Classical solutions of open string field theory. Martin Schnabl Institute of Physics, Prague Academy of Sciences of the Czech Republic. ICHEP, July 22, 2010. What is String Field Theory?. Field theoretic description of all excitations of a string (open or closed) at once.
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Institute of Physics, Prague
Academy of Sciences of the Czech Republic
ICHEP, July 22, 2010
Open string field theory uses the following data
Let all the string degrees of freedom be assembled in
Witten (1986) proposed the following action
This action has a huge gauge symmetry
provided that the star product is associative, QB acts as a
graded derivation and < . > has properties of integration.
Note that there is a gauge symmetry for gauge symmetry
so one expects infinite tower of ghosts – indeed they can
be naturally incorporated by lifting the ghost number
restriction on the string field.
We have just seen that the star product obeys
And therefore states obeyThe star product and operator multiplication are thus isomorphic!
This new understanding lets us construct solutions to OSFT equations of motion easily.
More general solutions are of the form
Here F=F(K) is arbitraryM.S. 2005, Okawa, Erler 2006
… trivial solution
…. ‘tachyon vacuum’ only c and K turned on
…. M.S. ‘05
… Erler, M.S. ’09 – the simplest solution so far
The basic ingredient is the correlator
Now insert the identity in the form
And after some human-aided computer algebra
we find very simple expression
On the second line we have a total derivative which does
not contribute. For a function of the form
To get further support let us look at the Ellwood invariant(or Hashimoto-Itzhaki-Gaiotto-Rastelli-Sen-Zwiebach invariant) . Ellwood proposed that for general OSFT solutions it would obeylet us calculate the LHS:For we find !