Abstract
In this short paper we review basic ideas of string field theory with the emphasis on the recent developments. We show how without much technicalities one can look for analytic solutions to Witten’s open string field theory. This is an expanded version of a talk given by the author over the last year at a number of occasions1 and notably at the conference Selected Topics in Mathematical and Particle Physics in honor of Prof. JiˇrLi Niederle’s 70th birthday.
Highlights
In this short paper we review basic ideas of string field theory with the emphasis on the recent developments
String field theory is an attempt to turn string theory into some sort of field theory by writing a field theory action for each of the single string modes and combining them together with very particular interactions. Perturbative quantization of this field theory yields all of the perturbative string theory, and one might hope that one day we could get a truly nonperturbative description of the theory
One of the most interesting applications of string field theory to date has been in studies of the classical backgrounds of string theory
Summary
The traditional rules of first quantized string theory allow one to compute on-shell perturbative amplitudes, but they tell us little about collective phenomena or non-perturbative effects. For CFT’s related by exactly marginal deformations, the two theories may bear some resemblance, but for theories related by relevant deformations it is very hard to see how one background can be a solution of a theory formulated around another background This is in stark contrast to general relativity, where the Einstein-Hilbert action does not depend on any particular background, but it allows for solutions describing very different geometries. String field theory (SFT) goes half-way towards this goal It gives us a formulation which is background independent in form (not truly in essence) and which posseses a multitude of classical solutions representing different backgrounds. This seemingly academic question is important for distinguishing gauge trivial and non-trivial solutions
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