Aspects of superstring compactification on (2,2) vacua
Compactification form ten to four dimensions for the point field limit of the type IIA and IIB superstring theories is investigated. Initially an SU(3) invariant reduction of the type IIB supergravity theory is performed and compared to a similar reduction of the type IIA theory to give an explicit realization of the c map. In general this c map relates the low-energy Lagrangians of the type II superstrings when compactified on the same (2,2) superconformal theory. The compactification on a general Calabi-Yau background for the type IIA and IIB supergravity is then performed. In this process the exact effective Lagrangian for (2,1) complex structure deformations in type II superstrings is obtained using techniques of algebraic geometry. By investigating the compactification of the vector sectors it is found that the transformation of the real cohomology basis of Calabi-Yau space is intimately related to the transformations that generalize the duality relations of electromagnetism. It is also found that Calabi-Yau spaces have a super extension due to their relation to type II superstrings. Another interesting result is that the H{sup (0,0)} + H{sup (3,3)} cohomology corresponds to the graviphoton and its dual in the type IIA theory just as the H{sup (3,0)} + H{sup (3,3)} is related to the graviphoton in the type IIB theory. Similarly the matter vector multiplets field strength and their dual correspond in the type IIB theory to the H{sup (2,1)} + H{sup (1,2)} cohomology and the H{sup (1,1)} + H{sup (2,2)} in the type IIA theory. This allows the using a geometrical argument of formal developments dealing with the mirror symmetry of Calabi-Yau moduli space. Finally in the type IIA compactification, for the Kaehler and quaternionic manifolds obtained it is found in both cases that the scalar manifolds are characterized by a homogeneous holomorphic function is a cubic polynomial, a result which is valid only in the classical large volume limit of the internal manifold.
- Research Organization:
- California Univ., Los Angeles, CA (United States)
- OSTI ID:
- 121174
- Country of Publication:
- United States
- Language:
- English
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