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arXiv 1102.1357hep-th
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规范理论和弦论的非微扰方面及其全息关系

Non-perturbative aspects of gauge and string theories and their holographic relations

Marine Samsonyan

摘要:

在这篇论文中,我们讨论了规范理论和弦/超引力理论中出现的非微扰现象。本文计算了一般Ω背景下具有额外伴随物质的五维极小超对称U(1)规范理论的配分函数。这些N=2^* 理论是N=4 SYM的大量变形,可以被认为是在圆上紧致化的最小超对称五维理论。这种配分函数编码非常丰富的拓扑信息。我们证明了这个配分函数在某些特殊的参数值下直接再现了瞬子的模空间的庞加莱多项式的母函数。我们讨论了超弦理论中的世界面和五膜瞬子以及(无定向)D膜瞬子和对BPS饱和耦合的阈值修正的基本方面。我们认为非微扰的超势产生的“规范”和“异国情调”的瞬子生活在D3膜orientifold奇点。我们还讨论了T^4/Z_2上世界片与D弦瞬子的相互作用。我们专注于一个4费米振幅,并提供一个多D弦瞬子的解释。我们还讨论了AdS/CFT对应和瞬子的作用。我们专注于AdS 4/CFT 3对应。我们利用群论技巧重新讨论了S^7/Z_k上11-d超引力的卡鲁扎-克莱因紧化,这种方法可能在其他具有内部陪集空间的通量真空中找到应用。在SO(2)中性态中,我们确定了与最近讨论的CP ^[3]上IIA型世界面瞬子耦合的边缘形变和场。我们还讨论了Osp(8)的荷电态、对偶算符和Z_k投影|4)单例及其张量积。我们指出,在边界CS理论中,在T Hooft耦合消失的极限下,双重态谱可以解释N =6的高自旋对称性增强。

英文摘要:

In this thesis we discuss non-perturbative phenomena emerging in gauge and in string/supergravity theories. We compute the partition function of 5D minimal supersymmetric U(1) gauge theory with extra adjoint matter in general Omega-background. These N=2^* theories are massive deformations of N=4 SYM and can be thought of as a minimal supersymmetric five dimensional theory compactified on a circle. Such partition functions encode very rich topological information. We show that this partition function at some special values of the parameters directly reproduces the generating function for the Poincare` polynomial of the moduli space of instantons. We discuss the basic aspects of worldsheet and penta-brane instantons as well as (unoriented) D-brane instantons and threshold corrections to BPS-saturated couplings in superstring theories. We consider non-perturbative superpotentials generated by `gauge' and `exotic' instantons living on D3-branes at orientifold singularities. We also discuss the interplay between worldsheet and D-string instantons on T^4/Z_2. We focus on a 4-fermi amplitude and offer a multi D-string instanton interpretation. We discuss also AdS/CFT correspondence and the role of instantons there. We concentrate on AdS4/CFT3 correspondence. We revisit Kaluza-Klein compactification of 11-d supergravity on S^7/Z_k using group theory techniques that may find application in other flux vacua with internal coset spaces. Among the SO(2) neutral states, we identify marginal deformations and fields that couple to the recently discussed worldsheet instanton of Type IIA on CP^3. We also discuss charged states, dual to monopole operators, and the Z_k projection of the Osp(8|4) singleton and its tensor products. We show that the doubleton spectrum may account for N =6 higher spin symmetry enhancement in the limit of vanishing 't Hooft coupling in the boundary CS theory.

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