On N = 1 superconformal algebra in the non-critical bosonic string theory

Abstract

In a recent work it has been shown that the bosonic strings could be embedded into a special class of N = 1 fermionic strings. We argue that the superpartners of any physical state in the spectrum of this fermionic string are non-physical. So, there is no supersymmetry in the space of physical states and the embedding is, in this sense, “trivial”. We here propose two different constructions as possible candidates of non-trivial embeddings of the non-critical bosonic strings into some special class of N = 1 fermionic strings of which one is the non-critical NSR string. The BRST charge of the N = 1 fermionic strings in both cases decomposes as Q N=1 = Q B + Q ̃ , where Q B is the BRST charge of the bosonic string.