The action of long strings in supersymmetric field theories

Long strings emerge in many Quantum Field Theories, for example as vortices in Abelian Higgs theories, or flux tubes in Yang-Mills theories. The actions of such objects can be expanded in the number of derivatives, around a long straight string solution. This corresponds to the expansion of energy levels in powers of 1/L, with L the length of the string. Doing so reveals that the first few terms in the expansions are universal, and only from a certain term do they become dependent on the originating field theory. Such classifications have been made before for bosonic strings. In this work we expand upon that and classify also strings with fermionic degrees of freedom, where the string breaks D=4 N=1 SUSY completely. An example is the confining string in N=1 SYM theory. We find a general method for generating supersymmetric action terms from their bosonic counterparts, as well as new fermionic terms which do not exist in the non-supersymmetric case. These terms lead to energy corrections at a lower order in 1/L than in the bosonic case.