# Conformally soft theorem in gauge theory

## Abstract

Asymptotic particle states in four-dimensional celestial scattering amplitudes are labeled by their SL(2,C) Lorentz/conformal weights ($$h, \bar{h}$$) rather than the usual energy-momentum four-vector. These boost eigenstates involve a superposition of all energies. As such, celestial gluon (or photon) scattering cannot obey the usual (energetically) soft theorems. In this paper we show that tree-level celestial gluon scattering, in theories with sufficiently soft UV behavior, instead obeys conformally soft theorems involving $h$ → 0 or $$\bar{h}$$ → 0. Unlike the energetically soft theorem, the conformally soft theorem cannot be derived from low-energy effective field theory.

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 1571686

- Alternate Identifier(s):
- OSTI ID: 1595980

- Grant/Contract Number:
- SC0007870

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 8; 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; symmetries

### Citation Formats

```
Pate, Monica, Raclariu, Ana-Maria, and Strominger, Andrew. Conformally soft theorem in gauge theory. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.085017.
```

```
Pate, Monica, Raclariu, Ana-Maria, & Strominger, Andrew. Conformally soft theorem in gauge theory. United States. doi:10.1103/PhysRevD.100.085017.
```

```
Pate, Monica, Raclariu, Ana-Maria, and Strominger, Andrew. Thu .
"Conformally soft theorem in gauge theory". United States. doi:10.1103/PhysRevD.100.085017.
```

```
@article{osti_1571686,
```

title = {Conformally soft theorem in gauge theory},

author = {Pate, Monica and Raclariu, Ana-Maria and Strominger, Andrew},

abstractNote = {Asymptotic particle states in four-dimensional celestial scattering amplitudes are labeled by their SL(2,C) Lorentz/conformal weights ($h, \bar{h}$) rather than the usual energy-momentum four-vector. These boost eigenstates involve a superposition of all energies. As such, celestial gluon (or photon) scattering cannot obey the usual (energetically) soft theorems. In this paper we show that tree-level celestial gluon scattering, in theories with sufficiently soft UV behavior, instead obeys conformally soft theorems involving $h$ → 0 or $\bar{h}$ → 0. Unlike the energetically soft theorem, the conformally soft theorem cannot be derived from low-energy effective field theory.},

doi = {10.1103/PhysRevD.100.085017},

journal = {Physical Review D},

number = 8,

volume = 100,

place = {United States},

year = {2019},

month = {10}

}

Free Publicly Available Full Text

Publisher's Version of Record

DOI: 10.1103/PhysRevD.100.085017

DOI: 10.1103/PhysRevD.100.085017

Other availability

Cited by: 7 works

*Citation information provided by*

Web of Science

Web of Science

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

##
Heterotic string theory

journal, March 1986

- Gross, David J.; Harvey, Jeffrey A.; Martinec, Emil
- Nuclear Physics B, Vol. 267, Issue 1

##
2D Stress Tensor for 4D Gravity

journal, September 2017

- Kapec, Daniel; Mitra, Prahar; Raclariu, Ana-Maria
- Physical Review Letters, Vol. 119, Issue 12

##
S-matrix singularities and CFT correlation functions

journal, August 2017

- Cardona, Carlos; Huang, Yu-tin
- Journal of High Energy Physics, Vol. 2017, Issue 8

##
Construction of a crossing-simmetric, Regge-behaved amplitude for linearly rising trajectories

journal, September 1968

- Veneziano, G.
- Il Nuovo Cimento A, Vol. 57, Issue 1

##
2D Kac-Moody symmetry of 4D Yang-Mills theory

journal, October 2016

- He, Temple; Mitra, Prahar; Strominger, Andrew
- Journal of High Energy Physics, Vol. 2016, Issue 10

##
Aspects of the BMS/CFT correspondence

conference, April 2011

- Barnich, Glenn; Troessaert, Cédric
- Proceedings of Corfu Summer Institute on Elementary Particles and Physics - Workshop on Non Commutative Field Theory and Gravity — PoS(CNCFG2010)

##
Aspects of the BMS/CFT correspondence

journal, May 2010

- Barnich, Glenn; Troessaert, Cédric
- Journal of High Energy Physics, Vol. 2010, Issue 5

##
On BMS invariance of gravitational scattering

journal, July 2014

- Strominger, Andrew
- Journal of High Energy Physics, Vol. 2014, Issue 7

##
A d-dimensional stress tensor for Minkd+2 gravity

journal, May 2018

- Kapec, Daniel; Mitra, Prahar
- Journal of High Energy Physics, Vol. 2018, Issue 5

##
Conformally soft photons and gravitons

journal, January 2019

- Donnay, Laura; Puhm, Andrea; Strominger, Andrew
- Journal of High Energy Physics, Vol. 2019, Issue 1

##
A holographic reduction of Minkowski space–time

journal, August 2003

- de Boer, Jan; Solodukhin, Sergey N.
- Nuclear Physics B, Vol. 665

##
Symmetries of celestial amplitudes

journal, June 2019

- Stieberger, Stephan; Taylor, Tomasz R.
- Physics Letters B, Vol. 793

##
Gluon amplitudes as $2d$ conformal correlators

journal, October 2017

- Pasterski, Sabrina; Shao, Shu-Heng; Strominger, Andrew
- Physical Review D, Vol. 96, Issue 8

##
Strings on celestial sphere

journal, October 2018

- Stieberger, Stephan; Taylor, Tomasz R.
- Nuclear Physics B, Vol. 935

##
4D scattering amplitudes and asymptotic symmetries from 2D CFT

journal, January 2017

- Cheung, Clifford; de la Fuente, Anton; Sundrum, Raman
- Journal of High Energy Physics, Vol. 2017, Issue 1

##
Scattering Amplitudes from Soft Theorems and Infrared Behavior

journal, February 2019

- Rodina, Laurentiu
- Physical Review Letters, Vol. 122, Issue 7

##
Null infinity and unitary representation of the Poincare group

journal, January 2019

- Banerjee, Shamik
- Journal of High Energy Physics, Vol. 2019, Issue 1

##
Conformal structure of massless scalar amplitudes beyond tree level

journal, April 2018

- Banerjee, Nabamita; Banerjee, Shamik; Bhatkar, Sayali Atul
- Journal of High Energy Physics, Vol. 2018, Issue 4

##
Supersymmetric dual string theory

journal, May 1982

- Green, Michael B.; Schwarz, John H.
- Nuclear Physics B, Vol. 198, Issue 2

##
Semiclassical Virasoro symmetry of the quantum gravity S $$ \mathcal{S} $$ -matrix

journal, August 2014

- Kapec, Daniel; Lysov, Vyacheslav; Pasterski, Sabrina
- Journal of High Energy Physics, Vol. 2014, Issue 8

##
Tree-level gluon amplitudes on the celestial sphere

journal, June 2018

- Schreiber, Anders Ø.; Volovich, Anastasia; Zlotnikov, Michael
- Physics Letters B, Vol. 781

##
Symmetries of Asymptotically Flat Four-Dimensional Spacetimes at Null Infinity Revisited

journal, September 2010

- Barnich, Glenn; Troessaert, Cédric
- Physical Review Letters, Vol. 105, Issue 11

##
Flat space amplitudes and conformal symmetry of the celestial sphere

journal, September 2017

- Pasterski, Sabrina; Shao, Shu-Heng; Strominger, Andrew
- Physical Review D, Vol. 96, Issue 6

##
Soft limits of Yang-Mills amplitudes and conformal correlators

journal, May 2019

- Fan, Wei; Fotopoulos, Angelos; Taylor, Tomasz R.
- Journal of High Energy Physics, Vol. 2019, Issue 5

##
Conformal basis, optical theorem, and the bulk point singularity

journal, July 2018

- Lam, Ho Tat; Shao, Shu-Heng
- Physical Review D, Vol. 98, Issue 2

##
Conformal basis for flat space amplitudes

journal, September 2017

- Pasterski, Sabrina; Shao, Shu-Heng
- Physical Review D, Vol. 96, Issue 6