Research
Themes
- Hidden symmetries in quantum gravity via m-theory, supergravity, string theory, and Einstein's gravity
- Kac-Moody algebras, affine and very-extended Lie algebras
- $E_{11}$, $K_{27}$, $A_1^{+++}$
Overview
My work explores hidden Kac-Moody algebraic structures in gravity, string theory, and M-theory. It has broadly ranged from applications to: M-theory via $E_{11}$; to Einstein gravity via $A_1^{+++}$; to closed bosonic strings via $K_{27}$.
A central theme of this work is the identification and exploitation of hidden Kac-Moody symmetries underlying four-dimensional general relativity, low-energy ten- and twenty-six-dimensional string theories, and eleven-dimensional M-theory.
In particular, it has shown that $K_{27}$ is a hidden symmetry of the twenty-six-dimensional closed bosonic string, paralleling the hidden $E_{11}$ symmetry of M-theory.
A Broader Perspective
This work may be viewed as part of a bigger program aimed at understanding how Kac-Moody symmetries extend beyond more familiar two-dimensional spacetime systems into higher-dimensional theories.
Two-dimensional Kac-Moody symmetries have profoundly shaped theoretical physics over the past fifty years; from conformal field theory and string theory to condensed matter physics and integrability, they reveal how infinite-dimensional symmetry can control the structure of quantum field theories.
This program explores the next stage of that development in higher-dimensional gravity, string theory, and M-theory.
Publications
A list of my publications is given on arXiv, Google Scholar, and InspireHEP.
For each work, I give a short non-technical motivation; the linked abstract gives the more technical introduction.