Application of symbol-operator technique for effective action computation

In the present talk we briefly demonstrate an elegant and effective technique for calculation of the trace expansion in the derivatives of background fields. One of main advantages of the technique is manifestly (super)symmetrical and gauge invariant form of expressions on all stages of calculations. Other advantage is the universality of the calculation method. Some particular examples and results are presented.Comment: 11 pages, LaTex, Extended version of the talk given at the Fifth Workshop on Quantum Field Theory under the Influence of External Conditions, Leipzig, 10-15 Sept. 200

"Induced" N=4 conformal supergravity

We consider an abelian N=4 super Yang-Mills theory coupled to background N=4 conformal supergravity fields. At the classical level, this coupling is invariant under global SU(1,1) transformation of the complex ("dilaton-axion") supergravity scalar combined with an on-shell vector-vector duality. We compute the divergent part of the corresponding quantum effective action found by integrating over the super Yang-Mills fields and demonstrate its SU(1,1) invariance. This divergent part related to the conformal anomaly is one-loop exact and should be given by the N=4 conformal supergravity action containing the Weyl tensor squared term. This allows us to determine the full non-linear form of the bosonic part of the N=4 conformal supergravity action which has manifest SU(1,1) invariance.Comment: 13 pages. v2: minor misprints corrected; v3: note added about missed terms in the actio

One-loop effective potential in N=1/2{\cal N}={1/2} generic chiral superfield model

We obtain the one-loop quantum corrections to the K\"ahlerian and superpotentials in the generic chiral superfield model on the nonanticommutative superspace. Unlike all previous works, we use a method which does not require to rewrite a star-product of superfields in terms of ordinary products. In the K\"ahlerian potential sector the one-loop contributions are analogous to ones in the undeformed theory while in the chiral potential sector the quantum corrections contain a deformation parameter.Comment: LaTeX, 9 pages, Typos correcte