Theoretical and Mathematical Physics Mani L. Bhaumik Institute for Theoretical Physics

Professor Eric D’Hoker

Eric D’Hoker, in collaboration with Oliver Schlotterer and Martijn Hidding of Uppsala University, has been developing a novel mathematical framework for the investigation of superstring scattering amplitudes, with potential applications to gravity and gauge amplitudes. In particular, they reduced the major bottleneck of spin structure summations to a more tractable problem in modular forms and cast the result in terms of polylogarithms on higher-genus Riemann surfaces, which they developed along the way.

In collaboration with graduate student Sriram Bharadwaj, D’Hoker investigated the relatively poorly understood but physically exciting Argyres-Douglas superconformal Yang-Mills theories. These theories contain massless particles with electric and magnetic charges that are mutually non-local and defy standard quantum field theory methods. Using small mass deformations, the authors developed a reliable quantitative approach to the study of these theories. 

Finally, during the covid years, D’Hoker worked on a book project in collaboration with Justin Kaidi (who obtained his PhD from UCLA in 2020 and is currently a junior faculty member at the University of Washington in Seattle), a project that grew out of a graduate course D’Hoker taught in 2017. The book, entitled Modular Forms and String Theory, is to be published by Cambridge University Press by late 2024. Its subject is the unification of concepts and methods that are common to string theory (an extension of quantum field theory in Physics) and to the theory of modular forms (a key ingredient in Andrew Wiles’s proof of Fermat’s Last Theorem in Mathematics).