The derivation of the conformal anomaly for dilaton coupled electromag
netic field in curved space is presented. The models of this sort natu
rally appear in stringy gravity or after spherical reduction Of multid
imensional Einstein-Maxwell theory. It is shown that unlike the case o
f minimal vector in curved space or dilaton coupled scalar the anomaly
induced effective action cannot be derived. The reason is the same wh
y anomaly induced effective action cannot be constructed for interacti
ng theories (like QED) in curved space. (C) 1998 Elsevier Science B.V.
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