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）资助的。超弦理论和它的非微扰完备性（称为M理论）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。该项目解决了对于理解M/超弦理论的原理以及与高能粒子物理学相关的实际方向具有根本重要性的突出问题，最终目标是找到一个可以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-对偶群及其扩展的表示，并且将进一步发展产生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。统一的N = 2麦克斯韦-爱因斯坦和杨-米尔斯-爱因斯坦超引力理论在五维和四维将进一步发展和他们的应用超对称现象学的调查。它们的M/超弦理论起源以及它们的黑洞解也将被研究。进一步发展非紧超群幺正表示的振子构造，以解决M/超弦理论及相关自旋链系统中AdS/CFT对偶中的一些突出问题。PI还将研究规范/弦对偶与减少超对称性，其对世界单理论和规范理论扩张算子的可积性的影响，以及对相关规范理论渐近Bethe Answer与微扰世界单计算的直接比较。Co-pi-Radu Roiban将研究以下问题：新技术的构建和现有技术的应用，用于超对称规范理论中的高效高循环高多重数计算，特别关注四维最大超对称理论;识别该理论散射矩阵的所有阶对称性。他还将研究超引力理论的高能量行为，特别是四维空间中最大超对称无规范超引力的行为，以及引力的微扰有限点量子理论的存在;确定所需微扰抵消的起源。关于更广泛的影响，对称性原理是所有现代物理学的基础。因此，一些方法的开发和获得的结果在这里将有应用在其他领域的理论物理以及在数学。类似地，为充分利用规范/弦对偶的可积性的结果而开发的技术在统计力学和凝聚态物理学中有应用。一些研究生将参与这里提出的研究，从而提高了培养博士的机会。宾夕法尼亚州立大学的学生。

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.