Category Archives: String Theory

Fermions in 2-dimensions can be taken to be two-component objects with real entries, that is, Majorana spinors. Using the proper Gamma matrices,  the equation of motion implies that the top component is only a function of and the bottom component … Continue reading →

Let us begin by answering why does in bosonic string theory?  You have scalars on the worldsheet, each of which has central charge 1. The reparametrization ghosts which arise during the Faddeev-Popov procedure have central charge . For the trace … Continue reading →

M-theory is an 11-dimensional theory that is one of the weak-coupling limits of the “theory of everything”. The other five weak coupling limits are the five superstring theories. The low-energy description of all these theories are supergravity theories. I would … Continue reading →

The cylinder coordinates are time and angle . Define new coordinates and . The line element in these coordinates is given by . We start with the Polyakov action, . The equation of motion is to which the solution is … Continue reading →

Strings are 1-dimensional objects which trace out 2-dimensional surfaces called worldsheets as they travel in time.Let and be coordinates that parametrize the worldsheet. is taken to be timelike and to be spacelike. To generate dynamics, we postulate that the string … Continue reading →

Conformal transformations are transformations that preserve angles. In other words, the metric is multiplied by a function of the coordinates. The condition for an infinitesimal transformation to be a conformal transformation is . A consequence of the above condition is … Continue reading →

The usual action for the relativistic point particle is given by , where is the usual time coordinate and is the mass of the particle. Note that this reproduces the fact that for a nonrelativistic particle () the action is … Continue reading →