Amplitudes in CFT vanish. Why does N=4 have them?

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SUMMARY

N=4 Super Yang-Mills theory, despite being a conformal field theory (CFT), exhibits non-vanishing scattering amplitudes at tree level, such as the MHV amplitude. This phenomenon arises from a controlled breaking of conformal invariance. The discussion highlights the significance of the BDS (Bern-Dixon-Smirnov) method for computing infrared safe amplitudes in these theories, which provides a framework for understanding the non-trivial scattering behavior in CFTs.

PREREQUISITES
  • Understanding of N=4 Super Yang-Mills theory
  • Familiarity with conformal field theory (CFT) principles
  • Knowledge of scattering amplitudes in quantum field theory
  • Basic grasp of infrared (IR) safety in quantum amplitudes
NEXT STEPS
  • Research the BDS method for computing amplitudes in N=4 Super Yang-Mills theory
  • Study the properties of MHV amplitudes in quantum field theories
  • Explore the implications of breaking conformal invariance in CFTs
  • Investigate the role of infrared safety in scattering amplitude calculations
USEFUL FOR

The discussion is beneficial for theoretical physicists, particularly those specializing in quantum field theory, string theory, and anyone interested in the properties of conformal field theories and their scattering amplitudes.

earth2
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Hi guys,

one question in this growing amplitude business that i don't understand. Usually one says that conformal field theories do not have any non-trivial scattering amplitudes because one cannot define asymptotic states. But say we consider now N=4 Super Yang Mills and moreover treelevel. It is a conformal theory but it has non-vanishing amplitudes, like the infamous MHV amplitude. How can that be that an conformal field theory has non-vanishing amplitudes?

Cheers,
earth2
 
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I think they have a method of breaking the conformal invariance in a controlled way. If you google "Bern Dixon Smirnov" or "BDS" you might turn up some information on the computation of IR safe amplitudes in these theories. I don't really understand it well enough to explain it though...
 

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