This week

The study of non-abelian gauge theories in compact or non-flat spaces can be useful to gather insights and new perspectives on the confinement problem. We consider Yang-Mills theory on four dimensional Anti-de Sitter space and wonder how signals of confinement in the bulk can be detected from boundary observables. The Dirichlet boundary condition cannot exist at arbitrarily large radius because it would give rise to colored asymptotic states in flat space and hence a deconfinement-confinement transition has to occur as the radius is increased. By perturbative computations we provide evidence for the scenario of merger and annihilation. Namely, the theory with Dirichlet boundary condition stops existing because it merges and annihilates with another theory. We also derive a general result for the leading-order anomalous dimension of the so called displacement operator for a generic perturbation in Anti-de Sitter, showing that it is related to the beta function of bulk couplings.

I will discuss recent work on N=4 SYM with Gaiotto-Witten boundaries, defects and interfaces. This broad class of theories with its high degree of supersymmetry and rich defect dynamics is a natural laboratory for exploring the physics of boundaries and defects, and it contains boundary conformal field theories that underlie string theory realizations of double holography. We will discuss a tight interplay between the holographic duals of these theories and the matrix models arising from supersymmetric localization, defect one-point functions, and large-charge operators.