74th North British Mathematical Physics Seminar

Abstract: The positivity of states is one of the foundational axioms of quantum theory. Like all good axioms, it is worthwhile to break it. We review an algebraic analogue of the Stone-Von Neumann theorem which gives a classification of indefinite representations of the Heisenberg algebra. Such representations are physical when the positive sector is preserved by a superselection rule. Jumping to field theory, we show that indefinite field theories are causal, unitary, and physical operators have well-defined Kallen-Lehmann spectral representations. As an example, we consider an indefinite analogue of the Abelian Higgs model with a non-compact O(1,1) gauge group. We find that the theory is unitary, renormalisable, and asymptotically free.

Abstract: We show that scattering amplitudes on any gauge theory background admitting a coherent state description double copy to amplitudes in a curved spacetime. The metric of the spacetime is built from the gauge background using a notion of classical double copy which emerges naturally at the amplitude level. In the self-dual sector this map relates backgrounds which are exact vacuum solutions in gauge theory and gravity.

Abstract: In optics, Malus' law describes the intensity of a polarised light beam passing through a linear polariser, depending on the angle between polarisation and polariser. In quantum mechanics, the same law also describes the dependence of the probability distribution in spin measurements with polarised initial states on the angle of the detector. A similar setup can be studied in quantum field theory. Using the measurement framework of Fewster and Verch, we model the measurement of the polarisation of a polarised light ray within quantum field theory by considering a complex Proca field linearly coupled to a complex scalar in a polarisation-dependent way. Up to second order in the coupling, the measured amplitude satisfies Malus' law, demonstrating that this model can indeed reproduce features of quantum and classical optics within quantum field theory.

Abstract: We introduce the ℤₙ-twisted trigonometric sigma models, a new class of integrable deformations of the principal chiral model. Starting from 4d Chern-Simons theory on a cylinder, the models are constructed by introducing a ℤₙ branch cut running along the non-compact direction. After explaining how the construction works for the simplest class of models, we will discuss their physical properties, including their symmetries, and possible applications.

Abstract: The quarter century since the pioneering work of Gomis and Ooguri has seen a massive surge in interest in non-Lorentzian string theories. We present a “proof of concept” of a wholly quantum mechanical construction of non-relativistic strings as chirally gauged WZW models on bargmannian Lie groups. We work through this procedure explicitly for the Nappi-Witten model and find string theories with different holomorphic and anti-holomorphic sectors. Choosing the appropriate matter content, we obtain a string theory whose holomorphic sector is identical to that of the Gomis-Ooguri string.

Abstract: Einstein's equations imply that a gravitationally collapsed object forms an event horizon. But what lies on the other side of this horizon? In this talk, I will introduce our recent paper (https://arxiv.org/abs/2412.09558) in which we question the reality of the conventional solution (the black hole), and point out another, topologically distinct solution: the black mirror. In the black hole solution, the horizon connects the exterior metric to an interior metric which contains a curvature singularity. In the black mirror, the horizon instead connects the exterior metric to its own CPT mirror image, yielding a solution with no curvature singularities. I will explain the general stationary (charged, rotating) black mirror solution, and also describe the general black mirror formed by gravitational collapse. The black mirror is the relevant stationary point when the quantum path integral is equipped with suitably CPT-symmetric boundary conditions, that we propose. It appears to avoid many vexing puzzles which plague the conventional black hole.