zbMATH — the first resource for mathematics

Vertex operators of ghost number three in Type IIB supergravity. (English) Zbl 1336.81074
Summary: We study the cohomology of the massless BRST complex of the Type IIB pure spinor superstring in flat space. In particular, we find that the cohomology at the ghost number three is nontrivial and transforms in the same representation of the supersymmetry algebra as the solutions of the linearized classical supergravity equations. Modulo some finite dimensional spaces, the ghost number three cohomology is the same as the ghost number two cohomology. We also comment on the difference between the naive and semi-relative cohomology, and the role of b-ghost.

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
17B69 Vertex operators; vertex operator algebras and related structures
81T70 Quantization in field theory; cohomological methods
83E50 Supergravity
PDF BibTeX Cite
Full Text: DOI
[1] Astashkevich, A.; Belopolsky, A., String center-of-mass operator and its effect on BRST cohomology, Commun. Math. Phys., 186, 109-136, (1997) · Zbl 0896.47054
[2] Nelson, P. C., Covariant insertion of general vertex operators, Phys. Rev. Lett., 62, 993, (1989)
[3] Mikhailov, A., Cornering the unphysical vertex, J. High Energy Phys., 082, (2012)
[4] Zwiebach, B., Closed string field theory: quantum action and the B-V master equation, Nucl. Phys. B, 390, 33-152, (1993)
[5] Lian, B. H.; Zuckerman, G. J., New perspectives on the BRST algebraic structure of string theory, Commun. Math. Phys., 154, 613-646, (1993) · Zbl 0780.17029
[6] Berkovits, N.; Howe, P. S., Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring, Nucl. Phys. B, 635, 75-105, (2002) · Zbl 0996.81075
[7] Chandia, O.; Mikhailov, A.; Vallilo, B. C., A construction of integrated vertex operator in the pure spinor sigma-model in \(A d S_5 \times S^5\), J. High Energy Phys., 1311, (2013)
[8] Bedoya, O. A.; Bevilaqua, L.; Mikhailov, A.; Rivelles, V. O., Notes on beta-deformations of the pure spinor superstring in \(A d S(5) \times S(5)\), Nucl. Phys. B, 848, 155-215, (2011) · Zbl 1215.81078
[9] Mikhailov, A., Pure spinors in AdS and Lie algebra cohomology, Lett. Math. Phys., 104, 1201-1233, (2014) · Zbl 1303.83042
[10] Jusinskas, R. L., On the field-antifield (a)symmetry of the pure spinor superstring · Zbl 1388.81844
[11] Berkovits, N.; Nekrasov, N., Multiloop superstring amplitudes from non-minimal pure spinor formalism, J. High Energy Phys., 0612, (2006) · Zbl 1226.81159
[12] Mikhailov, A., Symmetries of massless vertex operators in AdS(5) x S**5, J. Geom. Phys., (2011)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.