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Title: Quantum distillation of Hilbert spaces, semi-classics and anomaly matching

Abstract

A symmetry-twisted boundary condition of the path integral provides a suitable framework for the semi-classical 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 state-sum, 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 semi-classical analysis of the corresponding symmetry-twisted path integrals. We motivate quantum distillation in quantum mechanical examples, and then study its non-trivial action in QFT, with the example of the 2D Grassmannian sigma model Gr(N, M). We also discuss the connection of quantum distillation with large-N volume independence and flavor-momentum transmutation.

Authors:
 [1]; ORCiD logo [2];  [3]
  1. Univ. of California, Berkeley, CA (United States). Kavli Inst. for Theoretical Physics; Univ. of Connecticut, Storrs, CT (United States). Dept. of Physics
  2. Univ. of California, Berkeley, CA (United States). Kavli Inst. for Theoretical Physics; Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center
  3. 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) (SC-25); USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1507781
Grant/Contract Number:  
FG02-03ER41260; 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 1029-8479
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, semi-classics 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, semi-classics 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, semi-classics 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, semi-classics and anomaly matching},
author = {Dunne, Gerald V. and Tanizaki, Yuya and Ünsal, Mithat},
abstractNote = {A symmetry-twisted boundary condition of the path integral provides a suitable framework for the semi-classical 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 state-sum, 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 semi-classical analysis of the corresponding symmetry-twisted path integrals. We motivate quantum distillation in quantum mechanical examples, and then study its non-trivial action in QFT, with the example of the 2D Grassmannian sigma model Gr(N, M). We also discuss the connection of quantum distillation with large-N volume independence and flavor-momentum transmutation.},
doi = {10.1007/jhep08(2018)068},
journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 8,
volume = 2018,
place = {United States},
year = {2018},
month = {8}
}

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Cited by: 7 works
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Figures / Tables:

Figure 1 Figure 1: Schematic illustration of the advantages of the symmetry-twisted partition function $Z_Ω$(L) in comparison with the thermal partition function $Z(β)$. In the left column, we count the degrees of freedom of mesons. Mesons give a large, O(N2) contribution to $Z(β)$ since they are in the adjoint representation of themore » SU(N)=$\mathbb{Z}_N$ symmetry, while $Z_Ω$(L) is affected only by O(1). In the middle column, it is explained by the Kaluza-Klein (KK) or Matsubara decomposition of the fields, and the KK modes in $Z_Ω$(L) are much denser than those of $Z(β)$, due to the flavor-momentum transmutation. In the right column, we explain its consequence for the 't Hooft anomaly of the theory, and the 't Hooft anomaly in 2 dimensions persists in $Z_Ω$(L) for any L, while it survives in $Z(β)$ only for $β \rightarrow ∞$.« less

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