# A tale of two exponentiations in $\mathcal{N}=8$ supergravity

## Abstract

The structure of scattering amplitudes in supergravity theories continues to be of interest. Recently, the amplitude for 2→2 scattering in N=8 supergravity was presented at three-loop order for the first time. The result can be written in terms of an exponentiated one-loop contribution, modulo a remainder function which is free of infrared singularities, but contains leading terms in the high energy Regge limit. We explain the origin of these terms from a well-known, unitarity-restoring exponentiation of the high-energy gravitational S-matrix in impact-parameter space. Furthermore, we predict the existence of similar terms in the remainder function at all higher loop orders. Our results provide a non-trivial cross-check of the recent three-loop calculation, and a necessary consistency constraint for any future calculation at higher loops.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of California, Los Angeles, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); UK Science and Technology Facilities Council; Marie-Cklodowska-Curie Foundation; Simons Foundation; Knut and Alice Wallenberg Foundation

- OSTI Identifier:
- 1561340

- Alternate Identifier(s):
- OSTI ID: 1608235

- Report Number(s):
- BOW-PH-167; NORDITA-2019-076; QMUL-PH-19-20; CERN-TH-2019-133

Journal ID: ISSN 0370-2693; S0370269319306495; 134927; PII: S0370269319306495

- Grant/Contract Number:
- SC000993; SC0009937; PHY17-20202; 764850; 4036 342344; KAW 2018.0116; ST/P000754/1

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 798 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Di Vecchia, Paolo, Luna, Andrés, Naculich, Stephen G., Russo, Rodolfo, Veneziano, Gabriele, and White, Chris D. A tale of two exponentiations in N = 8 supergravity. Netherlands: N. p., 2019.
Web. doi:10.1016/j.physletb.2019.134927.
```

```
Di Vecchia, Paolo, Luna, Andrés, Naculich, Stephen G., Russo, Rodolfo, Veneziano, Gabriele, & White, Chris D. A tale of two exponentiations in N = 8 supergravity. Netherlands. doi:10.1016/j.physletb.2019.134927.
```

```
Di Vecchia, Paolo, Luna, Andrés, Naculich, Stephen G., Russo, Rodolfo, Veneziano, Gabriele, and White, Chris D. Fri .
"A tale of two exponentiations in N = 8 supergravity". Netherlands. doi:10.1016/j.physletb.2019.134927.
```

```
@article{osti_1561340,
```

title = {A tale of two exponentiations in N = 8 supergravity},

author = {Di Vecchia, Paolo and Luna, Andrés and Naculich, Stephen G. and Russo, Rodolfo and Veneziano, Gabriele and White, Chris D.},

abstractNote = {The structure of scattering amplitudes in supergravity theories continues to be of interest. Recently, the amplitude for 2→2 scattering in N=8 supergravity was presented at three-loop order for the first time. The result can be written in terms of an exponentiated one-loop contribution, modulo a remainder function which is free of infrared singularities, but contains leading terms in the high energy Regge limit. We explain the origin of these terms from a well-known, unitarity-restoring exponentiation of the high-energy gravitational S-matrix in impact-parameter space. Furthermore, we predict the existence of similar terms in the remainder function at all higher loop orders. Our results provide a non-trivial cross-check of the recent three-loop calculation, and a necessary consistency constraint for any future calculation at higher loops.},

doi = {10.1016/j.physletb.2019.134927},

journal = {Physics Letters B},

number = C,

volume = 798,

place = {Netherlands},

year = {2019},

month = {11}

}

DOI: 10.1016/j.physletb.2019.134927

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