target space (changes) in nLab
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Context
∞\infty-Chern-Simons theory
Ingredients
Definition
Examples
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For semisimple Lie algebra targets
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For discrete group targets
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For discrete 2-group targets
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For Lie 2-algebra targets
- BF-theory coupled to topological Yang-Mills theory
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For targets extending the super Poincare Lie algebra
(such as the supergravity Lie 3-algebra, the supergravity Lie 6-algebra)
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Chern-Simons-supergravity
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for higher abelian targets
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for symplectic Lie n-algebroid targets
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for the L ∞L_\infty-structure on the BRST complex of the closed string:
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higher dimensional Chern-Simons theory
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topological AdS7/CFT6-sector
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Quantum field theory
Physics
physics, mathematical physics, philosophy of physics
Surveys, textbooks and lecture notes
theory (physics), model (physics)
experiment, measurement, computable physics
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Axiomatizations
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Tools
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Structural phenomena
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Types of quantum field thories
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Contents
Idea
Generally, for Maps(Σ,X)Maps(\Sigma,X) a mapping space , the spaceXXspace is or the correspondingspacetime XX is the corresponding target space . ortarget spacetime.
Specifically, in a sigma-model quantum field theory a field configuration over a parameter space Σ\Sigma is a morphism Σ→X\Sigma \to X to some object XX. This is the target space of the theory. The σ\sigma-model is to be understood as describing the quantum mechanics of branes with trajectories of shape Σ\Sigma propagating in XX.
Examples
For sigma-models that are supposed to describe quantum objects in the observed world (such as the relativistic particle) the target space XX would be our spacetime. But the target space can be something more general or more exotic. For instance in Dijkgraaf-Witten theory the target space is the classifying space of a discrete group.
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target space
Last revised on January 18, 2015 at 22:25:40. See the history of this page for a list of all contributions to it.