Mitsuko Abe

Loop corrections to the heterotic string effective lagrangian

Abstract We derive string-loop corrections (torus topology) to the quartic curvature term in the low-energy effective lagrangian for the heterotic string theory. The one-loop correction is found to give the relative weight of two tensor structures different from the tree level.

Coupling Constant Relations and Effective Lagrangian in the Type I Superstring

On determine explicitement la relation entre les parametres du developpement en boucles g op pour des cordes ouvertes et g cl pour des cordes fermees dans la supercorde de type I a groupe de jauge SO(N)

Gravitational instantons and moduli spaces in topological two-form gravity.

A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual 2-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of conformally self-dual Einstein manifolds for the non-zero cosmological constant case and Einstein-Kahlerian manifold with the vanishing real first Chern class for the zero cosmological constant. In the non-zero cosmological constant case, we evaluate the index of the elliptic complex associated with the moduli space and calculate the partition function. We also clarify the moduli space and its dimension for the zero cosmological constant case which are related to the Plebanskys heavenly equations.

MODULI SPACE OF TOPOLOGICAL TWO-FORM GRAVITY

We propose a topological version of four-dimensional (Euclidean) Einstein gravity, in which anti-self-dual two-forms and an SU(2) connection are used as fundamental fields. The theory describes the moduli space of conformally self-dual Einstein manifolds. In the presence of a cosmological constant, we evaluate the index of the elliptic complex associated with the moduli space.

Puzzles on the duality between heterotic and type IIA strings

Abstract We discuss the possibility of the extension of the duality between the webs of heterotic string and the type IIA string to Calabi-Yau three-folds with another K3 fiber by comparing the dual polyhedron of Calabi-Yau three-folds given by Candelas, Perevalov and Rajesh.

Calabi-Yau manifolds by Borcea-Voisin method

We construct Calabi-Yau manifolds and their mirrors from K3 surfaces. This method was first developed by Borcea and Voisin. We examined their properties torically and checked mirror symmetry for the Calabi-Yau four-fold case. From Borcea-Voisin three-fold or four-fold examples, it may be possible to probe the S-duality of Seiberg-Witten.

MODULI SPACES IN THE FOUR-DIMENSIONAL TOPOLOGICAL HALF-FLAT GRAVITY

We classify the moduli spaces of the four-dimensional topological half-flat gravity models by using the canonical bundle. For a K3-surface or T4, they describe an equivalent class of a trio of the Einstein-Kahler forms (the hyperkahler forms). We calculate the dimensions of these moduli spaces by using the Atiyah-Singer Index theorem. We mention the partition function and the possibility of the observables in the Witten-type topological half-flat gravity model case.

The Partition Function in the Four-Dimensional Schwarz-Type Topological Half-Flat Two-Form Gravity

We derive the partition functions of the Schwarz-type four-dimensional topological half-flat two-form gravity model on K3-surface or T4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class of a trio of the Einstein–Kahler forms (the hyper-Kahler forms). The integrand of the partition function is represented by the product of some -torsions. -torsion is the extension of R-torsion for the de Rham complex to that for the -complex of a complex analytic manifold.

STRING-LOOP CORRECTION TO CALABI-YAU COMPACTIFICATION

String loop (torus) effect on the Calabi-Yau solutions is examined. In spite of different kinematical structure of one-loop effective Lagrangian, the loop-corrected solution still has vanishing first Chern class though it is not Ricci-flat. This shows the perturbative stability of the Calabi-Yau solution even including one-loop (torus) effects.