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

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In summary, the conversation discusses the issue of non-trivial scattering amplitudes in conformal field theories. While it is generally believed that conformal field theories do not have non-trivial scattering amplitudes due to the inability to define asymptotic states, the N=4 Super Yang Mills theory at tree level shows non-vanishing amplitudes. It is suggested that this is due to a controlled breaking of conformal invariance through methods such as the "Bern Dixon Smirnov" or "BDS" approach. However, there is limited understanding of this concept.
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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...
 

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

1. What are amplitudes in CFT?

Amplitudes in CFT, or conformal field theory, are mathematical objects that describe the probability amplitudes for various particle interactions in a specific type of quantum field theory. They are calculated using correlation functions of local operators on a conformally invariant manifold.

2. Why do amplitudes in CFT vanish?

Amplitudes in CFT vanish because of the conformal symmetry of the theory. This means that the correlation functions of local operators are zero unless certain conditions are met, such as the primary operator being a conformal scalar.

3. What is the significance of N=4 in relation to amplitudes in CFT?

N=4 refers to a specific type of supersymmetry in a CFT. This type of supersymmetry is special because it has a higher degree of symmetry than other types, which leads to the vanishing of amplitudes.

4. Why does N=4 supersymmetry lead to vanishing amplitudes in CFT?

N=4 supersymmetry, also known as maximal supersymmetry, leads to vanishing amplitudes because it has a larger symmetry group than other types of supersymmetry. This symmetry group includes conformal transformations, which is why amplitudes in CFT vanish.

5. How does the vanishing of amplitudes in CFT impact the study of particle interactions?

The vanishing of amplitudes in CFT has a significant impact on the study of particle interactions. It allows for simplification and more efficient calculations of correlation functions, making it easier to study and understand the behavior of particles in a conformally invariant system. It also has important implications for string theory and the AdS/CFT correspondence.

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