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Linda Parkes

Bio: Linda Parkes is an academic researcher from University of Texas at Austin. The author has contributed to research in topics: Instanton & Calabi–Yau manifold. The author has an hindex of 7, co-authored 9 publications receiving 2007 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, the prepotentials and geometry of the moduli spaces for a Calabi-Yau manifold and its mirror were derived and all the sigma model corrections to the Yukawa couplings and moduli space metric were obtained.

1,679 citations

Journal ArticleDOI
TL;DR: In this paper, the prepotentials and geometry of the moduli spaces for a Calabi-Yau manifold and its mirror were derived and all the sigma model corrections to the Yukawa couplings and moduli space metric were obtained.

189 citations

Journal ArticleDOI
TL;DR: In this paper, a geometrical interpretation of the mirror Z is presented, which is a representative of a class of generalized Calabi-Yau manifolds, which can be realized as manifolds of dimension five and seven.

126 citations

01 Jan 1991
TL;DR: In this paper, the prepotentials and geometry of the moduli spaces for a Calabi-Yau manifold and its mirror were derived and all the sigma model corrections to the Yukawa couplings and moduli space metric for the original manifold were obtained.
Abstract: We compute the prepotentials and the geometry of the moduli spaces for a Calabi-Yau manifold and its mirror. In this way we obtain all the sigma model corrections to the Yukawa couplings and moduli space metric for the original manifold. The moduli space is tbund to be subject to the action of a modular group which, among other operations, exchanges large and small values of the radius though the action on the radius is not as simple as R-, 1/R. It is shown also that the quantum corrections to the coupling decompose into a sum over instanton contributions and moreover that this sum converges. In particular there are no "sub-instanton" corrections. This sum over instantons points to a deep connection between the modular group and the rational curves of the Calabi-Yau manifold. The burden of the present work is that a mirror pair of Calabi-Yau manifolds is an exactly soluble superconformal theory, at least as far as the masslcss sector is concerned. Mirror pairs are also more general than exactly soluble models that have hitherto been discussed since we here solve the theo~' for all points of the moduli space.

90 citations

Journal ArticleDOI
TL;DR: In this paper, null and time-like geodesics in the Erez-Rosen space-time, that is, in the exterior gravitational field of a mass with quadrupole moment, were investigated.
Abstract: We investigate null and time-like geodesics in the Erez-Rosen space-time, that is, in the exterior gravitational field of a mass with quadrupole moment. By using the weak-field approximation of the Erez-Rosen metric, we find the solution of the equation for equatorial time-like geodesics and determine how they differ from the corresponding Schwarzschild geodesies. For the exact form of the Erez-Rosen metric, we only draw some qualitative conclusions about the influence of the quadrupole moment on the path of test particles and on the motion of photons. We derive the relativistic contribution of the quadrupole moment to the perihelion shift and to the precession of the ascending node.

20 citations


Cited by
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Journal ArticleDOI
TL;DR: In this paper, a natural relation between sigma models based on Calabi-Yau hypersurfaces in weighted projective spaces and Landau-Ginzburg models is found.

2,162 citations

Journal ArticleDOI
TL;DR: In this paper, the authors developed techniques to compute higher loop string amplitudes for twisted N = 2 theories with ε = 3 (i.e. the critical case) by exploiting the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured by a master anomaly equation.
Abstract: We develop techniques to compute higher loop string amplitudes for twistedN=2 theories withĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of theN=2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira-Spencer theory, which may be viewed as the closed string analog of the Chern-Simons theory. Using the mirror map this leads to computation of the ‘number’ of holomorphic curves of higher genus curves in Calabi-Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingN=2 theory. Relations withc=1 strings are also pointed out.

1,633 citations

Journal ArticleDOI
TL;DR: In this paper, it was argued that every Calabi-Yau manifold X with a mirror Y admits a family of supersymmetric toroidal 3-cycles and that the moduli space of such cycles together with their flat connections is precisely the space Y.

1,607 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider F/M/Type IIA theory compactified to four, three, or two dimensions on a Calabi-Yau fourfold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes.

1,516 citations

Book ChapterDOI
TL;DR: Mirror symmetry was discovered several years ago in string theory as a duality between families of 3-dimensional Calabi-Yau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeros).
Abstract: Mirror symmetry (MS) was discovered several years ago in string theory as a duality between families of 3-dimensional Calabi-Yau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeros). The name comes from the symmetry among Hodge numbers. For dual Calabi-Yau manifolds V, W of dimension n (not necessarily equal to 3) one has $$\dim {H^p}(V,{\Omega ^q}) = \dim {H^{n - p}}(W,{\Omega ^q}).$$ .

1,510 citations