• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,054 questions , 2,207 unanswered
5,347 answers , 22,726 comments
1,470 users with positive rep
818 active unimported users
More ...

  Multi-Cut Matrix Models

+ 2 like - 0 dislike

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 in Theoretical Physics by spietro (95 points) [ revision history ]
edited Jun 26, 2016 by Dilaton

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):
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:
Then 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

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights