# HEP – QFT Seminar Winter Term 2022/23

Prof. S. Hollands
Prof. R. Verch

Organization:
Dr. A. Much
Dr. J. Zahn

Tuesday, 15:15 – 16:45 (1 hour talk, followed by questions), seminar room 114 ITP
» how to reach the ITP
.

# Schedule for the winter term 2022/23:

Abstract: We present evidence that the structure of the standard model as a Yang-Mills Higgs theory is organised by the underlying Lie-Kac superalgebra su(3) x su(2/1). The model’s field spectrum, the existence of indecomposable replicated lepton and quark multiplets to accommodate mixing phenomena, and new results on anomaly cancellation, all support this claim. Progress towards a complete superalgebraic formulation will be discussed.
Abstract: General Relativity predicts that the black holes observed in Nature are described by the Kerr metric and its perturbations. In this talk, I consider perturbations of Kerr black holes by quantum gravitational fields reconstructed from Teukolsky variables and propose the canonical energy operator for analysing the semi-classical corrections to the black hole parameters. This scenario is particularly interesting in the extremal limit, because the semi-classical perturbations could convert the black hole to a naked singularity, thereby effectively destroying it.
Abstract: After briefly explaining the Dixmier, Poisson and Jacobian conjectures for purposes of motivation and will turn to the Mathieu conjecture and recent work concerning the latter. This is joint with with L. Tuset and K. Zwart.
Abstract: String-localized QFT improves perturbation theory by (a) preserving the Hilbert space, and (b) keeping the perturbation theory renormalizable. In massive gauge theories, (a) is achieved because the interaction is strictly BRST-invariant. (b) is achieved because the weaker localization tames the UV singularities. The ensuing string-dependence can be eliminated by allowing higher-order corrections. A prototype is the Abelian Higgs model: Interactions of a massive vector field can be renormalized without spontaneous symmetry breaking. But it must couple to a scalar field with a double-well potential self-coupling. A benefit compared to the standard BRST method is that off-shell interacting charged fields can be constructed on the Hilbert space.  Joint work with Jens Mund and Bert Schroer (arXiv:2209.06133)
Abstract: In this talk, I will outline a new scheme for nonperturbative analyses of quantized fields in contact with dynamical gravity, including full quantum gravity. In this scheme, QFTs are regularized as sequences of quasiphysical systems comprising a well-defined number of the field’s degrees of freedom. In dependence of this number, each system backreacts autonomously and selfconsistently on the gravitational (background) field. The limit which removes the regulator then automatically generates the physically correct spacetime geometry, i.e., the metric the quantum states of the field prefer to “live” in. This scheme has been probed for a scalar field and quantum metric fluctuations on self-consistent spherical background geometries as well as self-consistent hyperbolic background geometries. This elucidates the cosmological constant problem arising from the vacuum fluctuations of quantum matter fields — the problem disappears if the pertinent continuum limit is performed in the improved way advocated here.
Abstract:  We study the semi-classical Einstein equation for spherically symmetric space-times coupled to a linear scalar quantum field as a Goursat problem, i.e. an initial value problem where the initial surface is a light-cone. As a first step we adapt the Hadamard condition for two-point functions to states on the boundary-algebra of the quantum field associated with the initial null-cone, such that objects as the renormalized stress-tensor can be defined at this surface and discuss how their expectation value can be evaluated both at this surface and in the interior of the cone. From here, we can start to explore back-reaction effects.
Abstract: Given a unitary fusion category, one can define the Hilbert space of a so-called “anyonic spin-chain” and a class of nearest neighbor Hamiltonians providing a real-time evolution. There is considerable evidence that suitable scaling limits of such systems can lead to 1+1-dimensional conformal field theories (CFTs), and in fact, can be used potentially to construct novel classes of CFTs. Besides the Hamiltonians and their densities, the spin chain is known to carry an algebra of symmetry operators commuting with the Hamiltonian, and these operators have an interesting representation as matrix-product-operators (MPOs). On the other hand, fusion categories are well-known to arise from a von Neumann algebra-subfactor pair. I point out some interesting consequences of such structures for the corresponding anyonic spin-chain model: (i) There is a construction of a novel algebra of MPOs acting on a bi-partite anyonic chain (ii) This algebra is precisely isomorphic to the defect algebra of 1+1 *continuum* CFTs as constructed by Fröhlich et al. and Bischoff et al., even though the anyonic spin chain model is defined on a *finite lattice*. These results rely heavily on methods from subfactor theory, including the “double triangle algebra”, the braided structure of the categories, and the so-called $\alpha$-induction construction.