Superstring compactification: The geometry of three pairs of mirror manifolds

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1992

OSTI ID:7161544

Parkes, L J

The consequences of mirror symmetry are explored through three examples: P[sub 4](5); [var epsilon], a manifold obtained by taking quotients of P[sub 4](5); and the Z manifold. The most important result is that string theories compactified on a Calabi-Yay manifold can be solved exactly by geometrical methods. Using mirror symmetry, the geometry of the moduli space of the Calabi-Yau manifold and its mirror is completely described. All sigma model corrections to the Yukawa couplings and to the moduli space metric for the original manifold are obtained. The moduli space of P[sub 4](5) is subject to the action of a modular group which exchanges large and small values of the radius, though the action on the radius is not as simple as R [r arrow] (1/R). The corrections to the cubic coupling of the single parameter of P[sub 4](5) decompose into a sum over instantons and that this sum converges. Using this sum the number of rational curves on P[sub 4](5) of any degree can be predicted. Many manifolds, such as [var epsilon], have more than one parameter, each of which might lead to a different large radius limit. Using [var epsilon] as an example, a method is demonstrated for generating a basis for the ideal of partial derivatives of the polynomial defining the Calabi-Yau manifold. This basis can be used to compute the Yukawa couplings. The modular group which acts on [var epsilon] could coincide. The familiar duality invariance of tori is valid on the smooth Z manifold and the modular parameters of the Z are a ratio of integral periods on the manifold. The construction of the mirror of the Z is confirmed by comparing the orbifold limit of the Yukawa couplings on the Z manifold to previous calculations of the Yukawa couplings on the Z[sub 3] orbifold. The methods presented go beyond orbifold calculations since they can be used to solve for arbitrary values of the blowing-up modes.

• Research Organization: Texas Univ., Austin, TX (United States)
• OSTI ID: 7161544
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPACTIFICATION
COMPLEX MANIFOLDS
COMPOSITE MODELS
EXTENDED PARTICLE MODEL
MATHEMATICAL MANIFOLDS
MATHEMATICAL MODELS
PARTICLE MODELS
QUARK MODEL
STRING MODELS
SUPERSTRING MODELS