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

by Dr Ivan Kostov (Saclay, Parigi)

Tuesday 3 Dec 2013, 15:00 → 16:00 Europe/Rome

Aula Teorici (Dipartimento di Fisica e Astronomia)

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.