Berkovits, N., & Chandia, O. (2014). Simplified pure spinor b ghost in a curved heterotic superstring background. J. High Energy Phys., (6), 12 pp.
Abstract: Using the RNSlike fermionic vector variables introduced in arXiv:1305.0693, the pure spinor b ghost in a curved heterotic superstring background is easily constructed. This construction simplifies and completes the b ghost construction in a curved background of arXiv:1311.7012.

Chandia, O. (2014). The nonminimal heterotic pure spinor string in a curved background. J. High Energy Phys., (3), 16 pp.
Abstract: We study the nonminimal pure spinor string in a curved background. We find that the minimal BRST invariance implies the existence of a nontrivial stressenergy tensor for the minimal and nonminimal variables in the heterotic curved background. We find constraint equations for the b ghost. We construct the b ghost as a solution of these constraints.

Chandia, O., & Vallilo, B. C. (2015). C Ambitwistor pure spinor string in a type II supergravity background. J. High Energy Phys., (6), 15 pp.
Abstract: We construct the ambitwistor pure spinor string in a general type II supergravity background in the semiclassical regime. Almost all supergravity constraints are obtained from nilpotency of the BRST charge and further consistency conditions from additional worldsheet the case of AdS(5) x S (5) background.

Chandia, O., & Vallilo, B. C. (2015). Nonminimal fields of the pure spinor string in general curved backgrounds. J. High Energy Phys., (2), 16 pp.
Abstract: We study the coupling of the nonminimal ghost fields of the pure spinor superstring in general curved backgrounds. The coupling is found solving the consistency relations from the nilpotency of the nonminimal BRST charge.

Chandia, O., Bevilaqua, L. I., & Vallilo, B. C. (2014). AdS pure spinor superstring in constant backgrounds. J. High Energy Phys., (6), 16 pp.
Abstract: In this paper we study the pure spinor formulation of the superstring in AdS(5) x S5 around point particle solutions of the classical equations of motion. As a particular example we quantize the pure spinor string in the BMN background.

Chandia, O., Linch, W. D., & Vallilo, B. C. (2011). Compactification of the heterotic pure spinor superstring II. J. High Energy Phys., (10), 22 pp.
Abstract: We study compactifications of the heterotic pure spinor superstring to six and four dimensions focusing on two simple CalabiYau orbifolds. We show that the correct spectrum can be reproduced only if, in the twisted sector, there remain exactly 5 and 2 pure spinor components untwisted, respectively. This naturally defines a “small” Hilbert space of untwisted variables. We point out that the cohomology of the reduced differential on this small Hilbert space can be used to describe the states in the untwisted sector, provided certain auxiliary constraints are defined. In dimension six, the mismatch between the number of pure spinor components in the small Hilbert space and the number of components of a sixdimensional pure spinor is interpreted as providing the projective measure on the analytic subspace (in the projective description) of harmonic superspace.
