Dirichlet, Neumann, mixed and self-dual holography: (self-dual) Yang–Mills theory

A

bstract

Motivated by applications of self-dual theories to the AdS/CFT correspondence, we study self-dual Yang–Mills theory (SDYM) and its relation to Yang–Mills theory and to Chalmers–Siegel theory with Dirichlet, Neumann, and mixed boundary conditions. A Fefferman–Graham analysis of SDYM is performed to identify its boundary CFT data. We make a proposal for self-dual holography that defines 3 d “self-dual CFTs”. The bulk-to-bulk and boundary-to-bulk propagators for SDYM and for Yang–Mills/Chalmers–Siegel theory with mixed boundary conditions are derived in Feynman and axial gauges. Three- and four-point functions are computed in the spinor-helicity formalism, and the relations among the results in the various theories are clarified. The flat limit and the gauge-(in)dependence of the results are analyzed.