# Moving the CFT into the bulk with $T\overline{T}$

## Abstract

Recent work by Zamolodchikov and others has uncovered a solvable irrelevant deformation of general 2D CFTs, defined by turning on the dimension 4 operator $T\overline{T}$, the product of the left- and right-moving stress tensor. We propose that in the holographic dual, this deformation represents a geometric cutoff that removes the asymptotic region of AdS and places the QFT on a Dirichlet wall at finite radial distance r = r _{c} in the bulk. As a quantitative check of the proposed duality, we compute the signal propagation speed, energy spectrum, and thermodynamic relations on both sides. In all cases, we obtain a precise match. We derive an exact RG flow equation for the metric dependence of the effective action of the $T\overline{T}$ deformed theory, and find that it coincides with the Hamilton-Jacobi equation that governs the radial evolution of the classical gravity action in AdS.

- Authors:

- Princeton Univ., NJ (United States). Dept. of Physics
- Princeton Univ., NJ (United States). Princeton Center for Theoretical Science
- Princeton Univ., NJ (United States). Dept. of Physics. Princeton Center for Theoretical Science

- Publication Date:

- Research Org.:
- Princeton Univ., NJ (United States)

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

- OSTI Identifier:
- 1512424

- Grant/Contract Number:
- SC0016244; PHY-1620059

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 2018; Journal Issue: 4; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT correspondence; conformal field theory; renormalization group

### Citation Formats

```
McGough, Lauren, Mezei, Márk, and Verlinde, Herman.
```*Moving the CFT into the bulk with T T ¯*. United States: N. p., 2018.
Web. doi:10.1007/jhep04(2018)010.

```
McGough, Lauren, Mezei, Márk, & Verlinde, Herman.
```*Moving the CFT into the bulk with T T ¯*. United States. doi:10.1007/jhep04(2018)010.

```
McGough, Lauren, Mezei, Márk, and Verlinde, Herman. Tue .
"Moving the CFT into the bulk with T T ¯". United States. doi:10.1007/jhep04(2018)010. https://www.osti.gov/servlets/purl/1512424.
```

```
@article{osti_1512424,
```

title = {Moving the CFT into the bulk with T T ¯},

author = {McGough, Lauren and Mezei, Márk and Verlinde, Herman},

abstractNote = {Recent work by Zamolodchikov and others has uncovered a solvable irrelevant deformation of general 2D CFTs, defined by turning on the dimension 4 operator T T ¯ , the product of the left- and right-moving stress tensor. We propose that in the holographic dual, this deformation represents a geometric cutoff that removes the asymptotic region of AdS and places the QFT on a Dirichlet wall at finite radial distance r = rc in the bulk. As a quantitative check of the proposed duality, we compute the signal propagation speed, energy spectrum, and thermodynamic relations on both sides. In all cases, we obtain a precise match. We derive an exact RG flow equation for the metric dependence of the effective action of the T T ¯ deformed theory, and find that it coincides with the Hamilton-Jacobi equation that governs the radial evolution of the classical gravity action in AdS.},

doi = {10.1007/jhep04(2018)010},

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

issn = {1029-8479},

number = 4,

volume = 2018,

place = {United States},

year = {2018},

month = {4}

}

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