On Scale and Conformal Invariance in Four Dimensions

Dymarsky, Anatoly; Komargodski, Zohar; Schwimmer, Adam; Theisen, Stefan

doi:10.1007/JHEP10(2015)171

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On Scale and Conformal Invariance in Four Dimensions

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Theisen, Stefan
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Dymarsky, A., Komargodski, Z., Schwimmer, A., & Theisen, S. (2015). On Scale and Conformal Invariance in Four Dimensions. Journal of high energy physics: JHEP, 2015(10): 171. doi:10.1007/JHEP10(2015)171.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-6EEA-6

Abstract

We study the implications of scale invariance in four-dimensional quantum
field theories. Imposing unitarity, we find that infinitely many matrix
elements vanish in a suitable kinematical configuration. This vanishing is a
nontrivial necessary condition for conformality. We provide an argument why
this is expected to be a sufficient condition as well, thereby linking scale
and conformal invariance in unitary theories. We also discuss possible
exceptions to our argument.