Conformal properties of soft-operators. Part II. Use of null-states


Abstract:

Representations of the (Lorentz) conformal group with the soft operators as highest weight vectors have two universal properties, which we clearly state in this paper. Given a soft operator with a certain dimension and spin, the first property is about the existence of “(large) gauge transformation” that acts on the soft operator. The second property is the decoupling of (large) gauge-invariant null-states of the soft operators from the S-matrix elements. In each case, the decoupling equation has the form of zero field-strength condition with the soft operator as the (gauge) potential. Null-state decoupling effectively reduces the number of polarisation states of the soft particle and is crucial in deriving soft-theorems from the Ward identities of asymptotic symmetries. To the best of our understanding, these properties are not directly related to the Lorentz invariance of the S-matrix or the existence of asymptotic symmetries. We also verify that the results obtained from the decoupling of null-states are consistent with the leading and subleading soft-theorems with finite energy massive and massless particles in the external legs. Read More

Publication: Journal of High Energy Physics

Publisher: Springer Link

Authors: Shamik Banerjee & Pranjal Pandey

Keywords: Scattering Amplitudes, Space-Time Symmetries

Meet one of the Author:

Dr Pranjal Pandey earned his Ph.D. in Theoretical High Energy Physics from the Homi Bhabha National Institute, which is under the aegis of the Department of Atomic Energy in India. His publication on the topic of Flat Space Holography, has been cited by leading groups at Harvard, Princeton, and Oxford. His extensive experience in using mathematical models to price derivatives and forecast market movements based on alternative text data, like tweets and news headlines, distinguishes him from others.

Dr. Pranjal Pandey

Affiliations:

Institute of Physics, Sachivalaya Marg, Bhubaneshwar, 751005, India – The Institute of Physics in Bhubaneswar, India is a research institution that is funded jointly by the Department of Atomic Energy (DAE) and the government of Odisha. It was officially established in 1972 and began its academic activities in 1975 with two faculties and the director. From 1974 to 1981, the institute operated out of rented buildings before moving to its current campus in 1981. In 1985, the institute was taken over by the DAE. The predoctoral program at the institute provides a broad-based education in advanced physics and research methodology. Upon completion of the program, students are eligible to pursue a Ph.D. degree awarded by the Homi Bhabha National Institute of the DAE.

Homi Bhabha National Institute, Anushakti Nagar, Mumbai, 400085, India – The Homi Bhabha National Institute (HBNI) was founded in 2005 under the University Grants Commission Act. It has several constituent institutions and off-campus centers. HBNI’s role is to cultivate expertise in nuclear science and engineering and to encourage basic research that can be translated into technological development and applications through academic programs, such as Master’s and Ph.D. degrees in various fields of engineering, physical, chemical, mathematical, life, and medical and health sciences. HBNI also promotes interdisciplinary research.