# Unitarity and universality in nonrelativistic conformal field theory

## Abstract

We relate the notion of unitarity of a ($0+1$)-D conformally ($$SL(2,\mathbf{R})$$) invariant field theory with that of a nonrelativistic conformal (Schrödinger) field theory using the fact that $$SL(2,\mathbf{R})$$ is a subgroup of nonrelativistic conformal (Schrödinger) group. Exploiting $$SL(2,\mathbf{R})$$ unitarity, we derive the unitarity bounds and null conditions for a Schrödinger field theory (for the neutral as well as the charged sector). In noninteger dimensions the theory is shown to be nonunitary. The use of the $$SL(2,\mathbf{R})$$ subgroup opens up the possibility of borrowing results from ($0+1$)-D $$SL(2,\mathbf{R})$$ invariant field theory to explore Schrödinger field theory, in particular, the neutral sector, which has otherwise been unexplored.

- Authors:

- Univ. of California, San Diego, CA (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Univ. of California, San Diego, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1439761

- Alternate Identifier(s):
- OSTI ID: 1498883

- Grant/Contract Number:
- SC0009919

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 10; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Fermi gases; heavy-fermion systems; conformal field theory; conformal symmetry

### Citation Formats

```
Pal, Sridip. Unitarity and universality in nonrelativistic conformal field theory. United States: N. p., 2018.
Web. doi:10.1103/physrevd.97.105031.
```

```
Pal, Sridip. Unitarity and universality in nonrelativistic conformal field theory. United States. doi:10.1103/physrevd.97.105031.
```

```
Pal, Sridip. Thu .
"Unitarity and universality in nonrelativistic conformal field theory". United States. doi:10.1103/physrevd.97.105031.
```

```
@article{osti_1439761,
```

title = {Unitarity and universality in nonrelativistic conformal field theory},

author = {Pal, Sridip},

abstractNote = {We relate the notion of unitarity of a ($0+1$)-D conformally ($SL(2,\mathbf{R})$) invariant field theory with that of a nonrelativistic conformal (Schrödinger) field theory using the fact that $SL(2,\mathbf{R})$ is a subgroup of nonrelativistic conformal (Schrödinger) group. Exploiting $SL(2,\mathbf{R})$ unitarity, we derive the unitarity bounds and null conditions for a Schrödinger field theory (for the neutral as well as the charged sector). In noninteger dimensions the theory is shown to be nonunitary. The use of the $SL(2,\mathbf{R})$ subgroup opens up the possibility of borrowing results from ($0+1$)-D $SL(2,\mathbf{R})$ invariant field theory to explore Schrödinger field theory, in particular, the neutral sector, which has otherwise been unexplored.},

doi = {10.1103/physrevd.97.105031},

journal = {Physical Review D},

number = 10,

volume = 97,

place = {United States},

year = {2018},

month = {5}

}

DOI: 10.1103/physrevd.97.105031

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