Schedule

Monday, July 4

11:00 - 12:00 Symmetry in quantum gravity via n-groups

14:00 - 15:00 Gaudin integrability of conformal partial waves

15:00 - 16:00 Path-integral finiteness and the effective action for Regge quantum gravity

Tuesday, July 5

11:00 - 12:00 Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with boundary

14:00 - 15:00 Standing wave solutions in Born–Infeld theory

Venue

Room 3.24 Building 8 Campus de Gambelas

Titles and abstracts

• I. Burić

Gaudin integrability of conformal partial waves

Conformal partial waves are kinematic building blocks of any conformal field theory. Over recent years, it has become understood that partial waves for different kinds of correlation functions are closely related to wave functions of quantum integrable models. In this talk, I will explain the most general form of this relation, in which an arbitrary N-point function together with a choice of an OPE channel is associated with a particular limit of the Gaudin integrable system. Time permitting, I will discuss special cases in which the Gaudin model reduces to the Calogero-- Sutherland Schrödinger problem.

• N. Manojlović

Standing wave solutions in Born–Infeld theory

We study standing-wave solutions of Born–Infeld electrodynamics, with a nonzero electromagnetic field in a region between two parallel conducting plates. We consider the simplest case which occurs when the vector potential describing the electromagnetic field has only one nonzero component depending on time and on the coordinate perpendicular to the plates. The problem then reduces to solving the scalar Born–Infeld equation, a nonlinear partial differential equation in 1+1 dimensions. We apply two alternative methods to obtain standing-wave solutions to the Born–Infeld equation: an iterative method, and a “minimal surface” method. We also study standing wave solutions in a uniform constant magnetic field background. The results obtained in this work provide a theoretical background for experimental tests of Born–Infeld theory.

• A. Miković

Finiteness and effective action for Regge quantum gravity

We review the construction of the path integral and the corresponding effective action for the Regge formulation of General Relativity under the assumption that the short-distance structure of the spacetime is not a smooth 4-manifold, but a piecewise linear manifold based on a triangulation of a smooth 4-manifold. We point out that the exponentially damped 4-volume path-integral measure does not give a finite path integral, although it can be used for the construction of the perturbative effective action. We modify the 4-volume measure by multiplying it by an inverse power of the product of the edge lengths such that the new measure gives a finite path integral while it retains all the nice features of the unmodified measure.

• I. Salom

Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with boundary

After a general introduction on Algebraic Bethe Ansatz in the context of spin-chains and Gaudin algebras, we will discuss the non-periodic trigonometric sl(2) Gaudin model with triangular boundary, with an emphasis on specific freedom found in the local realization of the generators, as well as in the creation operators used in the algebraic Bethe ansatz. We will first find the Bethe vectors and then exploit this freedom to also obtain the solutions to Knizhnik-Zamolodchikov equations.

• M. Vojinović

Symmetry in quantum gravity via n-groups

Higher category theory can be employed to generalize the BF action to the so-called nBF action, by passing from the notion of a gauge group to the notion of a gauge n-group. The novel algebraic structures called n-groups are designed to generalize notions of connection, parallel transport and holonomy from curves to manifolds of dimension higher than one. Thus they generalize the concept of gauge symmetry, giving rise to a class of topological actions called nBF actions.

Similarly as for the Plebanski action, one can add appropriate simplicity constraints to topological nBF actions, in order to describe the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl and Majorana fields coupled to Einstein-Cartan gravity. Specifically, one can rewrite the whole Standard Model coupled to gravity as a constrained 3BF or 4BF action. The split of the full action into a topological sector and simplicity constraints sector is adapted to the spinfoam quantization technique, with the aim to construct a full model of quantum gravity with matter.

In addition, the properties of the gauge n-group structures open up a possibility of a nontrivial unification of all fields. An n-group naturally contains additional novel gauge groups which specify the spectrum of matter fields present in the theory, just like the ordinary gauge group specifies the spectrum of gauge bosons in the Yang-Mills theory. The presence and the properties of these new gauge groups has the potential to explain fermion families, and other structure in the matter spectrum of the theory.

Based on [1,2,3,4,5,6].

[1] A. Miković and M. Vojinović, Class. Quant. Grav. 29, 165003 (2012), arXiv:1110.4694.

[2] T. Radenković and M. Vojinović, JHEP 10, 222 (2019), arXiv:1904.07566.

[3] A. Miković and M. Vojinović, Europhys. Lett. 133, 61001 (2021), arXiv:2008.06354.

[4] T. Radenković and M. Vojinović, Class. Quant. Grav. 39, 135009 (2022), arXiv:2101.04049.

[5] T. Radenković and M. Vojinović, Symmetry 12, 620 (2020), arXiv:2004.06901.

[6] T. Radenković and M. Vojinović, accepted for publication in JHEP (2022), arXiv:2201.02572.