Editing String field theory (section)

===Berkovits superstring field theory===
A very different supersymmetric action for the open string was constructed by Nathan Berkovits.  It takes the form<ref>{{cite journal | last=Berkovits | first=Nathan | title=Super-Poincaré invariant superstring field theory | journal=Nuclear Physics B | publisher=Elsevier BV | volume=450 | issue=1–2 | year=1995 | issn=0550-3213 | doi=10.1016/0550-3213(95)00259-u | pages=90–102|arxiv=hep-th/9503099| bibcode=1995NuPhB.450...90B | s2cid=14495743 }}</ref>
:: <math>
  S = \tfrac{1}{2} \langle e^{-\Phi} Q_B e^{\Phi} | e^{-\Phi} \eta_0 e^{\Phi} \rangle
 - \tfrac{1}{2} \int_0^1 dt\langle e^{ -\hat{\Phi}} \partial_t e^{\hat{\Phi}}|\{e^{-\hat{\Phi}} Q_B
e^{\hat{\Phi}} , e^{-\hat{\Phi}} \eta_0 e^{\hat{\Phi}} \} \rangle
</math>
where all of the products are performed using the <math>*</math>-product including the anticommutator <math> \{,\} </math>, and <math>\hat{\Phi}(t) </math> is any string field such that <math> \hat{\Phi}(0)  = 0</math> and <math> \hat{\Phi}(1)  = \Phi</math>.  The string field <math> \Phi </math> is taken to be in the NS sector of the large Hilbert space, i.e. ''including'' the zero mode of <math> \xi </math>.  It is not known how to incorporate the R sector, although some preliminary ideas exist.<ref>{{cite journal | last=Michishita | first=Yoji | title=A Covariant Action with a Constraint and Feynman Rules for Fermions in Open Superstring Field Theory | journal=Journal of High Energy Physics | volume=2005 | issue=1 | date=2005-01-07 | issn=1029-8479 | doi=10.1088/1126-6708/2005/01/012 | pages=012|arxiv=hep-th/0412215| bibcode=2005JHEP...01..012M |doi-access=free}}</ref>

The equations of motion take the form
::<math> \eta_0 \left(e^{-\Phi} Q_B e^{\Phi} \right) = 0 .</math>

The action is invariant under the gauge transformation
:: <math> e^{\Phi} \to e^{Q_B \Lambda} e^{\Phi} e^{\eta_0 \Lambda'} .</math>

The principal advantage of this action is that it free from any insertions of picture-changing operators.  It has been shown to reproduce correctly tree level amplitudes<ref>{{cite journal | last1=Berkovits | first1=Nathan | last2=Echevarria | first2=Carlos Tello | title=Four-point amplitude from open superstring field theory | journal=Physics Letters B | publisher=Elsevier BV | volume=478 | issue=1–3 | year=2000 | issn=0370-2693 | doi=10.1016/s0370-2693(00)00246-x | pages=343–350|arxiv=hep-th/9912120| bibcode=2000PhLB..478..343B | s2cid=17003177 }}</ref> and has been found, numerically, to have a tachyon vacuum with appropriate energy.<ref>{{cite journal | last=Berkovits | first=Nathan | title=The tachyon potential in open Neveu-Schwarz string field theory | journal=Journal of High Energy Physics | volume=2000 | issue=4 | date=2000-04-19 | issn=1029-8479 | doi=10.1088/1126-6708/2000/04/022 | pages=022|doi-access=free|arxiv=hep-th/0001084| bibcode=2000JHEP...04..022B }}</ref><ref>{{cite journal | last1=Berkovits | first1=Nathan | last2=Sen | first2=Ashoke | last3=Zwiebach | first3=Barton | title=Tachyon condensation in superstring field theory | journal=Nuclear Physics B | volume=587 | issue=1–3 | year=2000 | issn=0550-3213 | doi=10.1016/s0550-3213(00)00501-0 | pages=147–178| arxiv=hep-th/0002211 | bibcode=2000NuPhB.587..147B | s2cid=11853254 }}</ref>  The known analytic solutions to the classical equations of motion include the tachyon vacuum<ref>{{cite journal | last=Erler | first=Theodore | title=Analytic solution for tachyon condensation in Berkovits' open superstring field theory | journal=Journal of High Energy Physics | volume=2013 | issue=11 | year=2013 | issn=1029-8479 | doi=10.1007/jhep11(2013)007 | page=7|arxiv=1308.4400| bibcode=2013JHEP...11..007E | s2cid=119114830 }}</ref> and marginal deformations.