We construct a supersymmetric version of the critical nonrelativistic bosonic string theory [B. S. Kim, Phys. Rev. D 76, 106007 (2007).] with its manifest global symmetry. We introduce the anticommuting $bc$ conformal field theory (CFT) which is the super partner of the $\beta \gamma$ CFT. The conformal weights of the $b$ and $c$ fields are both $1/2$. The action of the fermionic sector can be transformed into that of the relativistic superstring theory. We explicitly quantize the theory with manifest $SO(8)$ symmetry and find that the spectrum is similar to that of type IIB superstring theory. There is one notable difference: the fermions are nonchiral. We further consider noncritical generalizations of the supersymmetric theory using the superspace formulation. There is an infinite range of possible string theories similar to the supercritical string theories. We comment on the connection between the critical nonrelativistic string theory and the lightlike linear dilaton theory.

• Received 22 October 2007

DOI:https://doi.org/10.1103/PhysRevD.76.126013