arXiv:0905.2700v2 [hep-th] 6 Feb 2010 Duality covariant variables for STU-model in presence of non-holomorphic corrections Shamik Banerjee, Rajesh Kumar Gupta Harish-Chandra Research Institute Chhatnag Road, Jhusi, Allahabad 211019, INDIA E-mail: bshamik@mri.ernet.in, rajesh@mri.ernet.in Abstract It is known that non-holomorphic corrections are necessary in order to get duality invariant free energy and entropy function. However the present methods of incorporating non-holomorphic corrections are in conflict with special geometry properties of moduli space. The moduli fields do not transform in the duality covariant way and their duality transformation also involves the graviphoton field strength.In the present note we construct duality covariant moduli fields for STU- model perturbatively in powers of the graviphoton field strength and demonstrated their existence upto second order. 1Introduction The four dimensionalN= 2 supergravity lagrangian [1] coupled non-minimally to (n+1)-vector multiplets is described by a holomorphic prepotentialF(YI,Υ), which is a homogeneous function of degree 2 inYI(I= 0, ...., n) and Υ. Here theYIdenotes the (rescaled) complex scalar field which sits in the abelian vector multiplet and Υ denotes the (rescaled) square of the auxiliary, antiself- dual, antisymmetric Lorentz tensorTij abwhich sits in the weyl multiplet. The Υ dependent term in the prepotential gives rise to higher derivative curvature terms in the effective action. Under electric/magnetic duality transformation Sp(2n+ 2,Z), (YI, FI(Y,Υ)) transform as a symplectic vector. 1
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