Welcome to my homepage!
I'm a lecturer in mathematics at the Department of Mathematics at the University of Surrey. My research interests lie in mathematical physics, in particular, the interplay between string theory, quantum field theory and geometry.
This page was last updated April 2018.
CV, Grants, Publications and Talks
My CV with publications is available here.
My (mostly complete) list of talks is here.Courses I am teaching are listed here.
My research interests are in the interrelations between string theory, quantum field theory and geometry. Recently, I have focussed on the study of string theory vacua through three main routes: semi-classical supergravity, sigma models and duality. descriptions of string compactifications with vector bundles (via the heterotic string) and exploring the definition of mirror symmetry for vector bundles & sheaves.
The first two orders of alpha prime corrections to heterotic supergravity are known. Using this, together with a study of local symmetries, we have constructed in 1605.05256 the natural Kahler metric on the moduli space of heterotic vacua. Signficantly, we have found an expilict Kahler potential, whose form is remarkably similar to that found in the special geometry of Calabi--Yau manifolds. This is exciting! It might mean that many of the properties of special geometry persist in the much more general context of heterotic theories. Recently, we have been working on a universal geometry for heterotic geometry; this is the extension of what in mathematics is known as a universal bundle to the heterotic context, in which supersymmetry and anomaly cancellation play a role.
In 1606.05221 I calculated the remaining fermionic and Yukawa couplings for a large radius heterotic vacuum. What is interesting is that we can describe the complete set of couplings in a compact form through a holomorphic superpotential and Kahler potential discussed above. The burning question is: what are the relations, if any, between these? Is there an analogue of a prepotential, a holomorphic function(s) that determine all the couplings, as was the case in special geometry?
The aim of this work is to understand the underlying sigma model descriptions of heterotic string compactifications. Mirror symmetry, a conjecture that arose in the 1990s that Calabi-Yau manifolds come in topologically distinct pairs, proved to be a striking geometric relation. What we have been steadily uncovering over recent years is a new type of mirror symmetry for vector bundles and sheaves. If true, this conjecture would greatly improve our understanding of the geometry of vector bundles & sheaves on Calabi-Yau manifolds.
For example in 0712.3272 and 0810.0012 we developed techniques via linear sigma models for understanding the quantum cohomology of vector bundles attained as deformations of the tangent bundle. This means physically we computed worldsheet instanton corrections to certain Yukawa couplings. In 1001.2104 we explored the moduli space of deformations of the tangent bundle, expressing quantities in a combinatorial fashion. This makes manifest some of the issues and structure of algebraic mirror symmetry for deformations of the tangent bundle. Most recently, in 1103.1322 we explored a linear sigma model description of rank 4 bundles (those not attainable as deformation of the tangent bundle).
I have written an invited review (published by IJMPA) on the status of this topic, summarising some of the most recent developments. The review is aimed at a string theorist familiar with some of the basics of string compactifications.
I am interested in using string dualities to uncover otherwise obscure properties of string vacau. With Savdeep Sethi in 1208.0261, we used various duality sequences to construct new vacua of M-theory and type IIA with fluxes. These vacua evade a famous no-go theorem by the inclusion of new higher derivative corrections to the SUGRA action. Such corrections should allow the construction of a wide array of new vacua. We followed this up with Travis Maxwel and Daniel Robbins in 1309.2577 in which we found some novel examples of flux vacua. In 1004.5447 we showed how heterotic--F-theory duality can be used to understand generic features of heterotic vacua both with and without fluxes. This leads to an interesting conclusion that the generic (perturbative) heterotic vacuum is non-geometric. This is work with Savdeep Sethi and David Morrison.
In 1101.3552 and 1107.5895 we showed how to use dualities of string theory to construct a supergravity solution describing a pair of NS5-branes intersecting in a non-trivial fashion. The nice thing about this is the solution is localised in every direction except one and this amounts to solving a Monge-Ampere equation -- a non-linear PDE -- with source terms, solutions of which are hard to come by!
This work concerns embedding four-dimensional vacua in string theory that break supersymmetry spontaneously. The eventual hope of this work is to understand how six-dimensional geometries (either brane or Calabi-Yau geometries) may give rise to phenomenologically realistic vacua. We constructed brane geometries and Calabi-Yau geometries that exhibit supersymmetry breaking features. This involves solving for the geometry perturbatively, and showing how this geometry modifies four-dimensional physics. In 0904.0459 we showed how this works for particle physics (time-independent Minkowski space) while in 0909.3319, we studied how such configurations may manifest themselves in cosmology (time-dependent Minkowski space).
In this work 0804.0613 we showed how the Hybrid formalism of Berkovits may be used to understand worldsheet descriptions of RR flux vacua. We constructed the Gukov-Vafa-Witten superpotential and showed how warping of spacetime arises.
I have also worked on plasma astrophysics. This is work primarily with Don Melrose and arose from my M. Sc. and B. Sc. theses at the University of Sydney.