Abstract
We study three-point functions of single-trace operators in the su(1|1) sector of planar N = 4 SYM borrowing several tools based on Integrability. In the most general configuration of operators in this sector, we have found a determinant expression for the tree-level structure constants. We then compare the predictions of the recently proposed hexagon program against all available data. We have obtained a match once additional sign factors are included when the two hexagon form-factors are assembled together to form the structure constants. In the particular case of one BPS and two non-BPS operators we managed to identify the relevant form-factors with a domain wall partition function of a certain six-vertex model. This partition function can be explicitly evaluated and factorizes at all loops. In addition, we use this result to compute the structure constants and show that at strong coupling in the so-called BMN regime, its leading order contribution has a determinant expression.
Highlights
Were made both at strong and weak coupling in [5,6,7,8,9,10] providing very strong support for the correctness of the hexagon solution to the structure constants problem
We show that the relevant hexagon for the three-point function of one BPS and two non-BPS operators in the su(1|1) sector has the interpretation of a domain wall partition function of a certain six-vertex model
We have studied the three-point functions of operators in the su(1|1) sector, i.e., containing a single type of fermionic excitations
Summary
At tree-level, the wave-function ψ(i) associated to the operator Oi is given by the standard Bethe wave-function for a free fermion system that follows from the requirement that it diagonalizes the one-loop su(1|1) Hamiltonian (more details can be found in [14]). Given that the wave-functions in (2.10) are completely antisymmetric in all their arguments, we can extend the sums in (2.12) at the price of introducing a trivial overall combinatorial factor. Plugging their explicit expressions, we are left with. In the extremal limit L2 = L1 + L3 which implies that l23 = L3 and l12 = L1 Inserting these conditions on the previous formula, it gets simplified once we use the Bethe equations and both blocks get a similar form 1 − eip(j2)L1 e−ip(j2) − e−ip(k1).
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