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Collective theory for the three-point function in the SU(2) sector

by Dr. Ivan Kostov (Saclay, Parigi)

Dec 03, 2013 from 03:00 PM to 05:00 PM

Where Aula Teorici - Irnerio

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Abstract:

We study the thermodynamical limit of the 3-point function of heavy SU(2) type fields in N=4 SYM.
Technically the problem reduces to computing the inner product of  Bethe states in a  periodic inhomogeneous XXX spin-1/2 chain in the Sutherland limit,  where the Bethe roots condense into one or several macroscopic strings. We express the scalar product as a free fermions expectation value, which is given also  by a Fredholm determinant.  We develop a collective field approach for the bosonized theory by  evaluating exactly the contribution of the short wave length modes, considering the long-wave modes as an external field. The effective action for  the  the long-wave excitations is the Yang-Yang potential for certain TBA-like integral equation.