Abstract
Renormalisation group (RG) equations in two-dimensional $ \mathcal{N} = 1 $ supersymmetric field theories with boundary are studied. It is explained how a manifestly $ \mathcal{N} = 1 $ supersymmetric scheme can be chosen, and within this scheme the RG equations are determined to next-to-leading order. We also use these results to revisit the question of how brane obstructions and lines of marginal stability appear from a world-sheet perspective.
Highlights
Another phenomenon that has attracted a lot of attention recently [1,2,3] concerns lines of marginal stability: a supersymmetric brane may decay into a superposition of D-branes as the string background is modified
Among other things we identify the precise coupling constant which controls the bulk induced boundary Renormalisation group (RG) source term of [5], and we explain how the change in conformal dimension of a boundary field can be calculated [9] in this context
In our supersymmetric scheme the first order bulk induced boundary RG source term always vanishes for marginal boundary fields
Summary
After introducing some basic notation we will explain how one can write the perturbation in superspace in a manifestly supersymmetric manner
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