Linear dilaton conformal field theory

A linear dilaton conformal field theory improves the free-boson stress tensor by a second derivative, $T=-{\alpha }^{\prime -1}:\partial X\partial X:-q{\partial }^{2}X$. The improvement shifts the central charge to $c=1+6{\alpha }^{\prime }{q}^2$ and corresponds to a dilaton linear in the target coordinate $X$.

A background-charge scalar field is a free scalar coupled linearly to the worldsheet Ricci scalar. This curvature coupling produces the improved stress tensor of a linear dilaton conformal field theory.