# Multi-Cut Matrix Models

+ 2 like - 0 dislike
1153 views

I have a question pertaining specifically to a one-matrix model with a multi-cut solution. The standard procedure is to take a polynomial superpotential $W(x)$. In the classical limit (analogous to $\hbar =0$), all of the eigenvalues are sitting precisely at the extrema of $W$. As you turn some sort of coupling on, and pass to the large-$N$ 't Hooft limit (the matrices are $N \times N$), the eigenvalues "repel" each other and spread out to form "branch cuts."

I had been assuming that this spreading out from the extrema of $W$ happens symmetrically, but perhaps they won't spread symmetrically if the eigenvalues from the other cuts can repel them? To make my question more concrete, imagine just two extrema of $W$ at $\pm1$ on the real axis. Let's assume the cuts will spread out also on the real axis. Will each cut emerge symmetrically from $\pm1$? Or will they actually spread more on the "outside" since the eigenvalues might repel each other more on the "inside"?

I haven't seen this discussed in the matrix model literature so I was hoping perhaps someone had some insight!

This post imported from StackExchange Physics at 2016-06-26 09:55 (UTC), posted by SE-user spietro

asked Jun 25, 2016
edited Jun 26, 2016

## Your answer

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$y$\varnothing$icsOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). Please complete the anti-spam verification