Theory of Elementary Particles

弦理论最近最重要的发展之一是AdS/CFT对应两边的可积性的发现。Nepomechie的主要目标是将可积量子自旋链和可积量子场论的技术应用于弦/规范理论中的问题，这些技术是他在过去二十年中帮助发展起来的。他已经对精确的体积和边界散射矩阵的理解做出了贡献，他计划利用这些来获得进一步的精确结果。阿尔瓦雷斯将在量子场论和弦理论方面进行研究。Alvarez正在研究椭圆属到Dirac-Ramond算子族的推广。Dirac算子的Atiyah和Singer的族指标定理可用于规范理论中研究破坏理论量子化的异常。弦理论中的类比应该是Dirac-Ramond算子的族指标定理。即使我们并不真正知道什么是弦理论，这个族指标定理应该给我们一些关于理论结构的信息，超越摄动理论。这是一个重要的尝试，试图了解弦理论的非摄动方面。这项研究的广泛影响如下：这项工作可能为弦理论、数学以及凝聚态物理和统计力学开辟新的方向。阿尔瓦雷斯和内波梅契都将帮助为下一代美国公民，特别是迈阿密拉丁裔社区的公民提供科学培训。他们的研究结果将通过互联网和科学出版物以及研讨会和国际会议传播。这些pi还在当地的公立学校做科学讲座。

One of the most important recent developments in string theory is the discovery of integrability on both sides of the AdS/CFT correspondence. Nepomechie's main objective is to apply techniques of integrable quantum spin chains and integrable quantum field theories, which he has helped develop during the past two decades, to problems in string/gauge theory. He has already contributed to the understanding of exact bulk and boundary scattering matrices, which he plans to exploit to obtain further exact results. Alvarez will conduct research in quantum field theory and string theory. Alvarez is studying the extension of the elliptic genus to families of Dirac-Ramond operators. The families index theorem of Atiyah and Singer for the Dirac operator can be used in gauge theories to study the anomalies that spoil the quantization of the theory. The analog in string theory should be a families index theorem for the Dirac-Ramond operator. Even though we do not really know what is string theory, this families index theorem should give us some information about the structure of the theory beyond perturbation theory. This is an important attempt at trying to learn about non-perturbative aspects of string theory. The broader impacts of this research are as follows: this work may open new directions in string theory, mathematics, as well as condensed matter physics and statistical mechanics. Both Alvarez and Nepomechie will help provide scientific training to the next generation of American citizens, in particular to those from the Latino community in Miami. Their findings will be disseminated through the internet and scientific publications, as well as through seminars and international conferences. The PIs also give lectures at local public schools on science.