The hexagon in the mirror: the three-point function in the SoV representation

Autor(es)

Jiang, Yunfeng ^[1] ; Komatsu, Shota ^[2] ; Kostov, Ivan ^[1] ; Serban, Didina ^[1]

Afiliação do(s) autor(es)

^[1] CEA, CNRS Saclay URA2306, DSM, Inst Phys Theor, F-91191 Gif Sur Yvette - France

^[2] Perimeter Inst Theoret Phys, Waterloo, ON - Canada

• Tipo de documento: Artigo Científico
• Fonte: Journal of Physics A-Mathematical and Theoretical; v. 49, n. 17 APR 29 2016.
• Citações Web of Science: 12

Resumo

We derive an integral expression for the leading-order type I-I-I three-point functions in the su(2)-sector of N = 4 super Yang-Mills theory, for which no determinant formula is known. To this end, we first map the problem to the partition function of the six vertex model with a hexagonal boundary. The advantage of the six-vertex model expression is that it reveals an extra symmetry of the problem, which is the invariance under 90 degrees rotation. On the spin-chain side, this corresponds to the exchange of the quantum space and the auxiliary space and is reminiscent of the mirror transformation employed in the worldsheet S-matrix approaches. After the rotation, we then apply Sklyanin's separation of variables (SoVs) and obtain a multiple-integral expression of the three-point function. The resulting integrand is expressed in terms of the so-called Baxter polynomials, which is closely related to the quantum spectral curve approach. Along the way, we also derive several new results about the SoV, such as the explicit construction of the basis with twisted boundary conditions and the overlap between the orginal SoV state and the SoV states on the subchains. (AU)

• Processo FAPESP: 11/11973-4 - ICTP Instituto Sul-Americano para Pesquisa Fundamental: um centro regional para física teórica
• Beneficiário: Nathan Jacob Berkovits
• Linha de fomento: Auxílio à Pesquisa - Temático