Author:
Grassi Alba,Hao Qianyu,Neitzke Andrew
Abstract
Abstract
We study in detail the Schrödinger equation corresponding to the four dimensional SU(2) $$ \mathcal{N} $$
N
= 2 SQCD theory with one flavour. We calculate the Voros symbols, or quantum periods, in four different ways: Borel summation of the WKB series, direct computation of Wronskians of exponentially decaying solutions, the TBA equations of Gaiotto-Moore-Neitzke/Gaiotto, and instanton counting. We make computations by all of these methods, finding good agreement. We also study the exact quantization condition for the spectrum, and we compute the Fredholm determinant of the inverse of the Schrödinger operator using the TS/ST correspondence and Zamolodchikov’s TBA, again finding good agreement. In addition, we explore two aspects of the relationship between singularities of the Borel transformed WKB series and BPS states: BPS states of the 4d theory are related to singularities in the Borel transformed WKB series for the quantum periods, and BPS states of a coupled 2d+4d system are related to singularities in the Borel transformed WKB series for local solutions of the Schrödinger equation.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference91 articles.
1. R. Balian, G. Parisi and A. Voros, Quartic oscillator, in Feynman Path Integrals 106, Springer-Verlag (1979), pp. 337–360.
2. A. Voros, The return of the quartic oscillator. The complex WKB method, Ann. Inst. Henri Poincaré Phys. Theor. 39 (1983) 211.
3. A. Voros, Spectre de l’équation de Schrödinger et méthode BKW, Publications Mathématiques d’Orsay (1981).
4. E. Delabaere, H. Dillinger and F. Pham, Exact semiclassical expansions for one-dimensional quantum oscillators, J. Math. Phys. 38 (1997) 6126.
5. H. Dillinger, E. Delabaere and F. Pham, Résurgence de Voros et périodes des courbes hyperelliptiques, Ann. Inst. Fourier 43 (1993) 163.
Cited by
11 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献