Quantum distillation of Hilbert spaces, semiclassics and anomaly matching
Abstract
A symmetrytwisted boundary condition of the path integral provides a suitable framework for the semiclassical analysis of nonperturbative quantum field theories (QFTs), and we reinterpret it from the viewpoint of the Hilbert space. An appropriate twist with the unbroken symmetry can potentially produce huge cancellations among excited states in the statesum, without affecting the ground states; we call this effect “quantum distillation”. Quantum distillation can provide the underlying mechanism for adiabatic continuity, by preventing a phase transition under S ^{1} compactification. We revisit this point via the ’t Hooft anomaly matching condition when it constrains the vacuum structure of the theory on $$\mathbb{R} $$ ^{d} and upon compactification. We show that there is a precise relation between the persistence of the anomaly upon compactification, the Hilbert space quantum distillation, and the semiclassical analysis of the corresponding symmetrytwisted path integrals. We motivate quantum distillation in quantum mechanical examples, and then study its nontrivial action in QFT, with the example of the 2D Grassmannian sigma model Gr(N, M). We also discuss the connection of quantum distillation with largeN volume independence and flavormomentum transmutation.
 Authors:

 Univ. of California, Berkeley, CA (United States). Kavli Inst. for Theoretical Physics; Univ. of Connecticut, Storrs, CT (United States). Dept. of Physics
 Univ. of California, Berkeley, CA (United States). Kavli Inst. for Theoretical Physics; Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center
 Univ. of California, Berkeley, CA (United States). Kavli Inst. for Theoretical Physics; North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics
 Publication Date:
 Research Org.:
 North Carolina State Univ., Raleigh, NC (United States); Univ. of Connecticut, Storrs, CT (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25); USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 OSTI Identifier:
 1507781
 Grant/Contract Number:
 FG0203ER41260; SC0010339
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Volume: 2018; Journal Issue: 8; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Nonperturbative Effects; Sigma Models
Citation Formats
Dunne, Gerald V., Tanizaki, Yuya, and Ünsal, Mithat. Quantum distillation of Hilbert spaces, semiclassics and anomaly matching. United States: N. p., 2018.
Web. doi:10.1007/jhep08(2018)068.
Dunne, Gerald V., Tanizaki, Yuya, & Ünsal, Mithat. Quantum distillation of Hilbert spaces, semiclassics and anomaly matching. United States. doi:10.1007/jhep08(2018)068.
Dunne, Gerald V., Tanizaki, Yuya, and Ünsal, Mithat. Tue .
"Quantum distillation of Hilbert spaces, semiclassics and anomaly matching". United States. doi:10.1007/jhep08(2018)068. https://www.osti.gov/servlets/purl/1507781.
@article{osti_1507781,
title = {Quantum distillation of Hilbert spaces, semiclassics and anomaly matching},
author = {Dunne, Gerald V. and Tanizaki, Yuya and Ünsal, Mithat},
abstractNote = {A symmetrytwisted boundary condition of the path integral provides a suitable framework for the semiclassical analysis of nonperturbative quantum field theories (QFTs), and we reinterpret it from the viewpoint of the Hilbert space. An appropriate twist with the unbroken symmetry can potentially produce huge cancellations among excited states in the statesum, without affecting the ground states; we call this effect “quantum distillation”. Quantum distillation can provide the underlying mechanism for adiabatic continuity, by preventing a phase transition under S1 compactification. We revisit this point via the ’t Hooft anomaly matching condition when it constrains the vacuum structure of the theory on $\mathbb{R} $d and upon compactification. We show that there is a precise relation between the persistence of the anomaly upon compactification, the Hilbert space quantum distillation, and the semiclassical analysis of the corresponding symmetrytwisted path integrals. We motivate quantum distillation in quantum mechanical examples, and then study its nontrivial action in QFT, with the example of the 2D Grassmannian sigma model Gr(N, M). We also discuss the connection of quantum distillation with largeN volume independence and flavormomentum transmutation.},
doi = {10.1007/jhep08(2018)068},
journal = {Journal of High Energy Physics (Online)},
issn = {10298479},
number = 8,
volume = 2018,
place = {United States},
year = {2018},
month = {8}
}
Web of Science
Figures / Tables:
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