Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
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使用复兴解码微扰理论：斯托克斯现象、新鞍点和莱夫谢茨顶针
DOI：
10.1007/jhep10(2015)056
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发表时间：
2014
影响因子：
5.4
通讯作者：
M. Ünsal
中科院分区：
文献类型：
--
作者：
A. Cherman;Daniele Dorigoni;M. Ünsal
BstractResurise理论意味着QFT中的非微扰(NP)和微扰(P)数据是定量相关的，并且关于路径积分的非微扰鞍点场组态的详细信息可以从微扰理论中提取出来。传统上，QFT只考虑稳定的NP鞍点，并利用同伦群考虑对其进行分类。然而，在许多QFT中，相关的同伦群是平凡的，即使它们是非平凡的，它们也留下了许多NP鞍点没有被检测到。复活对NP-鞍点进行了精细的分类，超越了传统的拓扑考虑。为了证明其中的一些想法，我们研究了SU(N)主手征模型(PCM)，这是一个没有瞬子的二维渐近自由矩阵场理论，因为相关的同伦群是平凡的。绝热连续性被用来达到弱耦合区域，其中NP效应是可计算的。然后，我们使用回升理论来揭示新的‘Fragton’鞍点的存在和作用，这些鞍点被证明是先前观察到的不稳定的‘uniton’鞍点的分式成分。分形子在PCM的物理中起着至关重要的作用，并对理论中动态产生的质量间隙负责。此外，我们还证明了分形子-反分形子事件是‘t Hooft重整子的弱耦合实现，并论证了在半经典展开中系统地消除了重整化子的模糊性。我们的结果引发了这样的猜想：路径积分的半经典展开式可以几何化为Lefschetz顶针上的和。
A bstractResurgence theory implies that the non-perturbative (NP) and perturbative (P) data in a QFT are quantitatively related, and that detailed information about non-perturbative saddle point field configurations of path integrals can be extracted from perturbation theory. Traditionally, only stable NP saddle points are considered in QFT, and homotopy group considerations are used to classify them. However, in many QFTs the relevant homotopy groups are trivial, and even when they are non-trivial they leave many NP saddle points undetected. Resurgence provides a refined classification of NP-saddles, going beyond conventional topological considerations. To demonstrate some of these ideas, we study the SU(N) principal chiral model (PCM), a two dimensional asymptotically free matrix field theory which has no instantons, because the relevant homotopy group is trivial. Adiabatic continuity is used to reach a weakly coupled regime where NP effects are calculable. We then use resurgence theory to uncover the existence and role of novel ‘fracton’ saddle points, which turn out to be the fractionalized constituents of previously observed unstable ‘uniton’ saddle points. The fractons play a crucial role in the physics of the PCM, and are responsible for the dynamically generated mass gap of the theory. Moreover, we show that the fracton-anti-fracton events are the weak coupling realization of ’t Hooft’s renormalons, and argue that the renormalon ambiguities are systematically cancelled in the semi-classical expansion. Our results motivate the conjecture that the semi-classical expansion of the path integral can be geometrized as a sum over Lefschetz thimbles.
Lefschetz 顶针和随机量化：复平面中的复杂动作
影响因子：
5
作者：
Aarts G
通讯作者：
Aarts G
CPn sigma 模型中的扭结、链和环组
影响因子：
1.3
作者：
D. Harland
通讯作者：
D. Harland