Holomorphic Chern-Simons theory coupled to off-shell Kodaira-Spencer gravity

Stefano Giusto, Camillo Imbimbo, Dario Rosa
2012 Journal of High Energy Physics  
We construct an action for holomorphic Chern-Simons theory that couples the gauge field to off-shell gravitational backgrounds, comprising the complex structure and the (3,0)-form of the target space. Gauge invariance of the off-shell action is achieved by enlarging the field space to include an appropriate system of Lagrange multipliers, ghost and ghost-for-ghost fields. Both the BRST transformations and the BV action are compactly and neatly written in terms of superfields which include
more » ... , backgrounds and their antifields. We show that the anti-holomorphic target space derivative can be written as a BRST-commutator on a functional space containing the anti-fields of both the dynamical fields and the gravitational backgrounds. We derive from this result a Ward identity that determines the anti-holomorphic dependence of physical correlators.
doi:10.1007/jhep10(2012)192 fatcat:aldrqojckjhgzgpbvt4qjd6jvm