TY - JOUR
T1 - Anomalous dimensions of leading twist conformal operators
AU - Belitsky, Andrei
AU - Henn, J.
AU - Jarczak, C.
AU - Müller, D.
AU - Sokatchev, E.
PY - 2008/2/25
Y1 - 2008/2/25
N2 - We extend and develop a method for perturbative calculations of anomalous dimensions and mixing matrices of leading twist conformal primary operators in conformal field theories. Such operators lie on the unitarity bound and hence are conserved (irreducible) in the free theory. The technique relies on the known pattern of breaking of the irreducibility conditions in the interacting theory. We relate the divergence of the conformal operators via the field equations to their descendants involving an extra field and accompanied by an extra power of the coupling constant. The ratio of the two-point functions of descendants and of their primaries determines the anomalous dimension, allowing us to gain an order of perturbation theory. We demonstrate the efficiency of the formalism on the lowest-order analysis of anomalous dimensions and mixing matrices which is required for two-loop calculations of the former. We compare these results to another method based on anomalous conformal Ward identities and constraints from the conformal algebra. It also permits us to gain a perturbative order in computations of mixing matrices. We show the complete equivalence of both approaches.
AB - We extend and develop a method for perturbative calculations of anomalous dimensions and mixing matrices of leading twist conformal primary operators in conformal field theories. Such operators lie on the unitarity bound and hence are conserved (irreducible) in the free theory. The technique relies on the known pattern of breaking of the irreducibility conditions in the interacting theory. We relate the divergence of the conformal operators via the field equations to their descendants involving an extra field and accompanied by an extra power of the coupling constant. The ratio of the two-point functions of descendants and of their primaries determines the anomalous dimension, allowing us to gain an order of perturbation theory. We demonstrate the efficiency of the formalism on the lowest-order analysis of anomalous dimensions and mixing matrices which is required for two-loop calculations of the former. We compare these results to another method based on anomalous conformal Ward identities and constraints from the conformal algebra. It also permits us to gain a perturbative order in computations of mixing matrices. We show the complete equivalence of both approaches.
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U2 - 10.1103/PhysRevD.77.045029
DO - 10.1103/PhysRevD.77.045029
M3 - Article
AN - SCOPUS:41149109519
SN - 1550-7998
VL - 77
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
IS - 4
M1 - 045029
ER -