Narrow Results

We observe and study new nonlinear global space–time symmetries of the full ghost + matter action of RNS superstring theory. We show that these surprising new symmetries are generated by the special worldsheet currents (physical vertex operators) of RNS superstring theory, violating the equivalence of superconformal ghost pictures. We review the questions of BRST-invariance and nontriviality of picture-dependent vertex operators and show their relation to hidden space–time symmetries and hidden space–time dimensions. In particular, we relate the space–time transformations, induced by picture-dependent currents, to the symmetries observed in the 2T physics approach.

All the BRST-invariant operators in pure spinor formalism in d = 10 can be represented as BRST commutators, such as where λ₊ is the U(5) component of the pure spinor transforming as . Therefore, in order to secure nontriviality of BRST cohomology in pure spinor string theory, one has to introduce "small Hilbert space" and "small operator algebra" for pure spinors, analogous to those existing in RNS formalism. As any invariant vertex operator in RNS string theory can also represented as a commutator V = {Q_brst, LV} where L = -4c∂ξξe^-2ϕ, we show that mapping to L leads to identification of the pure spinor variable λ^α in terms of RNS variables without any additional nonminimal fields. We construct the RNS operator satisfying all the properties of λ^α and show that the pure spinor BRST operator ∮λ^αd_α is mapped (up to similarity transformation) to the BRST operator of RNS theory under such a construction.