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Geometry of mirror manifolds

Publication ,  Journal Article
Aspinwall, PS; Lütken, CA
Published in: Nuclear Physics, Section B
April 15, 1991

We analyze the mirror manifold hypothesis in one and three dimensions using the simplest available representations of the N = 2 superconformal algebra. The symmetries of these tensor models can be divided out to give an explicit representation of the mirror, and we give a simple group theoretical algorithm for determining which symmetries should be used. We show that the mirror of a superconformal field theory does not always have a geometrical interpretation, but when it does, deformations of complex structure of one manifold are reflected in deformations of the Kähler form of the mirror manifold, and we show how the large radius limit of a manifold corresponds to a large complex structure limit in the mirror manifold. The mirror of the Tian-Yau three generation model is constructed both as a conformal field theory and as an algebraic variety with Euler number six. The Hodge numbers of this manifold are fixed, but the intersection numbers are highly ambiguous, presumably reflecting a rich structure of multicritical points in the moduli space of the field theory. © 1991.

Duke Scholars

Published In

Nuclear Physics, Section B

DOI

ISSN

0550-3213

Publication Date

April 15, 1991

Volume

353

Issue

2

Start / End Page

427 / 461

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0105 Mathematical Physics
 

Citation

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Aspinwall, P. S., & Lütken, C. A. (1991). Geometry of mirror manifolds. Nuclear Physics, Section B, 353(2), 427–461. https://doi.org/10.1016/0550-3213(91)90343-V
Aspinwall, P. S., and C. A. Lütken. “Geometry of mirror manifolds.” Nuclear Physics, Section B 353, no. 2 (April 15, 1991): 427–61. https://doi.org/10.1016/0550-3213(91)90343-V.
Aspinwall PS, Lütken CA. Geometry of mirror manifolds. Nuclear Physics, Section B. 1991 Apr 15;353(2):427–61.
Aspinwall, P. S., and C. A. Lütken. “Geometry of mirror manifolds.” Nuclear Physics, Section B, vol. 353, no. 2, Apr. 1991, pp. 427–61. Scopus, doi:10.1016/0550-3213(91)90343-V.
Aspinwall PS, Lütken CA. Geometry of mirror manifolds. Nuclear Physics, Section B. 1991 Apr 15;353(2):427–461.
Journal cover image

Published In

Nuclear Physics, Section B

DOI

ISSN

0550-3213

Publication Date

April 15, 1991

Volume

353

Issue

2

Start / End Page

427 / 461

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0105 Mathematical Physics