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SUMMARY:Unitary matrix models\, free fermions\, and the giant graviton exp
 ansion - Sameer Murthy (King's College London)
DTSTART:20220822T133000Z
DTEND:20220822T143000Z
UID:TALK177197@talks.cam.ac.uk
DESCRIPTION:I will discuss a class of integrals over the unitary group&nbs
 p\;U(N)&nbsp\;with an infinite set of couplings characterized by a series&
 nbsp\;f(q)= \\sum_n a(n) q^n\, 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 couplin
 gs. Integrating out the fermions in a given quantum state leads to a conve
 rgent expansion as a series of determinants\, as shown by Borodin-Okounkov
  many years ago. By further averaging over the ensemble\, we obtain a form
 ula for the matrix integral as a q-series with successive terms suppressed
  by&nbsp\;q^(aN+b) where a\, b do not depend on N. I will explain the moti
 vation and interpretation of the formula\, which comes from the physics of
  AdS/CFT. In this context\, the matrix integral is the superconformal inde
 x of Super Yang-Mills theory\, and the terms in the expansion correspond t
 o giant gravitons in anti de Sitter space.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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