## Local renormalization group functions from quantum renormalization group and holographic bulk locality

## Abstract

Here, the bulk locality in the constructive holographic renormalization group requires miraculous cancellations among various local renormalization group functions. The cancellation is not only from the properties of the spectrum but from more detailed aspects of operator product expansions in relation to conformal anomaly. It is remarkable that one-loop computation of the universal local renormalization group functions in the weakly coupled limit of the N = 4 super Yang-Mills theory fulfils the necessary condition for the cancellation in the strongly coupled limit in its SL(2, Z) duality invariant form. From the consistency between the quantum renormalization group and the holographic renormalization group, we determine some unexplored local renormalization group functions (e.g. diffusive term in the beta function for the gauge coupling constant) in the strongly coupled limit of the planar N = 4 super Yang-Mills theory.

- Authors:

- California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. of Theoretical Physics

- Publication Date:

- Research Org.:
- California Inst. of Technology, Pasadena, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1455206

- Grant/Contract Number:
- SC0011632

- 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: 2015; Journal Issue: 6; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Gauge-gravity correspondence; AdS-CFT Correspondence; Renormalization Group; 1/N Expansion

### Citation Formats

```
Nakayama, Yu. Local renormalization group functions from quantum renormalization group and holographic bulk locality. United States: N. p., 2015.
Web. doi:10.1007/JHEP06(2015)092.
```

```
Nakayama, Yu. Local renormalization group functions from quantum renormalization group and holographic bulk locality. United States. doi:10.1007/JHEP06(2015)092.
```

```
Nakayama, Yu. Tue .
"Local renormalization group functions from quantum renormalization group and holographic bulk locality". United States. doi:10.1007/JHEP06(2015)092. https://www.osti.gov/servlets/purl/1455206.
```

```
@article{osti_1455206,
```

title = {Local renormalization group functions from quantum renormalization group and holographic bulk locality},

author = {Nakayama, Yu},

abstractNote = {Here, the bulk locality in the constructive holographic renormalization group requires miraculous cancellations among various local renormalization group functions. The cancellation is not only from the properties of the spectrum but from more detailed aspects of operator product expansions in relation to conformal anomaly. It is remarkable that one-loop computation of the universal local renormalization group functions in the weakly coupled limit of the N = 4 super Yang-Mills theory fulfils the necessary condition for the cancellation in the strongly coupled limit in its SL(2, Z) duality invariant form. From the consistency between the quantum renormalization group and the holographic renormalization group, we determine some unexplored local renormalization group functions (e.g. diffusive term in the beta function for the gauge coupling constant) in the strongly coupled limit of the planar N = 4 super Yang-Mills theory.},

doi = {10.1007/JHEP06(2015)092},

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

number = 6,

volume = 2015,

place = {United States},

year = {2015},

month = {6}

}

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