Polyakov model in ’t Hooft flux background: a quantum mechanical reduction with memory
Abstract
We construct a compactification of Polyakov model on T2 × $$\mathbb{R}$$ down to quantum mechanics which remembers non-perturbative aspects of field theory even at an arbitrarily small area. Standard compactification on small T2 × $$\mathbb{R}$$ possesses a unique perturbative vacuum (zero magnetic flux state), separated parametrically from higher flux states, and the instanton effects do not survive in the Born-Oppenheimer approximation. By turning on a background magnetic GNO flux in co-weight lattice corresponding to a non-zero ’t Hooft flux, we show that N-degenerate vacua appear at small torus, and there are N - 1 types of flux changing instantons between them. We construct QM instantons starting with QFT instantons using the method of replicas. For example, SU(2) gauge theory with flux reduces to the double-well potential where each well is a fractional flux state. Despite the absence of a mixed anomaly, the vacuum structure of QFT and the one of QM are continuously connected. We also compare the quantum mechanical reduction of the Polyakov model with the deformed Yang-Mills, by coupling both theories to TQFTs. In particular, we compare the mass spectrum for dual photons and energy spectrum in the QM limit. We give a detailed description of critical points at infinity in the semi-classical expansion, and their role in resurgence structure.
- Authors:
-
[1];
- Bogazici University, Istanbul (Turkey); North Carolina State University, Raleigh, NC (United States)
- North Carolina State University, Raleigh, NC (United States)
- Publication Date:
- Research Org.:
- North Carolina State University, Raleigh, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); Scientific and Technological Research Council of Türkiye (TUBITAK)
- OSTI Identifier:
- 1976511
- Grant/Contract Number:
- FG02-03ER41260
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2022; Journal Issue: 8; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; confinement; large-order behaviour of perturbation theory; renormalons; nonperturbative effects; solitons monopoles and instantons
Citation Formats
Pazarbaşı, Cihan, and Ünsal, Mithat. Polyakov model in ’t Hooft flux background: a quantum mechanical reduction with memory. United States: N. p., 2022.
Web. doi:10.1007/jhep08(2022)116.
Pazarbaşı, Cihan, & Ünsal, Mithat. Polyakov model in ’t Hooft flux background: a quantum mechanical reduction with memory. United States. https://doi.org/10.1007/jhep08(2022)116
Pazarbaşı, Cihan, and Ünsal, Mithat. Tue .
"Polyakov model in ’t Hooft flux background: a quantum mechanical reduction with memory". United States. https://doi.org/10.1007/jhep08(2022)116. https://www.osti.gov/servlets/purl/1976511.
@article{osti_1976511,
title = {Polyakov model in ’t Hooft flux background: a quantum mechanical reduction with memory},
author = {Pazarbaşı, Cihan and Ünsal, Mithat},
abstractNote = {We construct a compactification of Polyakov model on T2 × $\mathbb{R}$ down to quantum mechanics which remembers non-perturbative aspects of field theory even at an arbitrarily small area. Standard compactification on small T2 × $\mathbb{R}$ possesses a unique perturbative vacuum (zero magnetic flux state), separated parametrically from higher flux states, and the instanton effects do not survive in the Born-Oppenheimer approximation. By turning on a background magnetic GNO flux in co-weight lattice corresponding to a non-zero ’t Hooft flux, we show that N-degenerate vacua appear at small torus, and there are N - 1 types of flux changing instantons between them. We construct QM instantons starting with QFT instantons using the method of replicas. For example, SU(2) gauge theory with flux reduces to the double-well potential where each well is a fractional flux state. Despite the absence of a mixed anomaly, the vacuum structure of QFT and the one of QM are continuously connected. We also compare the quantum mechanical reduction of the Polyakov model with the deformed Yang-Mills, by coupling both theories to TQFTs. In particular, we compare the mass spectrum for dual photons and energy spectrum in the QM limit. We give a detailed description of critical points at infinity in the semi-classical expansion, and their role in resurgence structure.},
doi = {10.1007/jhep08(2022)116},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2022,
place = {United States},
year = {Tue Aug 09 00:00:00 EDT 2022},
month = {Tue Aug 09 00:00:00 EDT 2022}
}
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