# On quantum compatibility of counterterm deformations and duality symmetries in $$ \mathcal{N}\ge 5 $$ supergravities

## Abstract

In *N* = 5, 6, 8 supergravities there are hidden symmetries of equations of motion, described by duality groups SU(1, 5), SO*(12), *E* _{7(7)} respectively. UV divergences and known candidate counterterms violate the deformed duality symmetry current conservation. Extra higher derivative terms in the action are required to restore duality. We study the effect of a two-vector part of the counterterm for $$ \mathcal{N}\ge 5 $$ supergravities using the universality of the symplectic structure of extended supergravities. We construct a compact form of a deformed action with infinite number of higher derivative terms and restored duality symmetry with deformation parameter λ. We find, in λ ^{2} approximation, that the SU( *N*) symmetry of the deformed theory is restored on shell.

- Authors:

- Stanford Univ., Stanford, CA (United States)
- Max-Planck-Institut fur Gravitationsphysik (Albert-Einstein-Institut), Potsdam (Germany)
- The Pennsylvania State Univ., University Park, PA (United States)

- Publication Date:

- Research Org.:
- Pennsylvania State Univ., University Park, PA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1512491

- Grant/Contract Number:
- SC0013699

- 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: 2018; Journal Issue: 8; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Extended Supersymmetry; Supersymmetry and Duality; Scattering Amplitudes

### Citation Formats

```
Kallosh, Renata, Nicolai, Hermann, Roiban, Radu, and Yamada, Yusuke. On quantum compatibility of counterterm deformations and duality symmetries in $ \mathcal{N}\ge 5 $ supergravities. United States: N. p., 2018.
Web. doi:10.1007/jhep08(2018)091.
```

```
Kallosh, Renata, Nicolai, Hermann, Roiban, Radu, & Yamada, Yusuke. On quantum compatibility of counterterm deformations and duality symmetries in $ \mathcal{N}\ge 5 $ supergravities. United States. doi:10.1007/jhep08(2018)091.
```

```
Kallosh, Renata, Nicolai, Hermann, Roiban, Radu, and Yamada, Yusuke. Thu .
"On quantum compatibility of counterterm deformations and duality symmetries in $ \mathcal{N}\ge 5 $ supergravities". United States. doi:10.1007/jhep08(2018)091. https://www.osti.gov/servlets/purl/1512491.
```

```
@article{osti_1512491,
```

title = {On quantum compatibility of counterterm deformations and duality symmetries in $ \mathcal{N}\ge 5 $ supergravities},

author = {Kallosh, Renata and Nicolai, Hermann and Roiban, Radu and Yamada, Yusuke},

abstractNote = {In N = 5, 6, 8 supergravities there are hidden symmetries of equations of motion, described by duality groups SU(1, 5), SO*(12), E7(7) respectively. UV divergences and known candidate counterterms violate the deformed duality symmetry current conservation. Extra higher derivative terms in the action are required to restore duality. We study the effect of a two-vector part of the counterterm for $ \mathcal{N}\ge 5 $ supergravities using the universality of the symplectic structure of extended supergravities. We construct a compact form of a deformed action with infinite number of higher derivative terms and restored duality symmetry with deformation parameter λ. We find, in λ2 approximation, that the SU(N) symmetry of the deformed theory is restored on shell.},

doi = {10.1007/jhep08(2018)091},

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

number = 8,

volume = 2018,

place = {United States},

year = {2018},

month = {8}

}

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