In this paper we study the parallel phase and the coincident phase of D-brane systems with the compactification of one closed modulus. D-brane systems with two phases are described by different 4-folds in terms of Ty...
Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is rea...
We study four-dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K¨ahler structure.Using intersecting complex toric surfaces,we derive a class of N =1 quivers with charged fundamental ...
A certain class K of GR homogeneous spacetimes is considered. For each pair E, ?of spacetimes from K, ?where conformal transformation g is from . Each E (being ?or its double cover, as a manifold) is interpreted as re...
We calculate the D-brane superpotentials for two compact Calabi-Yau manifolds X14(1,1,2,3,7) and Xs (1,1,1,2,3) which are of non-Fermat type in the type II string theory. By constructing the open mirror symmetry, ...
Contractions of the Lie algebras d = u(2), f = u(1 ,1) to the oscillator Lie algebra l are realized via the adjoint action of SU(2,2) when d, l, f are viewed as subalgebras of su(2,2). Here D, L, F are the correspondi...
The geometrical description of BPS 3-string junction in the F-theory background is given by lifting a string junction in lib into F-theory and constructing a holomorphic curve in K3 with respect to a special complex s...