Abstract
We provide the covariant superspace equations that are sufficient to determine the complete θ expansion of the vertex operator of the open string massive states with (mass)2 = 1/α′ in pure spinor formalism of superstring theory. These equations get rid of the redundant degrees of freedom in superfields and are consistent with the BRST conditions derived in [1]. Further, we give the explicit θ expansion of the superfields appearing in the unintegrated vertex to O(θ3). Finally, we compute the contribution to a 3-point tree amplitude with the resulting vertex operator upto O(θ3) and find its kinematic structure to be identical to the corresponding RNS computation.
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References
N. Berkovits and O. Chandía, Massive superstring vertex operator in D = 10 superspace, JHEP 08 (2002) 040 [hep-th/0204121] [INSPIRE].
M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory, Volume 1, Cambridge University Press (1987).
N. Berkovits, Super Poincaré covariant quantization of the superstring, JHEP 04 (2000) 018 [hep-th/0001035] [INSPIRE].
N. Berkovits, Pure spinor formalism as an N = 2 topological string, JHEP 10 (2005) 089 [hep-th/0509120] [INSPIRE].
N. Berkovits, ICTP lectures on covariant quantization of the superstring, ICTP Lect. Notes Ser. 13 (2003) 57 [hep-th/0209059] [INSPIRE].
O.A. Bedoya and N. Berkovits, GGI Lectures on the Pure Spinor Formalism of the Superstring, arXiv:0910.2254 [INSPIRE].
C.R. Mafra, Superstring Scattering Amplitudes with the Pure Spinor Formalism, arXiv:0902.1552 [INSPIRE].
O. Schlotterer, Scattering amplitudes in open superstring theory, Ph.D. Thesis, Munich University, Germany (2011).
J. Hoogeveen, Fundamentals of the Pure Spinor Formalism, Amsterdam University Press, Amsterdam, The Netherlands (2010).
N. Berkovits and N. Nekrasov, Multiloop superstring amplitudes from non-minimal pure spinor formalism, JHEP 12 (2006) 029 [hep-th/0609012] [INSPIRE].
N. Berkovits, Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring, JHEP 09 (2004) 047 [hep-th/0406055] [INSPIRE].
N. Berkovits and B.C. Vallilo, Consistency of superPoincaré covariant superstring tree amplitudes, JHEP 07 (2000) 015 [hep-th/0004171] [INSPIRE].
N. Berkovits, Super-Poincaré covariant two-loop superstring amplitudes, JHEP 01 (2006) 005 [hep-th/0503197] [INSPIRE].
N. Berkovits and C.R. Mafra, Some Superstring Amplitude Computations with the Non-Minimal Pure Spinor Formalism, JHEP 11 (2006) 079 [hep-th/0607187] [INSPIRE].
N. Berkovits, Cohomology in the pure spinor formalism for the superstring, JHEP 09 (2000) 046 [hep-th/0006003] [INSPIRE].
N. Berkovits, Relating the RNS and pure spinor formalisms for the superstring, JHEP 08 (2001) 026 [hep-th/0104247] [INSPIRE].
N. Berkovits and D.Z. Marchioro, Relating the Green-Schwarz and pure spinor formalisms for the superstring, JHEP 01 (2005) 018 [hep-th/0412198] [INSPIRE].
N. Berkovits and C.R. Mafra, Equivalence of two-loop superstring amplitudes in the pure spinor and RNS formalisms, Phys. Rev. Lett. 96 (2006) 011602 [hep-th/0509234] [INSPIRE].
P.A. Grassi and P. Vanhove, Higher-loop amplitudes in the non-minimal pure spinor formalism, JHEP 05 (2009) 089 [arXiv:0903.3903] [INSPIRE].
P.A. Grassi and J.F. Morales Morera, Partition functions of pure spinors, Nucl. Phys. B 751 (2006) 53 [hep-th/0510215] [INSPIRE].
P.A. Grassi, G. Policastro and P. van Nieuwenhuizen, On the BRST Cohomology of Superstrings with/without Pure Spinors, Adv. Theor. Math. Phys. 7 (2003) 499 [hep-th/0206216] [INSPIRE].
P.A. Grassi and L. Tamassia, Vertex operators for closed superstrings, JHEP 07 (2004) 071 [hep-th/0405072] [INSPIRE].
J.P. Harnad and S. Shnider, Constraints and field equations for ten-dimensional super Yang-Mills theory, Commun. Math. Phys. 106 (1986) 183 [INSPIRE].
H. Ooguri, J. Rahmfeld, H. Robins and J. Tannenhauser, Holography in superspace, JHEP 07 (2000) 045 [hep-th/0007104] [INSPIRE].
G. Policastro and D. Tsimpis, R 4 purified, Class. Quant. Grav. 23 (2006) 4753 [hep-th/0603165] [INSPIRE].
I.Y. Park, Scattering of massive open strings in pure spinor, Nucl. Phys. B 852 (2011) 287 [arXiv:1101.1204] [INSPIRE].
U. Gran, GAMMA: A Mathematica package for performing gamma matrix algebra and Fierz transformations in arbitrary dimensions, hep-th/0105086 [INSPIRE].
S. Guttenberg, Superstrings in General Backgrounds, arXiv:0807.4968 [INSPIRE].
S. Chakrabarti, S.P. Kashyap and M. Verma, Construction of integrated vertex for massive states in pure spinor, work in progress.
S. Chakrabarti, S.P. Kashyap and M. Verma, Some amplitudes involving massive states in pure spinor, in preparation.
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ArXiv ePrint: 1706.01196
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Chakrabarti, S., Kashyap, S.P. & Verma, M. Theta expansion of first massive vertex operator in pure spinor. J. High Energ. Phys. 2018, 19 (2018). https://doi.org/10.1007/JHEP01(2018)019
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DOI: https://doi.org/10.1007/JHEP01(2018)019