16 Supersymmetries - a half-way meeting in the City

This grant will cover the costs of organising a workshop on recent developments in N=2 supersymmetric four-dimensional gauge theories and their string duals under the gauge/string correspondence. We aim to bring together the leading international researchers in the field to present their latest results, analyse the state-of-the-art of the field, and inspire collaborations to identify and tackle the outstanding problems in this research area.One of the most important developments in modern string theory has been the discovery of dualities between gauge theories and string theories. These remarkable dualities postulate the equivalence of non-abelian gauge theories and quantum theories of gravity, as described by string theories on curved spacetimes, unravelling an unexplored connection between these two, a priori very different, types of theories at a non-perturbative level. This has given us for the first time a quantitative handle on a strongly coupled gauge theory via string theory on a curved spacetime, which tackles one of the key questions in modern theoretical physics. Perhaps the most studied example of this duality is the maximally supersymmetric (32 supersymmetries) N=4 SU(n) super Yang-Mills (SYM) theory and the dual Type IIB superstring theory on AdS_5 x S^5. This dual pair has become relatively well understood in recent years, in part because of the large amount of supersymmetry preserved and in part because of integrable structures identified on both sides of the duality. Examples of N=2 dual pairs (16 supersymmetries) are known in the literature, but are in general less well understood. At the same time, gauge theories with N=2 supersymmetry have a much richer structure than N=4 gauge theories; for example N=2 theories can have fields in different representations of the gauge group, as is the case with the Standard Model. Following the celebrated work of Seiberg and Witten, N=2 gauge theories have been viewed as a half-way house: they have both many realistic features yet one retains a good deal of control due to the supersymmtry present. As a result, a detailed understanding of general N=2 theories and their string theory duals is lightly to shed light on our understanding of non-perturbative gauge theory dynamics.Recently, a number of novel results relating to theories with 16 supersymmetries have appeared in the literature. To name just three: Firstly, Gaiotto has identified an elegant construction of very general N=2 supersymmetric gauge theories, and, together with Maldacena, found a formalism for studying their gravity duals. Secondly, a number of authors (including the PI) have been extending the integrability approach used to study the maximally supersymmetric gauge/string dual pair to less supersymmetric cases (including cases with 16 supersymmetries), suggesting that such techniques may also be relevant for gauge/string dual pairs of N=2 supersymmetric four dimensional gauge theories. Finally, building on some previous results of Nekrasov, Alday, Gaiotto and Tachikawa and later Wyllard have conjectured a relation between certain sub-sectors of N=2 supersymmetric gauge theories and Liouville and Toda theories. To summarize, we believe that over the past year or so a growing body of literature has appeared which sheds new light on gauge theories with 16 supersymmetries. This suggests that a workshop on N=2 supersymmetric four-dimensional gauge theories and their string duals would be particularly timely, and may stimulate further significant breakthroughs.

The proposed workshop will bring together the leading international researchers in the field to present and discuss the state-of-the-art of the field. Interactions and discussions amongst such a critical mass of world experts in the field of N=2 supersymmetric gauge theories and related topics is likely to generate a high impact on several areas of mathematical physics including (i) non-perturbative dynamics of gauge theories and the gauge/string correspondence, (ii) the mathematics of mirror symmetry, topological invariants and the Langlands programme (iii) integrability techniques in string theory and other two-dimensional field theories such as Liouville and Toda theories (iv) string theories with fluxes. The workshop will allow ample time for formal and informal discussions amongst participants across these diverse fields with the aim of identifying key problems and establishing new collaborations amongst the attendees. We aim to make the workshop a high-visibility event, in order to increase its impact on theoretical and mathematical physics research given above and so as to promote the high standing of UK research in this area. To acheive these objectives we will: (i) publicise the workshop beforehand through the established channels in the field (see impact plan) so as to reach the widest possible audience (ii) a number of prominent researchers in the field have already agreed to participate in the workshop (see Workplan). (iii) Participants will be asked to acknowledge the workshop and EPSRC funding for it in any research papers that they may write which have benefited from the workshop (iv) build and promote a website for the conference; this will contain all the standard workshop information, as well as the transparencies of the talks given at the workshop so as to reach the widest possible audience in the post-conference phase. Finally, we will not be charging a conference fee and will encourage early-stage researchers to attend the meeting with the aim of promoting informal discussions with the world's leading experts in the field. Such exposure is often a vital part of training of young researchers and can significantly build their academic capacity.