Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model

Misumi, Tatsuhiro; Tanizaki, Yuya; Ünsal, Mithat

doi:10.1007/jhep07(2019)018

Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model

Journal Article · Wed Jul 03 00:00:00 EDT 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep07(2019)018· OSTI ID:1609453

Misumi, Tatsuhiro ^[1]; Tanizaki, Yuya ^[2]; Ünsal, Mithat ^[2]

Akita Univ. (Japan); Inst. of Physical and Chemical Research (RIKEN), Wako (Japan); Keio Univ. (Japan); DOE/OSTI
North Carolina State Univ., Raleigh, NC (United States)

This work examines non-perturbative dynamics of a 2-dimensional QFT by using discrete ’t Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge-q N-flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete ’t Hooft anomaly matching to theories on R² and its compactification to R× S¹_L. We then compare the ’t Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are Nq vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional θ dependence e^iθ/Nq, which provides the Nq-branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by “quantum” instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large-N limit of the Schwinger model with twisted boundary conditions satisfy volume independence.

View Accepted Manuscript (DOE)

Research Organization:: North Carolina State Univ., Raleigh, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-03ER41260

OSTI ID:: 1609453

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 7 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Undoing decomposition Sharpe, Eric International Journal of Modern Physics A, Vol. 34, Issue 35 https://doi.org/10.1142/s0217751x19502336	journal	December 2019

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