We study the transition between parallel and intersecting branes on a torus. Spontaneous symmetry breaking of nonabelian gauge symmetry is understood as brane separation, and a more general intermediate deformation is discussed. We argue that there exists supersymmetry preserving transition and we can always have parallel branes as a final state. The transition is interpreted due to dynamics of the F-and D-string junctions and their generalization to (F, Dp) bound states. The gauge group and coupling unification is achieved, also as a result of supersymmetry. From the tadpole cancelation condition, we naturally have some class of intersecting brane models as broken phases of Type I theory with SO(32) gauge group.
INTERSECTING BRANE WORLDWhen there are N sheets of coincident Dp-branes, the lowest lying degrees along the brane are U(N) gauge fields and a transverse fluctuation is described by a scalar field. Expanding Dirac-Born-Infeld (DBI) action to the quadratic order in α F MN , it reduces to (p+1)-dimensional Yang-Mills (YM) action with the YM cou-where T p and g s are the tension and Type II string coupling fixed by the vacuum expectation value (VEV) of dilaton.Location of branes X m is translated into gauge field A m in the T -dual spacewhere A m = ∑ A a m T a . The constant field can be always diagonalized by a suitable gauge transformation to X m = diag (a 1 , a 2 ,...,a N ).(2) From geometry, one can investigate the group structure. It corresponds to separation of branes located at x m = a 1 , a 2 ,...,a N . Depending on eigenvalues, it results in breaking U(N) down to U(N i ). It is understood as a Higgs mechanism of the adjoint Higgs X m and it is flat directions for any VEVs of a i .To have a realistic model, we need chiral fermions. They naturally emerge from intersecting branes [2]. When we have N a and N b coincident branes intersecting at angles, we obtain chiral fermions transforming as a bifundamental (N a , N b ) under U(N a ) × U(N b ), localized at the intersection. In a typical setup we have compact dimensions and each stack of branes wraps a different cycle, and we have intersections between brane stacks 1 Based on work done in collaboration with Jihn E. Kim [1]. in general. The same copy of intersections naturally explains the number of families and Yukawa couplings.The nonsupersymmetric intersecting brane models suffer the following problems. First, The four dimensional gauge couplings are different in general and it seems far from unification. From the dimensional reduction from the (p+1) dimensions to (3+1) dimensions the four dimensional coupling constant iswith V p−3 being the compact volume that each brane cycle wraps. Second, when we perform mode expansions of intersecting branes, we see that the lowest excitation is the tachyon for a generic angle θ between branes, m 2 = −θ /2πα with 0 ≤ θ ≤ π. For attempts of resolving this issues, see Refs. [3,4,5]. Consider the case where the branes wind on a compact torus T 2 , a parallelogram with sides L 1 and L 2 . We will use the winding vec...