# Betti multiplets, flows across dimensions and c-extremization

## Abstract

We consider 4d N = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N = (0; 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c _{2d}, similarly to the 4d picture, where the exact R-current maximizes the central charge a _{4d}. There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N = 2 truncation of T ^{1,1} with one Betti vector multiplet, dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS _{5} to AdS _{3} vacua in the supergravity picture. We verify the existence of the flow to AdS _{3} solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d N = 2 gauged supergravity with a generic number ofmore »

- Authors:

- City Univ. (CUNY), NY (United States). Physics Department; University of Bern (Switzerland). Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics
- Columbia Univ., New York, NY (United States)

- Publication Date:

- Research Org.:
- Columbia Univ., New York, NY (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1424743

- Grant/Contract Number:
- SC0011941

- 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: 2017; 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 Field Theory; Field Theories in Lower Dimensions; Supergravity Models

### Citation Formats

```
Amariti, Antonio, and Toldo, Chiara.
```*Betti multiplets, flows across dimensions and c-extremization*. United States: N. p., 2017.
Web. doi:10.1007/JHEP07(2017)040.

```
Amariti, Antonio, & Toldo, Chiara.
```*Betti multiplets, flows across dimensions and c-extremization*. United States. doi:10.1007/JHEP07(2017)040.

```
Amariti, Antonio, and Toldo, Chiara. Mon .
"Betti multiplets, flows across dimensions and c-extremization". United States.
doi:10.1007/JHEP07(2017)040. https://www.osti.gov/servlets/purl/1424743.
```

```
@article{osti_1424743,
```

title = {Betti multiplets, flows across dimensions and c-extremization},

author = {Amariti, Antonio and Toldo, Chiara},

abstractNote = {We consider 4d N = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N = (0; 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c2d, similarly to the 4d picture, where the exact R-current maximizes the central charge a4d. There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N = 2 truncation of T1,1 with one Betti vector multiplet, dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS5 to AdS3 vacua in the supergravity picture. We verify the existence of the flow to AdS3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d N = 2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.},

doi = {10.1007/JHEP07(2017)040},

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

number = 7,

volume = 2017,

place = {United States},

year = {Mon Jul 10 00:00:00 EDT 2017},

month = {Mon Jul 10 00:00:00 EDT 2017}

}

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