Communications in Mathematical Physics - Volume 203 - download pdf or read online

By A. Jaffe (Chief Editor)

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Special geometry. Commun. Math. Phys. : Potentials and symmetries of general gauged N = 2 supergravityYang–Mills models. Nucl. Phys. B 245, 89–117 (1984) Communicated by R. H. Dijkgraaf Commun. Math. Phys. 203, 53 – 69 (1999) Communications in Mathematical Physics © Springer-Verlag 1999 Chiral BRST Cohomology of N = 2 Strings at Arbitrary Ghost and Picture Number Klaus Jünemann, Olaf Lechtenfeld Institut für Theoretische Physik, Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany. de Received: 5 January 1998 / Accepted: 16 November 1998 Abstract: We compute the BRST cohomology of the holomorphic part of the N = 2 string at arbitrary ghost and picture number.

10) It follows that Re(dzi ) = dx i , Re(dwj ) = −dyj . 12) where τij = ∂wj . 13) Now the fact that ω has type (1, 1) implies that τij = τj i , and so there is a (local) holomorphic function F, determined up to a constant, so that wj = ∂F ∂ 2F , τ = . 14) F is called the holomorphic prepotential. 25 below. 5 Of course, so is {w }. 37). 15) Special Kähler Manifolds 35 and in terms of this data the Kähler form is √ √ √ −1 −1 ∂ 2F j j i ¯ dz ∧ dz = Im Im(τij )dzi ∧ dz . 1 reproduces the usual local characterization.

A) Choose a flat Darboux coordinate system {x i , yj }. Then the local 1-forms dx i , dyj define sections of T ∗ M → M whose image is an integral manifold of H . 11)) their graphs are complex submanifolds. 12) we compute that ∇ ∂/∂zi is a form of type (1, 0): 1 ∂τj ∂ ∂ dzk ⊗ . 23) Since ∂/∂zi is a local basis of holomorphic sections, the desired assertion follows. The Riemannian metric has a very special form in flat real coordinates – it is the Hessian of a function. This observation is due to Nigel Hitchin.

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Communications in Mathematical Physics - Volume 203 by A. Jaffe (Chief Editor)

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