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arXiv · 2602.21658

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

Evgeny Skvortsov·Richard Van Dongen
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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.

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Evgeny Skvortsov, Richard Van Dongen. 2026-08-26. Dirichlet, Neumann, Mixed and self-dual holography: (self-dual) Yang-Mills theory. https://arxiv.org/abs/2602.21658

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