References for phase-transitions in supersymmetric field theory

Question

Apart from other reasons, recently my interest in this area got piqued when I heard an awesome lecture by Seiberg on the idea of meta-stable-supersymmetry-breaking.

I am looking for references on learning about phase transitions/critical phenomenon in supersymmetric field theory - may be especially in the context of $\cal{N}=4$ SYM.

It would be great if along with the reference you can also drop in a few lines about what is the point about this line of research.

To start off,

• this one by Witten, Cachazo and Seiberg and this one by Gukov and Witten.

• this lecture by McGreevy and the references at its end.

• may be this paper by Alday, Gaiotto, Tachikawa, Gukov and Verlinde too..

I would be very happy to be pointed to may be some more pedagogical/expository references about this theme of supersymmetric phase transitions.

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Answer 1

While this isn't necessarily going to answer your request, I think it might be interesting none the less:

Phases of N=2 Theories in Two Dimensions

In a String Theory context: The Basic Idea is to study a GLSM in 2D which exhibits the interesting property to lead to Calabi-Yau compactification in one phase and Orbifold compactification in the other.

The hope & current research is to better understand Calabi-Yau compactification by taking a look at the Orbifold phase and perhaps find a suitable way to give rise to the standard model in String Theory.

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Comments

Thanks a lot for the reference and the insights. Probably this is an unfair help to ask for but you might appreciate that I am a newbie! - can you kindly tell me if the content of the above paper is more or less the same thing as these 3 lectures by Witten - http://www.math.ias.edu/QFT/spring/witten17.ps http://www.math.ias.edu/QFT/spring/witten18.ps http://www.math.ias.edu/QFT/spring/witten19.ps I am having a vague feeling that these lectures basically review the paper you linked. Is it?

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It might seem like that, as both the paper and lecture are about the geometrical properties of these theories, however, the lecture you linked is on a different subject. (Keep in mind however that I only read the Introductions to each lecture you posted) For example, the paper I linked is studying 2D N=2 SUSY (which you get by reducing 4D N=1 SUSY by 2 dimensions) and the lectures you posted are on 4D N=2 SUSY, which are both very different.

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Thanks for the clarification. I am probably going to be concentrating more along the lines of the paper you linked. It seems to be pedagogically coming before the papers that I mentioned. Can you pin-down as to in the context of this paper, what are the phases for this case of N=2 on 1+1 for which one is looking for the phase-transitions? What is the order parameter in question? It would be greatly helpful if you can give these big-picture ideas.

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The order Parameter in this case is the $r$-Parameter which arises by including the Fayet-Iliopoulos D-Term. Depending on what value $r$ takes, different constraints arise for our Compactification (Calabi-Yau or Orbifolds). The Big picture in this case is what I wrote as my last sentence in the answer above.

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Thanks for the outline! May be I will put up more detailed questions on this once I get through a substantial part of the paper.

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