Theoretical Particle Physics at City University London

With the arrival of the latest set of LHC on the Particle Physics arena, theoretical particle physics finds itself at a critical juncture. Having found the last missing element of the Standard Model, the Higgs boson, the LHC experiments are focussed on finding new physics that go beyond the Standard Model. At the same time, in the theoretical physics community there are a number of outstanding problems that will benefit from the information that we expect to arrive from the LHC. This project will investigate two key problems in modern theoretical physics.

Firstly, we will investigate strongly coupled gauge theories using the so-called gauge/string correspondence. Much remains to be learnt about strongly coupled gauge theories. In recent years, there have been significant breakthroughs in understanding certain gauge theories using the gauge/string correspondence. In particular, the mathematical tools known as integrability have provided an incredibly precise analytic handle on certain supersymmetric strongly interacting gauge theories. These tools have been extended, in part by our group, to certain settings with relatively little supersymmetry. Low-supersymmetry gauge theories have also been shown, through the so-called dimer models to have intimate links to the mathematics of algebraic geometry and algebraic number theory. In this project we will significantly build on these results to exploit these new mathematical tools and methods to understand the strong-coupling dynamics of less supersymmetric gauge theories and their gauge/string dualities.

Secondly, we will explore beyond-the-Standard-Model physics that can be obtained as a consistent low-energy theory from string theory. String theory has provided a framework for unifying gauge and gravity interactions into a single consistent quantum theory. One of the key challenges has been to identify particular examples of string theory compactifications which will lead to realistic low-energy physics. Our group will systematically search through the very large number of consistent string vacua, for those models which are consistent with the Standard Model and any new physics found by the LHC. Our past experience suggests that stringy geometries which could give the Standard Model are very rare. This in turn hints at the uniqueness, rather than the huge degeneracy, of string vacua, and we aim to extensively test this hypothesis.

This project will support Theoretical Particle research at City University London. Its two principal aims are (i) the study of gauge theories, which, for example, describe the interactions between elementary particles that in turn make up nuclei; and (ii) obtaining a theory of particle physics consistent with real-world observations from string theory.

The outcomes of this project will have a direct impact on academic research. We expect the proposed research to bridge a number of fields ranging from particle physics phenomenology, through mathematical disciplines such as algebraic geometry and integrability, to applications of computerised searches to theoretical physics. As such, we anticipate that the results our group will produce may well be of interest to these researchers. For example, our work on strongly coupled gauge theories is likely to be of interest to condensed matter physicists who are also interested in strongly coupled phenomena. Equally our work on applications of algebraic geometry to string theory is likely to be of considerable further interest to pure mathematicians working on geometry, representation theory and related areas. Finally, part of our project has a strong computational component and may lead to impact at the interface of computer science, numerical algebraic geometry and physics. In order to maximize this impact, we have requested travel funding and visitor money: presenting our work to a wide audience at conferences, and inviting short-term visitors represents a very effective way of impacting on a wide segment of the research community. Further we have requested some funds for the setting-up and maintenance of web-pages for the project, on which we intend to highlight the on-going results and achievements.

The project also intends to continue our strong collaborative links with other institutions. In particular, we have well-established connections with researchers at Imperial College, NORDITA, ETH Zurich, Oxford University, University of Pennsylvania, Northeastern University, Virginia Tech, Notre Dame and University of Witwatersrand, South Africa. Several of these include links with senior academics such as John McKay, Shing-Tung Yau, Arkady Tseytlin and Kostya Zarembo who are amongst the world-leaders in their fields and have made very significant contributions to theoretical physics. Our on-going collaborations are likely to produce a significant impact on the research outputs, as described in the main text of the application. They will also contribute to the strengthening of international scientific ties at City University, and strengthen our position as a growing young UK research group in particle physics.

Our group has a strong track record of pre- and post-doctoral research training with many of our students and junior collaborators going on to more senior academic positions (Ohlsson Sax, Sfondrini) or taking high-skilled jobs in industry and government (Lloyd, Matti). As well as continuing such mentoring, this project will contribute to the advanced training of a post-doctoral researcher, and in this way increase human capital. The cutting-edge theoretical physics and related skill-base, will enable a talented early-stage researcher to significantly enhance her/his know-how. The researcher will acquire a significant extra set of expertise during the project, both directly related to research, and more broadly the ability to think analytically while bridging a number of disciplines. This will produce impact by helping to establish the post-doctoral researcher as an independent active young scientist and significantly increase his/her chances of a permanent academic position following this post.