Asymptotic Structure of Higher Dimensional Yang-Mills Theory

Abstract

Using the covariant phase space formalism, we construct the phase space for non-Abelian gauge theories in $(d+2)$-dimensional Minkowski spacetime for any $d\ge 2$, including the edge modes that symplectically pair to the low energy degrees of freedom of the gauge field. Despite the fact that the symplectic form in odd and even-dimensional spacetimes appear ostensibly different, we demonstrate that both cases can be treated in a unified manner by utilizing the shadow transform. Upon quantization, we recover the algebra of the vacuum sector of the Hilbert space and derive a Ward identity that implies the leading soft gluon theorem in $(d+2)$-dimensional spacetime.

arXiv comment25 pages; v2: Corrected the discussion in sections 2.2 and 3.2

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• Finite actions and asymptotic charges at null infinity for any spin
• Effective density matrix for vacua in asymptotically flat gravity