Is N=4 Supersymmetric Yang-Mills Theory Self-Dual?

  • Thread starter metroplex021
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In summary, the conversation discusses the topic of S-duality and N=4 supersymmetric Yang-Mills theories. There are conflicting views on whether these theories are self-dual, and the conversation requests for further insights. A famous physicist mentions the Montonen-Olive duality, which shows both self- and non-self duality for certain gauge groups. They also mention the paper "Gauge Theories and Magnetic Charge" which shows that SO(2n+1) is dual to Sp(2n) and vice versa. Overall, the conversation highlights the complexities and varying perspectives on the topic.
  • #1
metroplex021
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Hi folks,

I am looking a bit at the phenomenon of S-duality (as a bit of an amateur) and looking at the literature I am getting mixed messages concerning whether or not N=4 supersymmetric Yang-Mills theories are in general self-dual. Does anyone happen to know anything about this?!

I'd appreciate any views or leads very much!
 
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  • #2
I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?
 
  • #3
I just received this in an email from a rather famous physicist whose name I'd rather not mention.

"The classic Montonen-Olive duality of N=4 super-Yang Mills illustrates both self- and non-self duality. For gauge group SU(n) or SO(2n) the dual theory is the same, but the paper

Gauge Theories and Magnetic Charge
P. Goddard (Cambridge U.), J. Nuyts (UMH, Mons), David I. Olive (CERN & Bohr Inst.). Dec 1976. 41 pp.
Published in Nucl.Phys. B125 (1977) 1

showed that SO(2n+1) is dual to Sp(2n) and vice versa. The global symmetries and SUSY have to be the same on both sides, but the fields and gauge symmetries differ. ... As one goes to less SUSY, there is more freedom and non-self-duality is common."

Hope that's of interest to others!
 

1. What is S-duality?

S-duality is a mathematical concept in theoretical physics that describes a symmetry between two different versions of a physical theory. This means that if we apply a certain transformation to one version of the theory, we get the other version. It is also known as electric-magnetic duality.

2. What is self-duality?

Self-duality is a special case of S-duality where the two versions of the theory are identical. In other words, there is a symmetry between two different descriptions of the same physical system. This is also known as strong-weak duality.

3. How do S-duality and self-duality relate to each other?

S-duality and self-duality are closely related concepts. S-duality is a more general concept that includes self-duality as a special case. In self-duality, the two versions of the theory are identical, while in S-duality, they are related by a transformation.

4. What are the implications of S-duality and self-duality in theoretical physics?

S-duality and self-duality have important implications in theoretical physics, particularly in the study of gauge theories and string theory. They allow us to make connections between seemingly different physical systems and provide insights into the underlying structure of the universe.

5. Are there any experimental evidence for S-duality and self-duality?

There is currently no direct experimental evidence for S-duality and self-duality. However, there have been many theoretical studies and calculations that support these concepts. Additionally, S-duality has been observed in some condensed matter systems, providing indirect evidence for its validity in physics.

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