Novel approaches to outstanding problems in M/Superstring theory, supergravity and supersymmetric gauge theories

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)提供资金的。超弦理论及其被称为M理论的非微扰完成为我们提供了唯一已知的框架，以量子力学一致的方式统一了爱因斯坦的引力和其他相互作用。这个项目解决了对理解M/超弦理论原理以及与其与高能粒子物理联系相关的实践方向具有根本重要性的突出问题，最终目标是找到能够解释我们周围宇宙的M/超弦理论的非微扰公式。Pi Gunaydin将专注于确定U-对偶群及其扩张的表示，并将进一步发展生成共形和拟共形对称群的谱，并将其应用于紧致M/超弦理论和相关超引力理论的谱。五维和四维的统一N=2麦克斯韦-爱因斯坦和杨-米尔斯-爱因斯坦超引力理论将进一步发展，并研究它们在超对称现象学中的应用。我们还将研究它们的M/超弦理论的起源以及它们的黑洞解。为了解决M/超弦理论和相关自旋链系统中ADS/CFT对偶中的一些突出问题，我们将进一步发展非紧超群的么正表示的振子结构。PI还将研究具有约化超对称性的规范/弦对偶，它对世界单理论和规范理论膨胀算符的可积性的影响，以及对相关规范理论渐近Bethe Anatz与微扰世界单计算的直接比较。Co-pi-Radu Roiban将致力于以下问题：超对称规范理论中高效高圈高重数计算的新技术的构建和现有技术的应用，特别是四维最大超对称理论；该理论散射矩阵的所有阶对称性的识别。他还将研究超引力理论的高能行为，特别是四维最大超对称无规范超引力的高能行为，以及扰动有限的类点引力量子理论的存在；识别所需的微扰抵消的起源。就更广泛的影响而言，对称性原理是现代物理学的全部基础。因此，这里发展的一些方法和所获得的结果将在理论物理的其他领域以及在数学中得到应用。同样，为充分利用规范/弦对偶的可积性结果而开发的技术在统计力学和凝聚态物理中也有应用。几名研究生将参与这里提出的研究，从而增加宾夕法尼亚州立大学博士生培训的机会。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Superstring Theory and its non-perturbative completion known as M-theory provide us with the only known framework unifying Einstein's gravity and other interactions in a quantum mechanically consistent way. This project addresses outstanding problems of fundamental importance for understanding the principles of M/Superstring theory as well as practical directions related to its connection to high energy particle physics, with the eventual goal of finding a non-perturbative formulation of M/Superstring theory that can explain the universe around us. The PI Gunaydin will focus on determining representations of U-duality groups and their extensions and spectrum generating conformal and quasiconformal symmetry groups will be further developed and applied to the spectra of compactified M/Superstring theory and related supergravity theories. Unified N = 2 Maxwell-Einstein and Yang-Mills-Einstein supergravity theories in five and four dimensions will be further developed and their applications to supersymmetry phenomenology investigated. Their M/Superstring theoretic origins as well as their black hole solutions will also be studied. The oscillator construction of unitary representations of noncompact supergroups will be further developed so as to solve some of the outstanding problems in AdS/CFT dualities in M/superstring theory and related spin chain systems. The PI will also study Gauge/string duality with reduced supersymmetry, its effects on the integrability of the world-sheet theory and of the gauge theory dilatation operator as well as on the direct comparison of the relevant gauge theory asymptotic Bethe Ansatz with perturbative worldsheet calculations. The Co-pi-Radu Roiban will work on the following problems: The construction of new techniques and the application of existing techniques for efficient higher-loop high-multiplicity calculations in supersymmetric gauge theories with particular focus on the maximally supersymmetric theory in four dimensions; the identification of all-order symmetries of the scattering matrix of this theory. He will also study the high energy behavior of supergravity theories, in particular that of the maximally supersymmetric ungauged supergravity in four dimensions, and the existence of perturbatively-finite point-like quantum theories of gravity; the identification of the origin of the required perturbative cancellations.With regard to broader impacts, symmetry principles underlie all of modern physics. Hence some of the methods developed and the results obtained here will have applications in other areas of theoretical physics as well as in mathematics. Similarly, the techniques developed for fully exploiting the consequences of integrability for the gauge/string duality have applications in statistical mechanics and condensed matter physics. Several graduate students will be involved in the research proposed here, thus enhancing the opportunities for the training of Ph.D. students at Penn State University.