# A conformal truncation framework for infinite-volume dynamics

## Abstract

Here, we present a new framework for studying conformal field theories deformed by one or more relevant operators. The original CFT is described in infinite volume using a basis of states with definite momentum, *P*, and conformal Casimir, C. The relevant deformation is then considered using lightcone quantization, with the resulting Hamiltonian expressed in terms of this CFT basis. Truncating to states with C ≤ C _{max}, one can numerically find the resulting spectrum, as well as other dynamical quantities, such as spectral densities of operators. This method requires the introduction of an appropriate regulator, which can be chosen to preserve the conformal structure of the basis. We check this framework in three dimensions for various perturbative deformations of a free scalar CFT, and for the case of a free O(N) CFT deformed by a mass term and a non-perturbative quartic interaction at large- *N*. In all cases, the truncation scheme correctly reproduces known analytic results. As a result, we also discuss a general procedure for generating a basis of Casimir eigenstates for a free CFT in any number of dimensions.

- Authors:

- Boston Univ., Boston, MA (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Boston Univ., MA (United States)

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

- OSTI Identifier:
- 1358561

- Grant/Contract Number:
- SC0010025; PHY-1066293

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 7; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS-CFT correspondence; conformal and W symmetry; nonperturbative effects

### Citation Formats

```
Katz, Emanuel, Khandker, Zuhair U., and Walters, Matthew T.
```*A conformal truncation framework for infinite-volume dynamics*. United States: N. p., 2016.
Web. doi:10.1007/JHEP07(2016)140.

```
Katz, Emanuel, Khandker, Zuhair U., & Walters, Matthew T.
```*A conformal truncation framework for infinite-volume dynamics*. United States. doi:10.1007/JHEP07(2016)140.

```
Katz, Emanuel, Khandker, Zuhair U., and Walters, Matthew T. Thu .
"A conformal truncation framework for infinite-volume dynamics". United States.
doi:10.1007/JHEP07(2016)140. https://www.osti.gov/servlets/purl/1358561.
```

```
@article{osti_1358561,
```

title = {A conformal truncation framework for infinite-volume dynamics},

author = {Katz, Emanuel and Khandker, Zuhair U. and Walters, Matthew T.},

abstractNote = {Here, we present a new framework for studying conformal field theories deformed by one or more relevant operators. The original CFT is described in infinite volume using a basis of states with definite momentum, P, and conformal Casimir, C. The relevant deformation is then considered using lightcone quantization, with the resulting Hamiltonian expressed in terms of this CFT basis. Truncating to states with C ≤ Cmax, one can numerically find the resulting spectrum, as well as other dynamical quantities, such as spectral densities of operators. This method requires the introduction of an appropriate regulator, which can be chosen to preserve the conformal structure of the basis. We check this framework in three dimensions for various perturbative deformations of a free scalar CFT, and for the case of a free O(N) CFT deformed by a mass term and a non-perturbative quartic interaction at large-N. In all cases, the truncation scheme correctly reproduces known analytic results. As a result, we also discuss a general procedure for generating a basis of Casimir eigenstates for a free CFT in any number of dimensions.},

doi = {10.1007/JHEP07(2016)140},

journal = {Journal of High Energy Physics (Online)},

number = 7,

volume = 2016,

place = {United States},

year = {Thu Jul 28 00:00:00 EDT 2016},

month = {Thu Jul 28 00:00:00 EDT 2016}

}

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