Abstract
We propose a transformation between the off-shell field variables of Witten’s open bosonic string field theory and the traditional lightcone string field theory of Kaku and Kikkawa, based on Mandelstam’s interacting string picture. This is accomplished by deforming the Witten vertex into lightcone cubic and quartic vertices, followed by integrating out the ghost and lightcone oscillator excitations from the string field. Surprisingly, the last step does not alter the cubic and quartic interactions and does not generate effective vertices, and leads precisely to Kaku and Kikkawa’s lightcone string field theory.
Highlights
The celebrated no-ghost theorem [2,3,4,5,6] establishes that covariant and lightcone approaches lead to the same spectrum of physical states
We propose a transformation between the off-shell field variables of Witten’s open bosonic string field theory and the traditional lightcone string field theory of Kaku and Kikkawa, based on Mandelstam’s interacting string picture
We further explain that a lightcone effective field theory can be equivalently interpreted as a covariant string field theory which has been fixed to lightcone gauge
Summary
The first step in our analysis is understanding how to integrate out the longitudinal degrees of freedom from a covariant string field theory. The resulting “physical” string field theory will be called a lightcone effective field theory This is a slight abuse of terminology, since we are not integrating out high energy modes in a conventional sense. Integrating out the longitudinal modes essentially means that we eliminate states outside the kernel of L0 using the equations of motion This needs to be understood in the correct sense. The analogue of L0 in the covariant vector space was given long ago by Brink and Olive [28] We approach this problem from the point of view of a transformation introduced by Aisaka and Kazama [22]. Where Hlc consists of linear combinations of states with nonzero L0 eigenvalue This will imply a decomposition of the covariant vector space. The longitudinal states of the covariant vector space live in Hlong, and these are the states we need to integrate out
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