New Supersymmetric Localizations from Topological Gravity

Understand

Supersymmetric field theories can be studied exactly on suitable off-shell supergravity backgrounds.

• We show that in two dimensions such backgrounds are identifiable with BRST invariant backgrounds of topological gravity coupled to an abelian topological gauge multiplet.
• This latter background is required for the consistent coupling of the topological `matter' YM theory to topological gravity.
• We make use of this topological point of view to obtain, in a simple and straightforward way, a complete classification of localizing supersymmetric backgrounds in two dimensions.