Séminaire de Physique Théorique
Boundary calculus for gauge fields on asymptotically AdS spacesMikhail Markov (Université de Mons, Belgique)
Thursday 20 November 2025 14:00 - Salle des séminaires - Salle 1180, bâtiment E2
Résumé :
We employ gauge PDE approach to study the boundary structure of asymptotically AdS gravity and (gauge) fields defined on this background. The essential step of the construction is the incorporation of the boundary-defining function among the fields of the theory, which allows us to realise the asymptotic boundary as a space-time submanifold by employing the gauge PDE implementation of Penrose's concept of asymptotically-simple space. In so doing the gauge PDE describing the boundary structure is obtained by restricting to the boundary of spacetime and simultaneously restricting to the boundary in the field space by setting the boundary defining function to zero. The main concrete result of this work is the construction of the efficient boundary calculus, which gives a recursive procedure to obtain the explicit form of the equations satisfied by the boundary fields and their gauge transformations for boundary dimension $d \geq 3$. These include obstruction equations (such as Bach equation or Yang-Mills equation for $d=4$) and generalised conservation equations satisfied by subleading boundary values. The approach is very general and, in principle, applies to generic (gauge) fields on the Einstein gravity background and produces a conformally-invariant gauge theory on the boundary, which describes their boundary stricture. It can be considered as an extension of the Fefferman-Graham construction that fully takes into account both the leading and the subleading boundary values of the bulk gravitational field. At the same time it gives a generalisation of the gauge PDE approach to boundary values of gauge field on AdS space to the case of a gravitational background that admits consistent propagation of these fields.
Liens :