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

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.

Figures (9)

• Figure 1: SDYM Witten diagram for the three-point correlator.
• Figure 2: The YM three-point vertex is the sum of the SD and ASD vertices (top), which come from $(F_{AB})^2$ and $(\bar{F}_{A'B'})^2$, respectively. It can be rewritten as a vertex coming from $(F_{AB})^2$ and a topological one. The topological vertex is on the boundary, which corresponds to the gray region.
• Figure 3: SDYM Lorenz gauge $\text{AdS}_4$$s$-channel Witten diagram.
• Figure 4: The full exchange diagram splits into SD-SD ($\mathcal{W}^{\text{SD}}$), SD-Top ($\mathcal{T}^{\text{R}}$), Top-SD ($\mathcal{T}^{\text{R}}$) and Top-Top ($\mathcal{W}^{\text{L,R}}$) components.
• Figure 5: The YM $s$-channel diagram splits into two diagrams, depending on where the derivative (blue bullet) lands. The left diagram also belongs to SDYM/Chalmers--Siegel.