Holography and d-dimensional Superconformal Field Theories

This project falls within the EPSRC Mathematical Physics research area.
My work as a DPhil is in the field of mathematical physics. More specifically,
my research centers around string theory, which has proved exceedingly useful
in studying novel facets of quantum field theories and gravitational systems in
various dimensions. In short, I am interested in employing string theory methods to gain a deeper understanding of these physical theories.
Two of my projects live at the intersection of gravity and quantum field theory furnished by the framework of holography. The holographic duality consists of a gravitational theory on one side, and a quantum field theory in one
less dimension on the other, which describe the same physics. We employ the
gravitational description to study properties of quantum field theories that are
otherwise difficult to probe.

In my work with Sebastjan Cizel, James Sparks, and Sakura Schafer-Nameki we expand upon the gravitational dual of so-called I/c-extremization, which
allows one to determine the central charge of a 1d/2d superconformal field theory
by a simple optimization procedure. In our paper, we extend the procedure to
account for the presence of string theory 7-branes, making the analysis suitable
for F-theory supergravity solutions.

My most recent research project was a collaboration with Fabio Apruzzi,
Dewi S. W. Gould, and Sakura Schafer-Nameki. We study confinement and chiral symmetry breaking from a holographic point of view, and using the modern
perspective of generalized symmetries. From the gravitational theory, we successfully identify the topological quantum field theory that lives at low energies,
and which had previously not been derived from first principles.
I have also worked with Antoine Bourget, Julius Eckhard, and Sakura SchaferNameki on higher-dimensional superconformal field theories, realised as geometric constructions in M-theory or on brane-webs in string theory [3, 4]. As for
the holographic duality, the point of employing the string/M-theory frameworks
to construct quantum field theories is that they allow us to explore regimes
which would otherwise be out of reach. The focus of this project was to bring
the geometric and brane-web descriptions of 5-dimensional superconformal field
theories closer to one another. For a small subset of theories these descriptions
embed into a unified framework, however, for the vast majority of theories this
larger picture is not yet completely understood. We provide a significant step
towards a generalization of the unified framework which should cover the full
set of 5d field theories.