A Note on Stress-Energy Tensor and Variational Principle for Null Strings

A straightforward application of the variational principle to null strings meets difficulties since string's world-sheets are degenerate. It is known that the variational principle in this case can be formulted with the help of two-vector density on the string world-sheet which plays a role of Lagrange multipliers. It is shown that recently suggested stress-energy tensor of null strings can be derived by variation over the background metric of the action used to describe tensionless limit in the string theory. One of the Lagrange multipliers is related to the energy of the null string.