Dr Matthew Buican

Dr Matthew Buican

Royal Society University Research Fellow
School of Physics and Astronomy
Queen Mary, University of London
327 Mile End Road, London, E1 4NS

Telephone: 020 7882 3462
Room: G O Jones 601

My current research interests include:

• Non-perturbative aspects of Superconformal Field Theories (SCFTs) and Supersymmetric Renormalization Group flows in various dimensions

• Conformal manifolds and exactly marginal deformations of SCFTs

• Relations between conformal manifolds and moduli spaces of vacua

• Emergent / accidental symmetries in Quantum Field Theory (QFT)

• Hidden operator algebras in QFT

• Relations between Topological Field Theories and CFTs

• Understanding topological and analytic properties of the space of QFTs

• New microscopic models for CFTs in various dimensions

• Hitchin Systems, M5 branes, and SCFTs in 3D and 4D

My teaching

I am in the process of creating a course called "Supersymmetric Methods in Theoretical Physics" for the MSci program. The course will debut in January 2018.

Here is a rough idea of what will be covered (if you have any comments or are interested in taking the course, please feel free to email me):

Aims and objectives:

The main aim of this course is to introduce fundamental aspects of theoretical physics---symmetries and constraints on the behavior of quantum systems, renormalization, and dualities---through the filter of supersymmetry. In particular, we will tackle various non-trivial examples of these phenomena in a manageable and calculable way. By spending most of the course in three space-time dimensions, we can learn some of the basics of quantum dynamics at strong coupling just using matter superfields and abelian gauge multiplets. This course is designed to be useful for students interested in various theoretical sub-disciplines like particle physics, condensed matter, and string theory.


Starting with supersymmetric quantum mechanics as a toy model, the course covers the supersymmetry algebra, its representations, the Witten Index, and the resulting constraints on quantum dynamics. We then move on to introduce supersymmetric field theories in three space-time dimensions consisting of scalars and fermions while giving a basic introduction to symmetry currents, the classical and quantum Wilsonian renormalization group flow, moduli spaces, spurions, and non-renormalization arguments. The course is designed to culminate with a study of dualities in three-dimensional supersymmetric abelian gauge theories. However, if time permits, we may also discuss basic aspects of dualities with broken supersymmetry, explicit applications of superspace techniques to condensed matter systems, or embeddings of some of our dualities in string theory.


SPA6413 Quantum Mechanics B, SPA6324 Mathematical Techniques 4 or equivalents


SPA7018P Relativistic Waves and Quantum Fields or equivalent

My grants / recent awards

• "Argyres-Douglas Theories, S1 Reductions, and Topological Symmetries" (written in collaboration with Dr. Takahiro Nishinaka) was recently included in the  ​Journal of Physics A Highlights of 2016 Collection

• Royal Society University Research Fellowship, "New Constraints and Phenomena in Quantum Field Theory"

Some Selected Talks

• 8/2016, Strings 2016 (Beijing, China), "Conformal Manifolds, Moduli Spaces, and Chiral Algebras," https://www.youtube.com/watch?v=jq-5dcNQiRs

• 7/2016, GGI Workshop on Conformal Field Theories and Renormalization Group Flows in Dimensions d>2 (Florence, Italy), "Conformal Manifolds and Chiral Algebras"

• 3/2015, Princeton University, "Conformal Manifolds and Argyres-Douglas Theories"

• 1/2014, Quantum Fields Beyond Perturbation Theory (KITP, UC Santa Barbara), "Minimal Distances Between SCFTs," http://online.kitp.ucsb.edu/online/qft-c14/buican/

• 11/2013, Solvay Workshop on Exploring Higher Energy Physics (Brussels, Belgium), "Minimal Distances and the RG Flow"

 • 5/2012, Planck 2012 (Warsaw, Poland), "R Symmetry and Emergent Symmetry"

• 11/2011, Harvard University, "R Symmetry and Non-Perturbative QFT" 

PhD Projects

•  Microscopic Models for New Rational Conformal Field Theories

•  New Constraints on the Supersymmetric Renormalization Group Flow in Three and Four Dimensions

•  Infinite Dimensional Symmetries and QFT in d > 2

•  Non-Local Operators and Condensed Matter Systems