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Supersymmetry is a theoretical framework in physics that suggests the existence of a symmetry between particles with integer spin and particles with half-integer spin ().It proposes that for every known particle, there exists a partner particle with different spin properties. [1]
A third area mentioned in Atiyah's address is Witten's work relating supersymmetry and Morse theory, [29] a branch of mathematics that studies the topology of manifolds using the concept of a differentiable function.
In the original approach, [1] [2] by Seiberg and Witten, holomorphy and electric-magnetic duality constraints are strong enough to almost uniquely constrain the prepotential (a holomorphic function which defines the theory), and therefore the metric of the moduli space of vacua, for theories with SU(2) gauge group.
Raoul Bott used Morse–Bott theory in his original proof of the Bott periodicity theorem. Round functions are examples of Morse–Bott functions, where the critical sets are (disjoint unions of) circles. Morse homology can also be formulated for Morse–Bott functions; the differential in Morse–Bott homology is computed by a spectral ...
Given a Lie subgroup , the / gauged WZW model (or coset model) is a nonlinear sigma model whose target space is the quotient / for the adjoint action of on . This gauged WZW model is a conformal field theory, whose symmetry algebra is a quotient of the two affine Lie algebras of the G {\displaystyle G} and H {\displaystyle H} WZW models, and ...
Here "(2,0)" refers to the particular type of supersymmetry that appears in the theory. In this example, the spacetime of the gravitational theory is effectively seven-dimensional (hence the notation AdS 7), and there are four additional "compact" dimensions (encoded by the S 4 factor). In the real world, spacetime is four-dimensional, at least ...
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. Quantum chromodynamics and quantum electrodynamics are famous examples of gauge theories.
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.