The Holomorphic Tension of Vortices

We study the tension of vortices in N=2 SQCD broken to N=1 by asuperpotential W(\Phi), in color-flavor locked vacua. The tension can bewritten as T = T_{BPS} + T_{non BPS}. The BPS tension is equal to 4\pi|\T|where we call \T the holomorphic tension. This is directly related to thecentral charge of the supersymmetry algebra. Using the tools of theCachazo-Douglas-Seiberg-Witten solution we compute the holomorphic tension as aholomorphic function of the couplings, the mass and the dynamical scale: \T =\sqrt{W'^2+f}. A first approximation is given using the generalized Konishianomaly in the semiclassical limit. The full quantum corrections are computedin the strong coupling regime using the factorization equations that relate theN=2 curve to the N=1 curve. Finally we study the limit in which the non-BPScontribution can be neglected because small with respect to the BPS one. In thecase of linear superpotential the non-BPS contribution vanishes exactly and theholomorphic tension gets no quantum corrections.Comment: 32 pages, 2 figures. v2: typos corrected and references added. v3: Minor changes, accepted on JHEP. v4: Added a note on the non-BPS correction in the strong coupling regim