Large matrices and Virasoro Conjecture

Details Large matrices and Virasoro Conjecture Large matrices and Virasoro Conjecture

2009-04-13

arxiv.org/abs/0904.1916v3

Physics

Mathematical Physics

29 pages

Scientific paper

In this paper, we first review one of difficult parts of the proof of Witten's conjecture by Kontsevich that had not been emphasized before. In the derivation of the KdV equations, we review the boson-fermion correspondence method \cite{K} to show that the trajectory of $\rm GL_\infty$ action on 1 as an element of the ring $\mathbb{C}[x_1,x_2,...]$ yields the solutions of KP hierarchies. Then we consider the corresponding theory in which the target manifold is a K\"{a}hler manifold. We conjecture that this nonlinear sigma model is equivalent to a "planar graph" theory. Assuming the conjecture holds, we are able to get the Virasoro constraints in the Virasoro conjecture.

Affiliated with

Also associated with

No associations

Rating

Large matrices and Virasoro Conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Large matrices and Virasoro Conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Large matrices and Virasoro Conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-324054