Week 16.01.2022 – 22.01.2022

We will study some aspects of Quantum Chromodynamics (QCD) in d=1+1 spacetime dimensions. The theory presents many of the same challenges as d=3+1 dimensional QCD (e.g., strong interactions where perturbation theory breaks down, chiral quarks which are hard to put on the lattice, etc.). But, in 2d, there are also some special features that make the problem more tractable. We will see that one can effectively solve the system at strong coupling, revealing interesting connections to other well-studied theories such as 2d rational CFTs (minimal models, WZW models, etc.).

The black hole information paradox has been tightened to a precise contradiction by the small corrections theorem. Resolving the puzzle thus needs an order unity correction to semiclassical dynamics at the horizon. Remarkably, in string theory we find that microstates of black holes are `fuzzballs' with no horizon, which resolves the paradox. An alternative to the fuzzball paradigm is has been sought through a `wormhole paradigm' where the horizon would be continue to be described by semiclassical physics on a code subspace of the full quantum degrees of freedom. This wormhole paradigm can however can be ruled out by an extension of the small corrections theorem. We argue that the notions of ER=EPR etc underlying the wormhole paradigm are incorrect, and that the error arises from using the eternal spacetime geometry which is itself inconsistent with the requirements of unitarity.

Relative theories are non-topological theories living at the boundaries of TQFTs in one higher dimension. An interesting and well-studied class of relative theories are 6d N=(2,0) theories. I will introduce the notion of relative defects in relative theories, which are non-topological defects of the relative theory living at the boundary of a topological defect of the above-mentioned TQFT in one higher dimension. I will argue that codimension two defects of 6d N=(2,0) theories are relative defects. Relative defects carry ''trapped'' higher-form symmetries localized on their world-volume which are independent from the higher-form symmetries of the bulk theory. When the bulk theory is compactified with the insertion of relative defects, the trapped higher-form symmetries provide extra contributions to the higher-form symmetries of the lower-dimensional theory resulting from the compactification. For example, when 6d N=(2,0) theories are compactified on a Riemann surfaces with punctures (which are relative codimension-two defects) then the 1-form symmetry of the resulting 4d N=2 Class S theory obtains contributions from the 1-form symmetries trapped at the punctures, along with the well-known contribution coming from the 2-form symmetry of the 6d N=(2,0) theory; part of London TQFT Journal Club; it will be possible to follow this talk on Zoom (please register at https://london-tqft.vercel.app)