Seminar talk, 24 December 2025

Speaker: Mikhail Markov

Title: Boundary calculus for gauge fields on asymptotically AdS spaces

Abstract:
I plan to discuss the applications of the gauge PDE approach to the study of the boundary structure of gauge fields on the conformal boundary of asymptotically AdS (also known as Poincaré-Einstein) manifolds.

The main result is the construction of an efficient calculus for the gauge PDE induced on the boundary, which allows one to systematically derive Weyl-invariant equations induced on the boundary. The so-called obstruction equations (e.g. Bach in dimension d=4), higher conformal Yang-Mills equations, and GJMS operators are derived systematically, as the constraints on the leading boundary value of, respectively,  the metric, YM field, and the critical scalar field. In particular, the higher conformal Yang-Mills equation in dimension d=8, obtained within this framework appears to be new. The Weyl-invariant equations on the subleading boundary data for these fields are also derived.

The approach is very general and  can be considered as an extension of the Fefferman-Graham construction that is applicable to generic gauge fields and explicitly takes into account both the leading and the subleading sector.

References:
arXiv:2512.06576