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

TL;DR

This paper explores self-dual Yang-Mills theory and its holographic duals, analyzing boundary conditions and propagators to propose a new self-dual holography framework related to 3D self-dual conformal field theories.

Contribution

It introduces a novel holographic approach for self-dual Yang-Mills theories, including boundary condition analysis and explicit propagator computations in various gauges.

Findings

Derived bulk-to-bulk and boundary-to-bulk propagators for SDYM.

Computed three- and four-point functions in spinor-helicity formalism.

Proposed a framework for self-dual holography relating SDYM to 3D self-dual CFTs.

Abstract

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 $3d$ ``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.