Domain Walls Zoo in Supersymmetric QCD
A. V. Smilga, A. I. Veselov
TL;DR
This work maps the spectrum of domain walls in SU(2) supersymmetric QCD using the TVY effective Lagrangian, focusing on complex walls connecting chirally asymmetric vacua and their fate as the quark-mass parameter $m$ varies. By solving both BPS first-order equations and full second-order equations, the authors identify two BPS branches (upper and lower) existing for $m\le m_*$ and two non-BPS sphaleron branches that merge with the BPS branches at $m_*$ and $m_{**}\approx 4.83$, beyond which no complex wall solutions remain; in the large-$m$ limit only real walls between asymmetric and symmetric vacua survive. They show how the wall structure tightens into a minimal, nearly marginally stable spectrum as $m\to m_*$ and $m\to m_{**}$, and discuss the role of the gluino condensate $\Sigma$ in scaling the critical masses. The results illuminate the nonperturbative vacuum landscape of SUSY QCD, the existence of a chirally symmetric phase, and the subtle interplay between wall stability, topology, and effective field theory descriptions in the infinite-volume limit.
Abstract
Solving numerically the equations of motion for the effective lagrangian describing supersymmetric QCD with the SU(2) gauge group, we find a menagerie of complex domain wall solutions connecting different chirally asymmetric vacua. Some of these solutions are BPS saturated walls; they exist when the mass of the matter fields does not exceed some critical value m < m* < 4.67059... There are also sphaleron branches (saddle points of the ebergy functional). In the range m* < m < m** \approx 4.83, one of these branches becomes a local minimum (which is not a BPS saturated one). At m > m*, the complex walls disappear altogether and only the walls connecting a chirally asymmetric vacuum with the chirally symmetric one survive.