Stringy Things

# Pure Spinor Formalism

In recent days, pure spinors have become my life. And that is by no means a bad thing.

I don’t want to divulge too much at this time. The short of it is that I’ve been looking into the pure spinor formalism for a possible research project. Whether the project comes to fruition or not has yet to be determined. Regardless of the outcome, the time will have been well spent as I’ve immensely enjoyed learning the topic. What is intriguing is the power of the formalism when studying superstrings on different curved backgrounds. It is also useful when studying multiloop amplitudes. More personally, I have also found it nice to work through and think about because there is some connection with my interests in twistor theory, among other things.

As it is quite a rich area, there is a lot to comment on. Given time, I will type and upload my own notes as a sort of tour through the formalism. For now I’ve put together a select list of preprint papers that give an overview, organised by date. I haven’t listed everything, and the reader may find other works that adequately study pure spinors. For me, I found it useful to simultaneously read [2, 3, 6] as review, having then marched on from there.

[1] N. Berkovits, ‘Super-Poincare Covariant Quantization of the Superstring’, (2000) preprint in arXiv [arXiv:hep-th/0001035 [hep-th]].

[2] N. Berkovits, ‘ICTP Lectures on Covariant Quantization of the Superstring’ [lecture notes], (2002) preprint in arXiv [arXiv:hep-th/0209059 [hep-th]].

[3] N. Berkovits and D. Z. Marchioro, ‘Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring’, (2004) preprint in arXiv [arXiv:hep-th/0412198 [hep-th]].

[4] N.I. Farahat and H.A. Elegla, ‘Path Integral Quantization of Brink-Schwarz Superparticle’, EJTP 5, No. 19 (2008) 57–64.

[5] C.R. Mafra, ‘Superstring Scattering Amplitudes with the Pure Spinor Formalism’, (2008) preprint in arXiv [arXiv:0902.1552v3 [hep-th]].

[6] O. A. Bedoya and N. Berkovits, ‘GGI Lectures on the Pure Spinor Formalism of the Superstring’, (2009) preprint in arXiv [arXiv:0910.2254v1 [hep-th]].

[7] T. Adamo and E. Casali,’Scattering equations, supergravity integrands, and pure spinors’, (2015) preprint in arXiv [arXiv:1502.06826v2 [hep-th]].

[8] N. Berkovits, ‘Untwisting the Pure Spinor Formalism to the RNS and Twistor String in a Flat and $AdS_5 \times S^5$ Background’, (2015) preprint in arXiv [arXiv:1604.04617v2 [hep-th]].

[9] N. Berkovits, ‘Origin of the Pure Spinor and Green-Schwarz Formalisms’, (2015) preprint in arXiv [arXiv:1503.03080 [hep-th]]

*Image: A 2005 poster by the IHES promoting a pure spinor workshop.

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