16 Supersymmetries - a half-way meeting in the City

16个超对称——城市的中途相遇

• 批准号: EP/I001638/1
• 负责人: Bogdan Stefanski
• 金额: $ 1.88万
• 依托单位: City, University of London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2010
• 资助国家: 英国
• 起止时间: 2010 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FI001638%2F1
• 关键词: 16; Supersymmetries; half; way; meeting

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.

该赠款将涵盖关于n = 2个超对称的四维规定理论及其在仪表/字符串对应下的弦二维理论的最新发展的研讨会的成本。我们旨在将该领域的主要国际研究人员汇集在一起​​，以呈现最新结果，分析该领域的最新成果，并激发合作，以识别和解决该研究领域中的杰出问题。现代弦乐理论中最重要的发展之一是发现了衡量理论和弦理论之间的二元性。这些显着的二元性假设非亚伯仪表理论和重力理论的等效性，如曲线空位上的弦理论所描述的那样，在非逆转级别上揭示了这两种截然不同的这两种理论之间的尚无探索的联系。这是我们首次通过曲线时空的字符串理论对强耦合量规理论进行了定量处理，该理论解决了现代理论物理学中的关键问题之一。也许该二元性的最多的例子是最大超对称（32个超对称性）n = 4 su（n）超级阳性（sym）理论（SYM）理论和双型IIB IIB SuperString理论，ads_5 x s^5。近年来，这对双对已经变得相对充分理解，部分原因是保留了大量的超对称性，部分原因是在双重性的两侧都可以识别出可集成的结构。 n = 2对双对的例子（16个超对称性）在文献中是已知的，但通常不太了解。同时，具有n = 2超对称性的量规理论的结构比n = 4量规理论更丰富。例如，n = 2理论可以在量规组的不同表示中具有字段，就像标准模型一样。在Seiberg和Witten的著名作品之后，N = 2量规的理论被视为中途房屋：它们具有许多现实的特征，但由于出席了超级符号，人们保留了很大的控制。结果，对一般n = 2理论的详细理解及其弦理论双重偶然阐明了我们对非扰动仪表理论动力学的理解。实际上，文献中已经出现了许多与具有16个超对称性的理论有关的新颖结果。仅举三个：首先，盖托（Gaiotto）确定了非常通用的n = 2超对称仪表理论的优雅结构，并与马尔达奇纳（Maldacena）一起发现了一种形式主义，用于研究其重力双重双重二元。其次，许多作者（包括PI）一直在扩展用于研究最大超对称性计/弦双对的整合性方法，以减少超对称病例（包括具有16个超对称性的案例），这表明此类技术也可能与N = 2 SuperSymmetrical QuaperMetricric four dimemensione的计量/字符串相关。最后，基于Nekrasov，Alday，Gaiotto和Tachikawa的一些先前结果，以及后来的Wyllard猜想了N = 2个超对称仪表理论的某些子领域与Liouville和Toda理论之间的关系。总而言之，我们认为，在过去的一年左右的时间里，出现了越来越多的文学作品，这为仪表理论提供了新的灯光，并具有16个超对称性。这表明关于N = 2个超对称的四维规定的研讨会及其串联二维理论将特别及时，并且可能会刺激进一步的显着突破。