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A local symmetry is a symmetry which is position dependent. Gauge symmetry is an example of a local symmetry, with the symmetry described by a Lie group (which mathematically describe continuous symmetries), which in the context of gauge theory is called the gauge group of the theory.
However, as was shown by Sidney Coleman and Erick Weinberg, even if the renormalized mass is zero, spontaneous symmetry breaking still happens due to the radiative corrections (this introduces a mass scale into a classically conformal theory - the model has a conformal anomaly). The same can happen in other gauge theories.
The symmetry classes are ordered according to the Bott clock (see below) so that the same values repeat in the diagonals. [5] An X in the table of "Symmetries" indicates that the Hamiltonian of the symmetry is broken with respect to the given operator. A value of ±1 indicates the value of the operator squared for that system.
A gauge symmetry of a Lagrangian is defined as a differential operator on some vector bundle taking its values in the linear space of (variational or exact) symmetries of . Therefore, a gauge symmetry of L {\displaystyle L} depends on sections of E {\displaystyle E} and their partial derivatives. [ 1 ]
The components of the gauge field for i = 4 to 9 become scalars upon eliminating the extra dimensions. This also gives an interpretation of the SO(6) R-symmetry as rotations in the extra compact dimensions. By compactification on a T 6, all the supercharges are preserved, giving N = 4 in the 4-dimensional theory.
A gauge theory is a type of theory in physics.The word gauge means a measurement, a thickness, an in-between distance (as in railroad tracks), or a resulting number of units per certain parameter (a number of loops in an inch of fabric or a number of lead balls in a pound of ammunition). [1]
In theoretical physics, more specifically in quantum field theory and supersymmetry, supersymmetric Yang–Mills, also known as super Yang–Mills and abbreviated to SYM, is a supersymmetric generalization of Yang–Mills theory, which is a gauge theory that plays an important part in the mathematical formulation of forces in particle physics.
A gauge group is a group of gauge symmetries of the Yang–Mills gauge theory of principal connections on a principal bundle. Given a principal bundle P → X {\displaystyle P\to X} with a structure Lie group G {\displaystyle G} , a gauge group is defined to be a group of its vertical automorphisms.