Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP01(2019)079
Keywords
Nonperturbative Effects; Solitons Monopoles and Instantons; Topological Strings
Categories
Funding
- Rikkyo University Special Fund for Research
- JSPS KAKENHI [18K03657]
- European Research Council [ERC-2012-AdG 320769]
- Grants-in-Aid for Scientific Research [18K03657] Funding Source: KAKEN
Ask authors/readers for more resources
We study the Harper-Hofstadter Hamiltonian and its corresponding non-perturbative butterfly spectrum. The problem is algebraically solvable whenever the magnetic flux is a rational multiple of 2. For such values of the magnetic flux, the theory allows a formulation with two Bloch or -angles. We treat the problem by the path integral formulation, and show that the spectrum receives instanton corrections. Instantons as well as their one loop fluctuation determinants are found explicitly and the finding is matched with the numerical band width of the butterfly spectrum. We extend the analysis to all 2-instanton sectors with different -angle dependence to leading order and show consistency with numerics. We further argue that the instanton-anti-instanton contributions are ambiguous and cancel the ambiguity of the perturbation series, as they should. We hint at the possibility of exact 2-instanton solutions responsible for such contributions via Picard-Lefschetz theory. We also present a powerful way to compute the perturbative fluctuations around the 1-instanton saddle as well as the instanton-anti-instanton ambiguity by using the topological string formulation.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available