Pure gauge configurations and solutions to fermionic superstring field theory equations of motion

Abstract

Recent results on solutions to the equation of motion of the cubic fermionic string field theory and an equivalence of non-polynomial and cubic string field theory are discussed. To have a possibility to deal with both GSO(+) and GSO(−) sectors in the uniform way a matrix formulation for the NS fermionic SFT is used. In constructions of analytical solutions to open string field theories truncated pure gauge configurations parameterized by wedge states play an essential role. The matrix form of this parametrization for the NS fermionic SFT is presented. Using the cubic open superstring field theory as an example we demonstrate explicitly that for the large parameter of the perturbation expansion these truncated pure gauge configurations give divergent contributions to the equation of motion on the subspace of the wedge states. The perturbation expansion is cured by adding extra terms that are nothing but the terms necessary for the equation of motion contracted with the solution itself to be satisfied.

Nonlocal quantum gravity and M-theory

“…The exponential operator is a general feature of the particle-field limit of certain string field theories, but not of others (for instance, Berkovits's nonpolynomial theory) in which the low-energy spacetime limit has never been derived while retaining nonlocality. However, several dualities between different open SFTs are known, including a mapping between supersymmetric and bosonic classical solutions [43,44], cubic and Berkovits's supersymmetric SFTs [45,46], and different polynomial supersymmetric SFTs [47,48]. These results have been found only for the open string, but they are encouraging enough to put us in the position of submitting a reasonable exploratory proposal.…”

Level truncation analysis of a simple tachyon vacuum solution in cubic superstring field theory

“…In the framework of the modified cubic superstring field theory [25], the analytic construction of the tachyon vacuum solution was analyzed by Erler [26]. Using the KBcγ subalgebra introduced in [27,28], many gauge equivalent tachyon vacuum solutions [29,30,31,32,33] have been proposed and the computation of the energy associated to these solutions was performed giving results in agreement with Sen's conjecture. The analysis of multibrane solutions has been given in a set of two papers [34,35].…”

A simple analytic solution for tachyon condensation

“…(2.6) is closely related to another solution which satisfies the string field reality condition 4 10) where the inverse square root of 1 + K is…”

“…(2.34) 10 We ignore the 1 + K factor since this would give a subleading contribution to the phantom piece, though such contributions can be important [8].…”

“…By now the regularization and phantom piece are better understood [2,5,6,7,8,9,10], and there is little doubt that the B 0 gauge solution is for practical purposes nonsingular. Yet, no one has found an adequate definition of the solution-or gauge equivalent alternative-which does not require the regulated sum and phantom piece.…”