Real symplectic formulation of local special geometry

Details Real symplectic formulation of local special geometry Real symplectic formulation of local special geometry

2006-03-14

arxiv.org/abs/hep-th/0603111v2

Phys.Lett.B637:102-106,2006

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, corrected typos

Scientific paper

10.1016/j.physletb.2006.04.010

We consider a formulation of local special geometry in terms of Darboux special coordinates $P^I=(p^i,q_i)$, $I=1,...,2n$. A general formula for the metric is obtained which is manifestly $\mathbf{Sp}(2n,\mathbb{R})$ covariant. Unlike the rigid case the metric is not given by the Hessian of the real function $S(P)$ which is the Legendre transform of the imaginary part of the holomorphic prepotential. Rather it is given by an expression that contains $S$, its Hessian and the conjugate momenta $S_I=\frac{\partial S}{\partial P^I}$. Only in the one-dimensional case ($n=1$) is the real (two-dimensional) metric proportional to the Hessian with an appropriate conformal factor.

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