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., & Vallilo, B. C. (2016). Onshell type II supergravity from the ambitwistor pure spinor string. Class. Quantum Gravity, 33(18), 9 pp.
Abstract: We obtain all the type II supergravity constraints in the pure spinor ambitwistor string by imposing consistency of local worldsheet gauge symmetries.

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.

Donnay, L., Giribet, G., González, H., Puhm, A., & Rojas, F. (2023). Celestial open strings at oneloop. J. High Energy Phys., (10), 47.
Abstract: We study celestial amplitudes in string theory at oneloop. Celestial amplitudes describe scattering processes of boost eigenstates and relate to amplitudes in the more standard basis of momentum eigenstates through a Mellin transform. They are thus sensitive to both the ultraviolet and the infrared, which raises the question of how to appropriately take the field theory limit of string amplitudes in the celestial basis. We address this problem in the context of fourdimensional genusone scattering processes of gluons in open string theory which reach the twodimensional celestial sphere at null infinity. We show that the Mellin transform commutes with the adequate limit in the worldsheet moduli space and reproduces the celestial oneloop field theory amplitude expressed in the worldline formalism. The dependence on alpha ' continues to be a simple overall factor in oneloop celestial amplitudes albeit with a power that is shifted with respect to treelevel, thus making manifest that the dimensionless parameter g102/alpha ' 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$$ {g}_{10}<^>2/{\alpha}<^>{\prime 3} $$\end{document} organizes the loop expansion in the celestial basis. The precise way in which the amplitudes scale with this parameter depends on the number of noncompact dimensions in such a way that in 4 dimensions the scaling with alpha ' does agree with that at treelevel.
