  We study stochastic Burgers turbulence without pressure. We first show that
the variational derivative of the Burgers equation is dependent on the velocity
field, suggesting the existence of an anomaly. The anomaly is created by an
operator that is non-self-adjoint. To calculate it correctly, we need to find
its square. There are similarities with conformal and chiral two-dimensional
field theories, but causality is the key that makes the difference. We
calculate the determinant and use two local symmetries to verify the result. By
requiring the disappearance of the anomaly, the velocity field is constrained
and the theory becomes anomaly-free. These symmetries obey Kolmogorov's second
law of self-similarity. One can choose an anomaly-free theory, a partially
broken theory, or a fully broken theory by choosing the constraint
appropriately. There is an analogy to gauge fixing or vacuum selection which
define the local configuration.
