Metastable vacua and complex deformations

Abstract

We use the non-normalizable complex deformations to describe the stringy realizations of the metastable vacua in N = 1, SU (N c ) SUSY theories with N f > N c massive fundamental flavors. The consideration of the non-normalizable deformations requires a modified Toric duality. The new approach considers the tachyon condensation between pairs of wrapped D5 branes and anti D5 branes and the resulting mixing between some cycles in the geometry. We enlarge the class of metastable vacua to the case of branes-antibranes wrapped on cycles of deformed A n singularities.

SQCD Vacua and Geometrical Engineering

“…The Seiberg duality is a flop in the geometry and the dynamics of branes is related to a tachyon condensation between D5 branes and anti D5 branes [9]. In the present discussion the tachyon condensation explains the ranks of the groups in the magnetic theory but also determine a reorientation of the cycle such they remain holomorphic in the magnetic theory.…”

“…As discussed in [9], in the magnetic theory there is tachyon instability between N c anti D5 branes wrapped on the C 2 cycle and N f D5 branes wrapped on a C 5 = C 2 + C 4 cycle. Because the cycles are fixed by the rigidity of their normal bundles, the only way to have In the brane configuration picture, the main obstacle against a redistribution of D-branes on holomorphic cycles is the fact that the ends of D4 branes on the v NS brane can touch each other whereas the other ends cannot because they are stuck on parallel NS branes.…”

“…As discussed in detail in [9], the deformation of N = 2 geometries give rise to N = 1 geometries with normalizable and non-normalizable deformations. The normalizable deformations are the ones which can go through a geometric transition to study strong coupling effects in the field theory on the wrapped D5 branes.…”

“…In [9] we saw that the mismatch of the non-normalizable deformations could be used as an explanation why the ISS solution cannot be constructed with D5 branes wrapped on holomorphic cycles. This was due to the fact that in the electric picture one has two masses for the adjoint fields whereas in the magnetic picture one has mass only for one adjoint fields.…”

“…To get the ISS model, in [9] we considered the case θ = π 2 in which case the branes v θ and w are parallel in the direction w. Their displacement in the v direction is the mass of the quarks in the electric theory. In the geometrical engineering, the interval between the v θ and v NS branes becomes a P 1 cycle denoted C 1 , the interval between the v and w NS branes becomes a P 1 cycle denoted C 2 and the interval between the v θ and w NS branes becomes a…”