The Holomorphic Tension of Vortices

TL;DR

This paper investigates the holomorphic tension of vortices in N=2 SQCD broken to N=1, deriving a formula for the tension as a holomorphic function of parameters and analyzing quantum corrections in various regimes.

Contribution

It provides a detailed computation of the holomorphic tension using the Cachazo-Douglas-Seiberg-Witten solution and explores quantum effects in different coupling regimes.

Findings

Holomorphic tension expressed as T = sqrt(W'^2 + f)

Quantum corrections computed via factorization equations

Non-BPS contributions vanish for linear superpotentials

Abstract

We study the tension of vortices in N=2 SQCD broken to N=1 by a superpotential W(\Phi), in color-flavor locked vacua. The tension can be written 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 the central charge of the supersymmetry algebra. Using the tools of the Cachazo-Douglas-Seiberg-Witten solution we compute the holomorphic tension as a holomorphic function of the couplings, the mass and the dynamical scale: \T = \sqrt{W'^2+f}. A first approximation is given using the generalized Konishi anomaly in the semiclassical limit. The full quantum corrections are computed in the strong coupling regime using the factorization equations that relate the N=2 curve to the N=1 curve. Finally we study the limit in which the non-BPS contribution can be neglected because small with respect to the BPS one. In the case of linear superpotential the non-BPS contribution vanishes exactly and the holomorphic tension gets no quantum corrections.