International Journal of Modern Physics A

In this paper, I review the basic ideas of “trace dynamics”, as formulated in my 2004 Cambridge University Press book “Quantum Theory as an Emergent Phenomenon”, and then discuss how they have influenced much of my work of the last two decades.

This paper is dedicated to the memory of Lars Bink, a close friend of IA, one of the pioneers of supergravity and string theory and a physics promoter over the world and particularly in the developing countries.

We review recent developments on generalized Fayet–Iliopoulos D-terms in four-dimensional supergravity and discuss their applications to natural models of inflation driven by supersymmetry breaking with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton.

These notes contain — apart from some physics — scattered reminiscences of everyday life at the Institute for Theoretical Physics in Göteborg in the early eighties. The text has been in the making for many years. Some of it was written inspired by the Lars Brink 70-fest at The Solvay Institute in Brussels in 2014, but was never finished or published. Parts of the old text have now been replaced by a review of the quite unexpected recent renaissance for light-front higher spin theory. Lars sadly did not live to experience more than the very beginnings of this quite remarkable development.

The notion of SIC-POVMs comes from quantum theory, and they were not on the horizon when I was Lars Brink’s student in the early 1980s. In the summer of 2022, I told Lars that I know how to use number theoretical insights to construct SIC-POVMs in any Hilbert space of dimension $n^2+3$, and that the construction provides a geometric setting for some deep number theoretical conjectures. I will give a sketch of this development, of what it was like to be Lars’ student, and of what his reaction to our construction was.

It is shown how the gluing theorem due to Corvino and Shoen can be naturally extended to accommodate supertranslations at spatial infinity. Logarithmic supertranslations play an interesting role in the construction.

We discuss intriguing relations between 5d supersymmetric gauge theories of eight supercharges based on 5-brane web and cubic prepotential and propose new relations between SU gauge theories and SO/Sp gauge theories when the parameters of SU gauge theories are specially tuned.

The Landau-Nordita conference that was held in Moscow in 1981 was the first place where I met Lars. This “marvelous meeting”, as Lars quoted in one of his reminiscence papers, was organized by Alan Luther. It was an event that generated a long-lasting friendship of scientists from East and West, provided a background for the future collaborations and, in particular, my own collaboration with Lars on a supersymmetric high-spin extension of the Poincaré group.

Motivated by string-theoretic swampland conjectures, the existence of a dark fifth dimension, whose size is roughly 1–10 microns, has been proposed. A great deal of supporting evidence has been presented, and definitive experimental tests are likely to be carried out. The basic idea is that the four-dimensional space–time that we observe is confined to a brane that is localized in the dark dimension. This short note points out that there are two distinct ways to realize such a scenario in string theory/M-theory. In the one considered previously, the dark dimension is topologically a circle and our observable 4d space–time is confined to a brane that is localized in a GUT-scale region of the circle. An alternative possibility is that the dark dimension is a line interval with “end-of-the-world-branes” at each end. The latter option would imply the existence of a parallel 4d space–time, with the same gravitational forces as ours, but otherwise its own physical laws, microns away from us!

Motivated by recent advances in non-Lorentzian physics, we revisit the light-cone formulation of quantum field theories. We discuss some interesting subalgebras within the light-cone Poincaré algebra, with a key emphasis on the Carroll, Bargmann and Galilean kinds. We show that theories on the light front possess a Hamiltonian of the magnetic Carroll type, thereby proposing a straightforward method for deriving magnetic Carroll Hamiltonian actions from Lorentzian field theories.