# Callum Brodie

# Callum Brodie

Graduate Student

I'm a final year DPhil student working in the particle theory group. More specifically I work with the string theory group under Andre Lukas. My research focuses on string model-building and string dualities, primarily models in heterotic string theory, and the duality between heterotic string theory and F-theory. More information can be found under the 'Research' tab.

I am fully-funded by an STFC Studentship, and I am a member of Brasenose College, where I am a Senior Hulme Scholar.

Previously I completed my undergraduate studies also at the University of Oxford (MPhysPhil Physics and Philosophy). My fourth year project was 'Statistical Correlations of Explicit Type IIB Flux Vacua', supervised by Dr David Marsh and Dr Joseph Conlon.

**Tutor for the Department of Physics, University of Oxford (May 2018 to June 2018)**

Tutor to Mathematical and Theoretical Physics Masters students in the Standard Model of particle physics.

**Tutor for St Peters College, University of Oxford (November 2017)**

Tutor to second year physics students in thermodynamics.

**Tutor for Brasenose College, University of Oxford (January 2017 - Present)**

Tutor to third year physics students in advanced classical mechanics.

**Physics tutoring at d’Overbroeck’s College, Oxford (Oct 2012 - Present)**

Tutor to students interested in applying for undergraduate Physics and undergraduate Engineering at the University of Oxford.

**Research achievements**

My areas of research are string model-building and string dualities. Two of the string theory frameworks in which I have worked most heavily are heterotic string theory and F-theory.

With Braun and Lukas, I built phenomenologically interesting heterotic string models in a novel class of situations. We extended the existing toolbox to new classes of manifolds, and performed a systematic search for phenomenologically interesting models. Using powerful tools from algebraic geometry we determined which models were phenomenologically interesting.

Myself, Braun, Lukas, and Ruehle extended the language of heterotic/F-theory duality, paving the way for the construction of the F-theory duals of the above heterotic models. As these models did not have a standard dual, we conjectured an extension of the duality and we performed many non-trivial checks of the conjecture.

In exploring extensions of the language of heterotic/F-theory duality, we characterised and classified how NS5-branes can be included. NS5-branes are a required ingredient in heterotic model-building, but the F-theory duals had not been extensively explored. We included NS5-branes systematically, and constructed the corresponding F-theory models. We also detailed many non-trivial aspects of the duality for these objects.

We also described the F-theory dual of intersecting or coincident NS5-branes. This is an ingredient in heterotic models that has not been explored, but which would give a completely new sector to utilise in model-building. We described in detail the dual F-theory picture, making explicit the global F-theory geometry. This dual picture has the potential to further the understanding of these objects in heterotic string theory.

**Current and future research**

I have been pursuing other extensions of heterotic/F-theory duality, in particular to situations where the heterotic elliptically fibered space has multiple sections, or where the flux is not 'flat on the fibre'. These extensions would allow the duality to be used for new classes of models, and would give a much richer understanding of this duality. There are also exciting possibilities to use heterotic/F-theory duality to understand heterotic superpotentials, and also to use this duality to make further progress on understanding stacks of NS5-branes in heterotic model-building.

I am also currently pursuing research on constructing SU(3) structures on internal spaces for model-building. The construction of these would allow the use of differential geometry tools to be systematically applied for the first time in this context. This in turn would allow for the first time the computation of quantities like Yukawa couplings which are crucial for model-building efforts. Additionally I am pursuing research on M-theory/F-theory/heterotic dualities, for manifolds with G2 holonomy, which are crucial for model-building with M-theory. These are promising areas with important consequences for our understanding of string dualities and model-building