted in literature and art as a land of innocence and ease, and was the title of Sir Philip Sidney’s pastoral romance (1590)
“America does to me what I knew it would do: it just bumps me.... The people charge at you like trucks coming down on you—no awareness. But one tries to dodge aside in time. Bump! bump! go the trucks. And that is human contact.”
—D.H. (David Herbert)