Goldstone bosons on celestial sphere and conformal soft theorems

Kampf, Karol; Novotný, Jiří; Trnka, Jaroslav; Vaško, Petr

doi:10.1007/jhep12(2023)135

Goldstone bosons on celestial sphere and conformal soft theorems

Journal Article · Tue Dec 19 00:00:00 EST 2023 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep12(2023)135· OSTI ID:2576178

Kampf, Karol ^[1]; Novotný, Jiří ^[1]; Trnka, Jaroslav ^[2]; Vaško, Petr ^[1]

Charles Univ., Prague (Czech Republic)
Charles Univ., Prague (Czech Republic); Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)

In this paper, we study celestial amplitudes of Goldstone bosons and conformal soft theorems. Motivated by the success of soft bootstrap in momentum space and the important role of the soft limit behavior of tree-level amplitudes, our goal is to extend some of the methods to the celestial sphere. The crucial ingredient of the calculation is the Mellin transformation, which transforms four-dimensional scattering amplitudes to correlation functions of primary operators in the celestial CFT. The soft behavior of the amplitude is then translated to the singularities of the correlator. Only for amplitudes in “UV completed theories” (with sufficiently good high energy behavior) the Mellin integration can be properly performed. In all other cases, the celestial amplitude is only defined in a distributional sense with delta functions. We provide many examples of celestial amplitudes in UV-completed models, including linear sigma models and Z-theory, which is a certain completion of the SU(N) non-linear sigma model. We also comment on the BCFW-like and soft recursion relations for celestial amplitudes and the extension of soft bootstrap ideas.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, Davis, CA (United States)

Sponsoring Organization:: MEYS; The Czech Science Foundation (GACR); USDOE Office of Science (SC)

Grant/Contract Number:: SC0009999

OSTI ID:: 2576178

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2023; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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Ultraviolet properties of N = 8 supergravity at five loops Bern, Zvi; Carrasco, John Joseph; Chen, Wei-Ming Physical Review D, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevD.98.086021	journal	October 2018
Ultraviolet Behavior of N = 8 Supergravity at Four Loops Bern, Z.; Carrasco, J. J. M.; Dixon, L. J. Physical Review Letters, Vol. 103, Issue 8 https://doi.org/10.1103/PhysRevLett.103.081301	journal	August 2009
Perturbative Quantum Gravity as a Double Copy of Gauge Theory Bern, Zvi; Carrasco, John Joseph M.; Johansson, Henrik Physical Review Letters, Vol. 105, Issue 6 https://doi.org/10.1103/PhysRevLett.105.061602	journal	August 2010
Five-Loop Four-Point Amplitude of N = 4 Super-Yang-Mills Theory Bern, Z.; Carrasco, J. J. M.; Johansson, H. Physical Review Letters, Vol. 109, Issue 24 https://doi.org/10.1103/PhysRevLett.109.241602	journal	December 2012
Ambitwistor Strings in Four Dimensions Geyer, Yvonne; Lipstein, Arthur E.; Mason, Lionel Physical Review Letters, Vol. 113, Issue 8 https://doi.org/10.1103/PhysRevLett.113.081602	journal	August 2014
Scattering of Massless Particles in Arbitrary Dimensions Cachazo, Freddy; He, Song; Yuan, Ellis Ye Physical Review Letters, Vol. 113, Issue 17 https://doi.org/10.1103/PhysRevLett.113.171601	journal	October 2014
Effective Field Theories from Soft Limits of Scattering Amplitudes Cheung, Clifford; Kampf, Karol; Novotny, Jiri Physical Review Letters, Vol. 114, Issue 22 https://doi.org/10.1103/PhysRevLett.114.221602	journal	June 2015
On-Shell Recursion Relations for Effective Field Theories Cheung, Clifford; Kampf, Karol; Novotny, Jiri Physical Review Letters, Vol. 116, Issue 4 https://doi.org/10.1103/PhysRevLett.116.041601	journal	January 2016
Vector Effective Field Theories from Soft Limits Cheung, Clifford; Kampf, Karol; Novotny, Jiri Physical Review Letters, Vol. 120, Issue 26 https://doi.org/10.1103/PhysRevLett.120.261602	journal	June 2018
New Soft Theorems for Goldstone-Boson Amplitudes Kampf, Karol; Novotny, Jiri; Shifman, Mikhail Physical Review Letters, Vol. 124, Issue 11 https://doi.org/10.1103/PhysRevLett.124.111601	journal	March 2020
Double Copy for Celestial Amplitudes Casali, Eduardo; Puhm, Andrea Physical Review Letters, Vol. 126, Issue 10 https://doi.org/10.1103/PhysRevLett.126.101602	journal	March 2021
Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory Britto, Ruth; Cachazo, Freddy; Feng, Bo Physical Review Letters, Vol. 94, Issue 18 https://doi.org/10.1103/PhysRevLett.94.181602	journal	May 2005
Lectures on celestial amplitudes Pasterski, Sabrina The European Physical Journal C, Vol. 81, Issue 12 https://doi.org/10.1140/epjc/s10052-021-09846-7	journal	December 2021
Celestial operator products of gluons and gravitons Pate, M.; Raclariu, A. -M.; Strominger, A. Reviews in Mathematical Physics, Vol. 33, Issue 09 https://doi.org/10.1142/S0129055X21400031	journal	July 2021
Lectures on the Infrared Structure of Gravity and Gauge Theory Strominger, Andrew https://doi.org/10.23943/9781400889853	book	January 2018

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