Exploring the Link between N=2 SUSY and Kahler Geometry

In summary, Brian Greene asserts that in order for the dimension of M to contribute nine to the central charge and for N=2 supersymmetry to be ensured, M must be a complex Kahler manifold. The paper "Chiral Rings in N=2 Superconformal Theories" by Vafa and colleagues or the paper "Calabi Yau Manifolds" by Greene may provide more details on this relationship. Additionally, chapter 15 of Green, Schwarz, Witten's book and the paper "Supersymmetry and Kahler Manifolds" by Zumino could also be useful resources on this topic. Some information may also be available on mirror servers such as xxx.lanl.gov.
  • #1
GoldPheonix
85
0
In this paper*, Brian Greene just asserts that:

"In order to contribute nine to the central charge, the dimension of M must be six, and to ensure the additional condition of N = 2 supersymmetry, M must be a complex Kahler manifold."

Is there some paper that discusses the relationship between Kahler geometry and N=2 SUSY? This assertion does not seem trivial, although I'm not very well-versed in string theory or SUSY.



*http://arxiv.org/PS_cache/hep-th/pdf/9702/9702155v1.pdf (Page 9, 2nd paragraph)
 
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  • #2
Ok arxiv isn't working now, but you should try the paper "Chiral Rings in N=2 Superconformal Theories", by Vafa and some friends. Unless I'm mistaken there should be some details there.

Otherwise Brian Greene should have another paper based on that one, maybe called "calabi yau manifolds", or something with geometry in it, I think around 1998 or so. Pretty sure that has more details.
 
  • #3
Oops actually I think the Greene paper I'm talking about is the one you've mentioned :D

arxiv's fault, can't check anything. For some reason I assumed you were talking about Greene's new paper
 
  • #4
negru said:
Ok arxiv isn't working now

For now, just change the initial part of the url for xxx.lanl.gov, or some other mirror server.
 
  • #5
Ch15 of Green, Schwarz, Witten should have something on this.
 
  • #6
This old school one could also be useful:
"Supersymmetry and Kahler Manifolds", by Zumino.
http://ccdb4fs.kek.jp/cgi-bin/img_index?7909068
 
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1. What is N=2 SUSY?

N=2 SUSY stands for N=2 Supersymmetry, which is a theoretical framework in particle physics that introduces a symmetry between fermions and bosons. It is an extension of N=1 SUSY, which only has one type of supersymmetry, and is an important concept in understanding the properties of elementary particles.

2. What is the significance of N=2 SUSY in particle physics?

N=2 SUSY has many theoretical implications in particle physics, including providing a possible solution to the hierarchy problem, which attempts to explain why the mass of the Higgs boson is significantly lighter than the Planck scale. It also plays a role in theories of quantum gravity and has implications for dark matter and dark energy.

3. What is Kahler Geometry?

Kahler Geometry is a type of differential geometry that combines the concepts of Riemannian geometry and complex geometry. It is used to study complex manifolds, which are spaces that can be locally described by complex coordinates. In N=2 SUSY, Kahler Geometry is used to describe the interactions between supersymmetric particles.

4. How are N=2 SUSY and Kahler Geometry related?

In N=2 SUSY, Kahler Geometry is used to construct a superpotential, which is a key part of the theory. The superpotential is a function that describes the interactions between the supersymmetric particles and is constructed using the Kahler potential, which is a function on the space of complex coordinates. Therefore, Kahler Geometry plays a crucial role in the formulation of N=2 SUSY.

5. What are some applications of N=2 SUSY and Kahler Geometry?

N=2 SUSY and Kahler Geometry have many applications in theoretical physics, including in the study of string theory, which is a candidate for a unified theory of all fundamental forces. They also have applications in cosmology, where they can be used to study the early universe and the large-scale structure of the universe. Additionally, they have applications in condensed matter physics, where they can be used to study exotic materials and their properties.

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