Editing String field theory (section)

===Modified cubic superstring field theory===
The first consistent extension of Witten's bosonic open string field theory to the RNS string was constructed by Christian Preitschopf, [[Charles Thorn]] and Scott Yost and independently by Irina Aref'eva, P. B. Medvedev and A. P. Zubarev.<ref>{{cite journal | last1=Preitschopf | first1=Christian R. | last2=Thorn | first2=Charles B. | last3=Yost | first3=Scott | title=Superstring field theory | journal=Nuclear Physics B | publisher=Elsevier BV | volume=337 | issue=2 | year=1990 | issn=0550-3213 | doi=10.1016/0550-3213(90)90276-j | bibcode=1990NuPhB.337..363P | pages=363–433| osti=7241635 | url=https://www.osti.gov/biblio/7241635 }}</ref><ref>{{cite journal | last1=Aref'eva | first1=I.Ya. | last2=Medvedev | first2=P.B. | last3=Zubarev | first3=A.P. | title=New representation for string field solves the consistency problem for open superstring field theory | journal=Nuclear Physics B | publisher=Elsevier BV | volume=341 | issue=2 | year=1990 | issn=0550-3213 | doi=10.1016/0550-3213(90)90189-k | bibcode=1990NuPhB.341..464A | pages=464–498}}</ref>  The NS string field is taken to be a ghostnumber one picture zero string field in the small Hilbert space (i.e. <math> \eta_0 |\Psi\rangle = 0 </math>). The action takes a very similar form to bosonic action,
:: <math> S(\Psi) = \tfrac{1}{2} \langle \Psi |Y(i) Y(-i) Q_B |\Psi \rangle
  +\tfrac{1}{3} \langle \Psi | Y(i) Y(-i) |\Psi * \Psi\rangle  \ ,</math>
where, 
:: <math> Y(z) = -\partial \xi e^{-2 \phi} c(z) </math>
is the inverse picture changing operator. The suggested <math> -\tfrac{1}{2} </math> picture number extension of this theory to the Ramond sector might be problematic.

This action has been shown to reproduce tree-level amplitudes and has a tachyon vacuum solution with the correct energy.<ref>{{cite journal | last=Erler | first=Theodore | title=Tachyon vacuum in cubic superstring field theory | journal=Journal of High Energy Physics | volume=2008 | issue=1 | date=2008-01-07 | issn=1029-8479 | doi=10.1088/1126-6708/2008/01/013 | pages=013|doi-access=free|arxiv=0707.4591| bibcode=2008JHEP...01..013E }}</ref> The one subtlety in the action is the insertion of picture changing operators at the midpoint, which imply that the linearized equations of motion take the form
:: <math> Y(i)Y(-i) Q_B \Psi = 0 \left.\right. \ .</math>
Because <math> Y(i) Y(-i) </math> has a non-trivial kernel, there are potentially extra solutions that are not in the cohomology of <math> Q_B </math>.<ref>N. Berkovits, "Review of open superstring field theory", hep-th/0105230</ref>  However, such solutions would have operator insertions near the midpoint and would be potentially singular, and importance of this problem remains unclear.