Role of Light-Front Coordinates in String Theory
May 06, 2020
May 26, 2020
In this work, we present a review of the role of light-front coordinates (LFC's) in string theory and also a review of the role of light-front (LF) zero modes (ZM's) in string theory as covered in my two talks at LC-2019. It is seen that the light-front coordinates play a central role in the understanding of not only the bosonic string theory (ST) but also in the understanding of the superstring theory (SST) that includes fermionic string fields. First we consider the bosonic string sigma model action known as the Polyakov action and study it in the so-called conformal gauge using the LFC's. The equation of motion (EoM) and the components of the conserved energy momentum tensor are solved in the LFC's. We introduce the LF Fourier modes for the left movers and right movers. The LF Fourier modes for the energy momentum tensor are the Virasoro operators. The Virasoro operators corresponding to the LF zero modes are seen to play a central role in obtaining the mass spectrum of ST and in determining the number of spacetime dimensions of the critical ST. We try to illustrate these important concepts using the LFC's. This eventually also helps in understanding the concept of the compactification of extra dimensions in ST. We then consider the Raymond-Nevieu-Schwarz (RNS) SST in LFC's and study its conserved super current, conserved energy-momentum tensor, EoM and the Raymond and Nevieu-Schwarz boundary conditions that are needed to make the boundary terms vanish. We then discuss that the consistency of the SST in the R-sector as well as separately in the NS-sector requires the number of spacetime dimensions of the SST to be $D = 10$ it also leads to the results that the spectrum of the SST in the R-sector leads to spacetime fermions and the spectrum of the theory in the NS-sector leads to spacetime bosons in $D = 10.$ dimensions.
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