# Celestial current algebra from Low’s subleading soft theorem

## Abstract

The leading soft photon theorem implies that four-dimensional scattering amplitudes are controlled by a two-dimensional (2D) U(1) Kac-Moody symmetry that acts on the celestial sphere at null infinity (I). This celestial U(1) current is realized by components of the electromagnetic vector potential on the boundaries of I. Here, we develop a parallel story for Low's subleading soft photon theorem. It gives rise to a second celestial current, which is realized by vector potential components that are subleading in the large radius expansion about the boundaries of I. The subleading soft photon theorem is reexpressed as a celestial Ward identity for this second current, which involves novel shifts by one unit in the conformal dimension of charged operators.

- Authors:

- Publication Date:

- Research Org.:
- Harvard Univ., Cambridge, MA (United States)

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

- OSTI Identifier:
- 1560289

- Alternate Identifier(s):
- OSTI ID: 1595981

- Grant/Contract Number:
- SC0007870; 1745303

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 6; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Gauge theories; Scattering amplitudes

### Citation Formats

```
Himwich, Elizabeth, and Strominger, Andrew. Celestial current algebra from Low’s subleading soft theorem. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.065001.
```

```
Himwich, Elizabeth, & Strominger, Andrew. Celestial current algebra from Low’s subleading soft theorem. United States. doi:10.1103/PhysRevD.100.065001.
```

```
Himwich, Elizabeth, and Strominger, Andrew. Tue .
"Celestial current algebra from Low’s subleading soft theorem". United States. doi:10.1103/PhysRevD.100.065001.
```

```
@article{osti_1560289,
```

title = {Celestial current algebra from Low’s subleading soft theorem},

author = {Himwich, Elizabeth and Strominger, Andrew},

abstractNote = {The leading soft photon theorem implies that four-dimensional scattering amplitudes are controlled by a two-dimensional (2D) U(1) Kac-Moody symmetry that acts on the celestial sphere at null infinity (I). This celestial U(1) current is realized by components of the electromagnetic vector potential on the boundaries of I. Here, we develop a parallel story for Low's subleading soft photon theorem. It gives rise to a second celestial current, which is realized by vector potential components that are subleading in the large radius expansion about the boundaries of I. The subleading soft photon theorem is reexpressed as a celestial Ward identity for this second current, which involves novel shifts by one unit in the conformal dimension of charged operators.},

doi = {10.1103/PhysRevD.100.065001},

journal = {Physical Review D},

number = 6,

volume = 100,

place = {United States},

year = {2019},

month = {9}

}

DOI: 10.1103/PhysRevD.100.065001

*Citation information provided by*

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