Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring

By N. Berkovits, P. Howe. 2001

223 citations recorded by the source corpus.

Abstract It has recently been shown that the ten-dimensional superstring can be quantized using the BRST operator Q =∮ λ α d α , where λ α is a pure spinor satisfying λγ m λ =0 and d α is the fermionic supersymmetric derivative. In this paper, the pure spinor version of superstring theory is formulated in a curved supergravity background and it is shown that nilpotency and holomorphicity of the pure spinor BRST operator imply the on-shell superspace constraints of the supergravity background. This is shown to lowest order in α ′ for the heterotic and Type II superstrings, thus providing a compact pure spinor version of the ten-dimensional superspace constraints for N =1 Type IIA and Type IIB supergravities. Since quantization is straightforward using the pure spinor version of the superstring, it is expected that these methods can also be used to compute higher-order α ′ corrections to the ten-dimensional superspace constraints.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9e9d8240757d80bbfb500a393a129ee9a2d969c6

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In Nuclear and High Energy Physics

1. A. Tseytlin
2. J. Maldacena
3. N. Beisert
4. S. Frolov
5. J. Boer
6. R. Roiban
7. L. Wulff
8. E. Witten

In Statistical and Nonlinear Physics

1. A. Tseytlin
2. J. Maldacena
3. L. Wulff
4. J. Boer
5. N. Berkovits
6. R. Myers
7. D. Harlow
8. S. Raju

Citations in the corpus

• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations (2016, background): “(4)More recently [5] it was shown that (classical) BRST invariance of the pure spinor superstring [6] (which may be viewed as an analog of kappa-symmetry in this formulation) implies the basic type I and type II constraints.”
• ICTP Lectures on Covariant Quantization of the Superstring (2002, methodology): “As was shown with Paul Howe in [25], classical BRST invariance of this action implies the Type II supergravity equations and quantum BRST invariance is expected to imply α ′ corrections to these equations.”
• An Introduction to Clifford Algebras and Spinors (2016, background): “In particular, the constraints in ten dimensions play an important role in Berkovits’s approach to superstrings (Berkovits and Howe, 2002; Berkovits, 2004).”
• Non-commutative superspace from string theory (2003, background): “The field equations appear as a set of equations for a set of superfields (see also [19]) which are the entries of the following matrix:”
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection (2008, methodology): “Furthermore, it was shown in [24] that BRST invariance of the sigma model implies the superspace torsion constraints T a αβ = i f a b γ b αβ, T a α̂β̂ = i f̂ b γ b α̂β̂ , (2.”