Gauge-invariant field theory of the Ramond string

Over the past two years bosonic string field theory has become fairly well understood. By defining a string functional Φ that depends on the first-quantized ghosts, one is lead to a field equation Q Φ = 0 (based on the BRST physical state condition) and an action ∫ Φ Q Φ. In this paper, after reviewing the bosonic case, this procedure is applied to the Ramond string. A new feature of the first-quantized Ramond theory is the presence of commuting ghost zero modes that cause an infinite degeneracy in the BRST ground state. Once a suitable inner product is defined in this sector, it is found that the canonical action above cannot work, but a modified version ∫ΦGQΦ is gauge-invariant and yields the correct equations of motion for a carefully chosen operator G. This form is then compared to a Ramond action found by Witten, which has similar features but is defined using bosonized ghosts. A possible mapping between the two formalisms is suggested