16 Supersymmetries - a half-way meeting in the City

这笔拨款将用于举办一个关于N=2超对称四维规范理论及其在规范/弦对应下的弦理论的最新发展的研讨会。我们的目标是汇集该领域的国际领先研究人员，展示他们的最新成果，分析该领域的最新技术，并激发合作，以确定和解决该研究领域的突出问题。现代弦理论最重要的发展之一是发现规范理论与弦理论之间的对偶。这些显著的对偶性假定了非阿贝尔规范理论与弯曲时空上的弦论所描述的引力量子理论是等价的，在非微扰水平上揭示了这两种先验上非常不同的理论之间未被探索的联系。这是我们第一次通过弯曲时空上的弦理论对强耦合规范理论进行定量处理，它解决了现代理论物理学中的一个关键问题。关于这种对偶性，研究得最多的例子可能是N=4的最大超对称（32个超对称）SU（n）超杨-米尔斯（SYM）理论和AdS_5 x S^5上的对偶IIB超弦理论。这种对偶对在最近几年已经得到了比较好的理解，部分原因是因为保留了大量的超对称性，部分原因是对偶两边都有可积结构。N=2对偶对（16个超对称）的例子在文献中是已知的，但通常不太清楚。与此同时，N=2超对称的规范理论比N=4规范理论有更丰富的结构;例如N=2的规范理论可以有不同表示的场，就像标准模型一样。继塞贝格和维滕的著名工作之后，N=2规范理论被看作是一个中途之家：它们都有许多现实的特征，但其中一个由于超对称性的存在而保留了大量的控制。因此，对一般N=2理论及其弦理论的详细了解，有助于我们理解非微扰规范理论动力学。最近，文献中出现了许多与16超对称性理论有关的新结果。仅举三例：首先，盖奥托发现了一个非常一般的N=2超对称规范理论的优雅结构，并与马尔达西纳一起发现了一个研究它们的引力理论的形式。其次，许多作者（包括PI）一直在将用于研究最大超对称规范/弦对偶对的可积性方法扩展到超对称性较差的情况（包括具有16个超对称性的情况），这表明此类技术也可能与N=2超对称四维规范理论的规范/弦对偶对相关。最后，在Nekrasov，Alday，Gaiotto和Tachikawa以及后来的Wyllard的一些结果的基础上，建立了N=2超对称规范理论的某些子扇区与Liouville和户田理论之间的关系。总之，我们相信，在过去的一年左右，越来越多的文献出现了新的光规范理论与16超对称。这表明，一个关于N=2超对称四维规范理论及其弦理论的研讨会将是特别及时的，并可能激发进一步的重大突破。

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.