SUPERSTRING PROPAGATION THROUGH SUPERGRAVITATIONAL SHOCKWAVES

In all previous works on strings (and superstrings) in curved space-times, explicit calculations were performed only in purely bosonic gravitational backgrounds. Here, we propose to introduce a background containing also fermionic degrees of freedom, solution of the N = 1 supergravity equations in D dimensions. We find an explicit N = 1 linearized supergravity shockwave solution giving the spin-3/2 Rarita-Schwinger field, and an exact (full non-linear) gravitational shockwave bosonic part. We study a Green-Schwarz superstring propagating in such a supergravity background. We write and solve the superstring equations. Contrarily to the purely bosonic shockwave case (in which spinor-string propagation is free), spinor-string coordinates couple here non-trivially to the transverse bosonic coordinates through the fermionic background. We find that outgoing fermionic-modes are mixed with ingoing bosonic (and fermionic) modes. This leads to a new feature of particle transmutation between bosons and fermions, described by the superstring ground states (and also by the excited states). The presence of the bosonic-fermionic background provides in string theory a natural physical mechanism to transform bosons into fermions (and vice versa).