6533b821fe1ef96bd127b8dc
RESEARCH PRODUCT
Real symplectic formulation of local special geometry
Oscar MaciaSergio Ferrarasubject
High Energy Physics - TheoryHessian matrixPhysicsPure mathematicsNuclear and High Energy PhysicsHolomorphic functionFOS: Physical sciencesLegendre functionLegendre transformationsymbols.namesakeAssociated Legendre polynomialsHigh Energy Physics - Theory (hep-th)Real-valued functionMetric (mathematics)symbolsParticle Physics - TheorySymplectic geometrydescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-06-01 | Physics Letters B |