University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Unitary matrix models, free fermions, and the giant graviton expansion

Unitary matrix models, free fermions, and the giant graviton expansion

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact nobody.

NC2W02 - Crossing the bridge: New connections in number theory and physics

I will discuss a class of integrals over the unitary group U(N) with an infinite set of couplings characterized by a series f(q)= \sum_n a(n) qn, that arise in the context of counting U(N) invariants. I will show that any such model can be expressed in terms of a system of free fermions in an ensemble parameterized by the above couplings. Integrating out the fermions in a given quantum state leads to a convergent expansion as a series of determinants, as shown by Borodin-Okounkov many years ago. By further averaging over the ensemble, we obtain a formula for the matrix integral as a q-series with successive terms suppressed by q(aN+b) where a, b do not depend on N. I will explain the motivation and interpretation of the formula, which comes from the physics of AdS/CFT. In this context, the matrix integral is the superconformal index of Super Yang-Mills theory, and the terms in the expansion correspond to giant gravitons in anti de Sitter space. 

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2022 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity