# 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:

- 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) (SC-25); USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1507781

- Grant/Contract Number:
- FG02-03ER41260; SC0010339

- 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: 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)},

number = 8,

volume = 2018,

place = {United States},

year = {2018},

month = {8}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

*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(N*contribution to $Z(β)$ since they are in the adjoint representation of themore »

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*