UNITARITY FOR THE BOSONIC NAPPI–WITTEN STRING FROM BRST VIEW

Abstract

In this paper, we present the proof of a no-ghost theorem for the bosonic string in Nappi–Witten spacetime by the BRST-technology. The key point in this proof is to compare the characters with the signature functions, where traces are taken over the whole state space. It includes the states of Nappi–Witten string, the states of some extra unitary CFT and the conformal ghost states. Only the signature function of the Nappi–Witten string part is not trivial. Here we obtain it in a new complete basis for the states space of Nappi–Witten string. For all real number b, which is a parameter of the Nappi–Witten metric, the characters and the signature functions are exactly equivalent. Then we can state that the physical string states in Nappi–Witten group are all of non-negative norm.