TY - JOUR
T1 - Crossing bridges with strong Szegő limit theorem
AU - Belitsky, A. V.
AU - Korchemsky, G. P.
N1 - Publisher Copyright:
© 2021, The Author(s).
PY - 2021/4
Y1 - 2021/4
N2 - We develop a new technique for computing a class of four-point correlation functions of heavy half-BPS operators in planar N = 4 SYM theory which admit factorization into a product of two octagon form factors with an arbitrary bridge length. We show that the octagon can be expressed as the Fredholm determinant of the integrable Bessel operator and demonstrate that this representation is very efficient in finding the octagons both at weak and strong coupling. At weak coupling, in the limit when the four half-BPS operators become null separated in a sequential manner, the octagon obeys the Toda lattice equations and can be found in a closed form. At strong coupling, we exploit the strong Szegő limit theorem to derive the leading asymptotic behavior of the octagon and, then, apply the method of differential equations to determine the remaining subleading terms of the strong coupling expansion to any order in the inverse coupling. To achieve this goal, we generalize results available in the literature for the asymptotic behavior of the determinant of the Bessel operator. As a byproduct of our analysis, we formulate a Szegő-Akhiezer-Kac formula for the determinant of the Bessel operator with a Fisher-Hartwig singularity and develop a systematic approach to account for subleading power suppressed contributions.
AB - We develop a new technique for computing a class of four-point correlation functions of heavy half-BPS operators in planar N = 4 SYM theory which admit factorization into a product of two octagon form factors with an arbitrary bridge length. We show that the octagon can be expressed as the Fredholm determinant of the integrable Bessel operator and demonstrate that this representation is very efficient in finding the octagons both at weak and strong coupling. At weak coupling, in the limit when the four half-BPS operators become null separated in a sequential manner, the octagon obeys the Toda lattice equations and can be found in a closed form. At strong coupling, we exploit the strong Szegő limit theorem to derive the leading asymptotic behavior of the octagon and, then, apply the method of differential equations to determine the remaining subleading terms of the strong coupling expansion to any order in the inverse coupling. To achieve this goal, we generalize results available in the literature for the asymptotic behavior of the determinant of the Bessel operator. As a byproduct of our analysis, we formulate a Szegő-Akhiezer-Kac formula for the determinant of the Bessel operator with a Fisher-Hartwig singularity and develop a systematic approach to account for subleading power suppressed contributions.
KW - AdS-CFT Correspondence
KW - Extended Supersymmetry
KW - Integrable Field Theories
KW - Integrable Hierarchies
UR - http://www.scopus.com/inward/record.url?scp=85104997288&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85104997288&partnerID=8YFLogxK
U2 - 10.1007/JHEP04(2021)257
DO - 10.1007/JHEP04(2021)257
M3 - Article
AN - SCOPUS:85104997288
VL - 2021
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1029-8479
IS - 4
M1 - 257
ER -