TY - JOUR

T1 - Three-point functions at strong coupling in the BMN limit

AU - Basso, Benjamin

AU - Zhong, De liang

N1 - Publisher Copyright:
© 2020, The Author(s).

PY - 2020/4/1

Y1 - 2020/4/1

N2 - We consider structure constants of single-trace operators at strong coupling in planar N = 4 SYM theory using the hexagon formalism. We concentrate on heavy-heavy- light correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator. They describe the couplings between two highly boosted strings and a supergravity mode in the bulk dual. In the hexagon framework, two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor. The former originates from giant mirror magnons scanning the AdS geometry while the latter stems from small fluctuations around the BMN vacuum. The resulting structure constants have poles at positions where an enhanced mixing with double-trace operators is expected and zeros whenever the process is forbidden by supersymmetry. We also discuss the transition to the classical regime, when the length of the light operator scales like the string tension, where we observe similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex.

AB - We consider structure constants of single-trace operators at strong coupling in planar N = 4 SYM theory using the hexagon formalism. We concentrate on heavy-heavy- light correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator. They describe the couplings between two highly boosted strings and a supergravity mode in the bulk dual. In the hexagon framework, two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor. The former originates from giant mirror magnons scanning the AdS geometry while the latter stems from small fluctuations around the BMN vacuum. The resulting structure constants have poles at positions where an enhanced mixing with double-trace operators is expected and zeros whenever the process is forbidden by supersymmetry. We also discuss the transition to the classical regime, when the length of the light operator scales like the string tension, where we observe similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex.

KW - Conformal Field Models in String Theory

KW - Field Theories in Higher Dimen- sions

KW - Integrable Field Theories

UR - http://www.scopus.com/inward/record.url?scp=85085486397&partnerID=8YFLogxK

U2 - 10.1007/JHEP04(2020)076

DO - 10.1007/JHEP04(2020)076

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AN - SCOPUS:85085486397

SN - 1126-6708

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 4

M1 - 76

ER -