Higher-Order Corrections to Instantons

Three-loop Correction to the Instanton Density. I. The Quartic Double Well Potential

This paper deals with quantum fluctuations near the classical instanton configuration. Feynman diagrams in the instanton background are used for the calculation of the tunneling amplitude (the instanton density) in the three-loop order for quartic double-well potential. The result for the three-loop contribution coincides in six significant figures with one given long ago by J.~Zinn-Justin. Unlike the two-loop contribution where all involved Feynman integrals are rational numbers, in the three-loop case Feynman diagrams can contain irrational contributions.

Instanton Correction, Wall Crossing And Mirror Symmetry Of Hitchin's Moduli Spaces

We study two instanton correction problems of Hitchin's moduli spaces along with their wall crossing formulas. The hyperkahler metric of a Hitchin's moduli space can be put into an instanton-corrected form according to physicists Gaiotto, Moore and Neitzke. The problem boils down to the construction of a set of special coordinates which can be constructed as Fock-Goncharov coordinates associated with foliations of quadratic differentials on a Riemann surface. A wall crossing formula of Kontsevich and Soibelman arises both as a crucial consistency condition and an effective computational tool. …

Instanton effects and quantum spectral curves

We study a spectral problem associated to the quantization of a spectral curve arising in local mirror symmetry. The perturbative WKB quantization condition is determined by the quantum periods, or equivalently by the refined topological string in the Nekrasov-Shatashvili (NS) limit. We show that the information encoded in the quantum periods is radically insufficient to determine the spectrum: there is an infinite series of instanton corrections, which are non-perturbative in \hbar, and lead to an exact WKB quantization condition. Moreover, we conjecture the precise form of the instanton corr…

来自拓扑弦的大N瞬子

Large N instantons from topological strings

本文利用拓扑弦瞬子振幅的精确结果，给出了通用多切割厄米矩阵模型中大N瞬子的非微扰贡献，并应用于ABJM理论自由能修正和轨形Gromov-Witten不变量的渐近分析。

Self-dual String and Higher Instanton Solutions

We present and discuss explicit solutions to the non-abelian self-dual string equation as well as to the non-abelian self-duality equation in six dimensions. These solutions are generalizations of the 't Hooft-Polyakov monopole and the BPST instanton to higher gauge theory. We expect that these solutions are relevant to the effective description of M2- and M5-branes.

可积sigma模型中的瞬子、重整化子与theta角

Instantons, renormalons and the theta angle in integrable sigma models

本研究针对在$\vartheta=0$和$\vartheta=\pi$下可积的含theta角sigma模型，通过Bethe ansatz计算磁场下基态能量的非微扰修正，分析theta角的影响，给出弱耦合下带磁场$O(3)$ sigma模型拓扑磁化率的显式非微扰公式。