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Register a new userA Note on Angular Momentum Commutators in Light-Cone Formulation of Open Bosonic String Theory
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Authors
Klaus Bering
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We recalculate in a systematic and pedagogical way one of the most important results of Bosonic open string theory in the light-cone formulation, namely the [J^{-i},J^{-j}] commutators, which together with Lorentz covariance, famously yield the critical dimension D=26 and the normal order constant a=1. We use traditional transverse oscillator mode expansions (avoiding the elegant but more advanced language of operator product expansions). We streamline the proof by introducing a novel bookkeeping/regularization parameter kappa to avoid splitting into creation and annihilation parts, and to avoid sandwiching between bras and kets.
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We study the multiloop amplitudes of the light-cone gauge closed bosonic string field theory for $d eq 26$. We show that the amplitudes can be recast into a BRST invariant form by adding a nonstandard worldsheet theory for the longitudinal variables $X^{pm}$ and the reparametrization ghost system. The results obtained in this paper for bosonic strings provide a first step towards the examination whether the dimensional regularization works for the multiloop amplitudes of the light-cone gauge superstring field theory.
We study light-cone gauge string field theory in noncritical space-time dimensions. Such a theory corresponds to a string theory in a Lorentz noninvariant background. We identify the worldsheet theory for the longitudinal coordinate variables $X^pm$ and study its properties. It is a CFT with the right value of Virasoro central charge, using which we propose a BRST invariant formulation of the worldsheet theory.
We review our recent proposals to dimensionally regularize the light-cone gauge string field theory.
We propose a method of constructing a gauge invariant canonical formulation for non-gauge classical theory which depends on a set of parameters. Requirement of closure for algebra of operators generating quantum gauge transformations leads to restrictions on parameters of the theory. This approach is then applied to bosonic string theory coupled to massive background fields. It is shown that within the proposed canonical formulation the correct linear equations of motion for background fields arise.
Feynman amplitudes of light-cone gauge superstring field theory are ill-defined because of various divergences. In a previous paper, one of the authors showed that taking the worldsheet theory to be the one in a linear dilaton background $Phi=-iQX^{1}$ with Feynman $ivarepsilon$ $(varepsilon>0)$ and $Q^{2}>10$ yields finite amplitudes. In this paper, we apply this worldsheet theory to dimensional regularization of the light-cone gauge NSR superstring field theory. We concentrate on the amplitudes for even spin structure with external lines in the (NS,NS) sector. We show that the multiloop amplitudes are indeed regularized in our scheme and that they coincide with the results in the first-quantized formalism through the analytic continuation $Qto0$.
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