Enhancement of hidden symmetries and Chern-Simons couplings

Understand

We study the role of Chern--Simons couplings for the appearance of enhanced symmetries of Cremmer--Julia type in various theories.

• It is shown explicitly that for generic values of the Chern--Simons coupling there is only a parabolic Lie subgroup of symmetries after reduction to three space-time dimensions but that this parabolic Lie group gets enhanced to the full and larger Cremmer--Julia Lie group of hidden symmetries if the coupling takes a specific value.
• This is heralded by an enhanced isotropy group of the metric on the scalar manifold.
• Examples of this phenomenon are discussed as well as the relation to supersymmetry.