TY - JOUR
T1 - Missing local operators, zeros, and twist-4 trajectories
AU - Henriksson, Johan
AU - Kravchuk, Petr
AU - Oertel, Brett
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/7
Y1 - 2024/7
N2 - The number of local operators in a CFT below a given twist grows with spin. Consistency with analyticity in spin then requires that at low spin, infinitely many Regge trajectories must decouple from local correlation functions, implying infinitely many vanishing conditions for OPE coefficients. In this paper we explain the mechanism behind this infinity of zeros. Specifically, the mechanism is related to the two-point function rather than the three-point function, explaining the vanishing of OPE coefficients in every correlator from a single condition. We illustrate our result by studying twist-4 Regge trajectories in the Wilson-Fisher CFT at one loop.
AB - The number of local operators in a CFT below a given twist grows with spin. Consistency with analyticity in spin then requires that at low spin, infinitely many Regge trajectories must decouple from local correlation functions, implying infinitely many vanishing conditions for OPE coefficients. In this paper we explain the mechanism behind this infinity of zeros. Specifically, the mechanism is related to the two-point function rather than the three-point function, explaining the vanishing of OPE coefficients in every correlator from a single condition. We illustrate our result by studying twist-4 Regge trajectories in the Wilson-Fisher CFT at one loop.
KW - Field Theories in Lower Dimensions
KW - Renormalization and Regularization
KW - Scale and Conformal Symmetries
UR - http://www.scopus.com/inward/record.url?scp=85200055530&partnerID=8YFLogxK
U2 - 10.1007/JHEP07(2024)248
DO - 10.1007/JHEP07(2024)248
M3 - Article
AN - SCOPUS:85200055530
SN - 1126-6708
VL - 2024
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 7
M1 - 248
ER -