Various studies have attempted to extend the Witten’s cubic open string field theory to the cubic closed string field theory, which may describe Einstein gravity in the low energy sector consistently. In the present study we propose a cubic closed string field theory, introducing a double layer to describe the closed string world-sheet as an extension of the open string world-sheet of the Witten’s cubic open string. We mapped the closed string world-sheet onto the complex plane, of which the lower half plane is completely covered by the extended part of the string world-sheet. Using the Green’s function on the complex plane, evaluated the Polyakov string path integral, from which we extracted the Neumann functions and the vertex operators. We obtained the one and two string vertices (identities) following this procedure and finally the cubic string vertex operator. It is notable that the obtained cubic string scattering amplitude coincide with the cubic graviton interaction of the Einstein gravity. Thus, the resultant cubic closed string field theory consistently describes the Einstein gravity. We also show that the Kawai-Lewellen-Tye (KLT) relations of the first quantized string theory may be manifested in the cubic closed string field theory.

Cubic Closed String Field Theory on a Double Layer

In this thesis we will explore three approaches to aspects of the fundamental structure of string theory. We first provide a brief review of perturbative string theory, and briefly discuss how each of the three topics to be discussed in the body of this thesis depart from this starting point. We then study the open string one-loop tadpole diagram in Witten cubic open string field theory. We compute this diagram both analytically and numerically and study the divergences arising from the collective behavior of open string fields in the short-distance region of the diagram. We demonstrate that this region of the diagram encodes information about the linearized Einstein equation describing the shift in the closed string fields in reaction to the D-brane supporting the open strings. We also show that the manner in which this information is encoded is somewhat singular, and comment on the implications for the quantum consistency of open bosonic string field theory. We next compute the closed string radiation from a decaying D-brane in type II string theory. The calculation is made possible by noting that the integrals involved in the requisite disk one-point functions reduce to integrals over the group manifold of a product of unitary groups. We find that the total number and energy of strings radiated during the decay process diverges for D-branes of small enough dimension, in precise analogy to the bosonic case. Finally, we investigate a simple class of type II string compactifications which incorporate nongeometric "fluxes" in addition to "geometric flux" and the usual H-field and R-R fluxes. We develop T-duality rules for NS-NS geometric and nongeometric fluxes, which we use to construct a superpotential for the dimensionally reduced four-dimensional theory. The resulting structure is invariant under T-duality, so that the distribution of vacua in the IIA and IIB theories is identical when nongeometric fluxes are included. Thesis Supervisor: Washington Taylor IV Title: Professor of Physics

Twisted and unstable: Approaches to the string equations of motion

In this thesis we show how to calculate off-shell low energy effective actions and how to study the dynamics of the tachyon from string field theory. We discuss how to obtain an effective action for the massless field and we explain how to relate it to well known results. We then study the tachyon dynamics both in cubic and in boundary string field theory. Thesis Supervisor: Taylor Washington Title: Professor of Physics

http://cds.cern.ch/record/945892/files/cer-002612858.pdf

Low energy effective actions and tachyon dynamics from string field theory

These lectures provide an introduction to the subject of tachyon condensation in the open bosonic string. The problem of tachyon condensation is first described in the context of the low-energy Yang-Mills description of a system of multiple D-branes, and then using the language of string field theory. An introduction is given to Witten’s cubic open bosonic string field theory. The Sen conjectures on tachyon condensation in open bosonic string field theory are introduced, and evidence confirming these conjectures is reviewed.

1 . 1 The status of string theory : a brief review

We study Witten's cubic open string field theory on multiple $Dp$-branes. On multiple $Dp$-branes the string fields carry $U(N)$ group indices. Mapping the string world-sheet onto the upper half complex plane and evaluating the Polyakov string path integral of Witten's cubic open string, we obtain a Fock space representation of one, two and three-string vertex operators. In the low energy region, the system is described by massless gauge fields and massless scalar fields, carrying $U(N)$ group indices. The two-string vertex induces mass terms for the gauge fields and the scalar fields. The cubic interaction reduces correctly to the cubic term of the non-Abelian gauge fields, cubic interaction terms of the gauge fields, and the scalar fields on $(p+1)$ dimensional space. Thus, Witten's string field theory may be a useful tool to study the quantum dynamics of open strings on multiple $Dp$-branes. 

/pdf/wittens-cubic-open-string-field-theory-on-multiple-dp-branes-qibbychz.pdf

Witten’s cubic open string field theory on multiple Dp-branes

Abstract Conformal mapping techniques are employed to obtain the oscillator representation of the three open string vertex in Witten's formulation of string field theory. It is argued that the physical state couplings are identical to those of the dual resonance model, and this is confirmed for the low lying states with our explicit construction.

E. Cremmer

Papers

The Vertex Function in Witten's Formulation of String Field Theory