Boundaries and Defects in Quantum Field Theory
The partnership between 3D gravity and Chern-Simons theory is well-known and powerful, but many aspects of this relation are unclear.
In this talk I'll discuss Wilson lines in Chern-Simons theory and their role in AdS3 gravity. Wilson lines are interesting objects to explore locality in Chern-Simons theory, and how they affect the partnership at the quantum level.
I will start by reviewing the definition and properties of complexity as well as the relevant holographic proposals. I will then describe the results of [1811.12549] where we studied the two holographic complexity proposals for the case of a 2d boundary CFT with a conformal defect using a Randall-Sundrum type model of a thin AdS_2 brane embedded in AdS_3. Our results indicate that this setup can be used to distinguish the two holographic proposals for the complexity.
We review recent results on the calculation of one-point functions in dCFTs corresponding to N=4 SYM with domain walls, discussing supersymmetric as well as non-supersymmetric cases. In particular, we address the integrability properties of the theories and the status of the comparison to dual string theoretical computations.
We will discuss a new anomaly in the space of coupling constants. We will demonstrate it and its applications in simple examples and in 4d gauge theories.
We show that when an external magnetic field parallel to the boundary is applied, Weyl anomaly give rises to a new anomalous current transport near the boundary. Similar to the Casimir effect, this transport phenomena has its origin in the effect of the boundary on the quantum fluctuations of the vacuum. The near-boundary current takes universal form for general boundary quantum field theories, which are covariant, gauge invariant, unitary and renormalizable. We verify the universal law of current by studying free QFT and holographic BCFT.
Four-dimensional Yang-Mills and (massive) QCD with minimal N=1 supersymmetry are theories with multiple gapped vacua. Therefore, different regions of space can sit in different vacua and be connected by BPS domain walls. I will present a compact 3D worldvolume description of the walls, capable of classifying all possible BPS walls between vacua and of capturing a 2nd order phase transition as the quark mass is varied. Such a proposal will be confirmed by explicit 4D constructions of BPS domain walls, extending the existing literature.
We study the spectrum of defect conformal field theories (CFTs), and show the existence of universal accumulation points in the defect spectrum. This is achieved by obtaining an inversion formula for the bulk to defect OPE, akin to the Lorentzian inversion formula of Caron-Huot for CFTs without defects. We conclude by applying the result in examples and with an outlook.