Removal of nonphysical states
We have seen that there are some unphysical deformations.
One way to look at them is to consider the so-called beta deformation which is adding to the
action the wedge product of two global symmetry currents:
The corresponding unintegrated vertex is .
This is nonphysical when where is the structure constants of
the global symmetry group (super-Poincare). Notice that:
Therefore, we must postulate that:
But what happens if we, still, deform the action with (5) with ? The worldsheet action will be perfectly consistent as a classical action, and enjoying a nice BRST symmetry. At the classical level, nothing is wrong. But:
the quantum theory will be anomalous at the level of one loop
(anomaly in the holomorphicity of the and antiholomorphicity of )