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A gauge theory is a field theory with gauge symmetry. Roughly, there are two types of symmetries, global and local. A global symmetry is a symmetry applied uniformly (in some sense) to each point of a manifold. A local symmetry is a symmetry which is position dependent.
The local SU(3) × SU(2) × U(1) gauge symmetry is the internal symmetry. The three factors of the gauge symmetry together give rise to the three fundamental interactions, after some appropriate relations have been defined, as we shall see.
In supersymmetry, 4D = global supersymmetry is the theory of global supersymmetry in four dimensions with a single supercharge.It consists of an arbitrary number of chiral and vector supermultiplets whose possible interactions are strongly constrained by supersymmetry, with the theory primarily fixed by three functions: the Kähler potential, the superpotential, and the gauge kinetic matrix.
Supersymmetry was coined by Abdus Salam and John Strathdee in 1974 as a simplification of the term super-gauge symmetry used by Wess and Zumino, although Zumino also used the same term at around the same time. [24] [25] The term supergauge was in turn coined by Neveu and Schwarz in 1971 when they devised supersymmetry in the context of string ...
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 ]
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.
This is allowed by the new vector bosons introduced from the adjoint representation of SU(5) which also contains the gauge bosons of the Standard Model forces. Since these new gauge bosons are in (3,2) −5/6 bifundamental representations, they violated baryon and lepton number. As a result, the new operators should cause protons to decay at a ...
Before taking the low-energy effective action, the theory is known as = supersymmetric Yang–Mills theory, as the field content is a single = vector supermultiplet, analogous to the field content of Yang–Mills theory being a single vector gauge field (in particle theory language) or connection (in geometric language).