Algebraic structure of the bosonic string with Newtonian background
Summary
I derive the symmetry group of the bosonic string with a non-relativistic background
which takes the form of a covariant Newton-Cartan geometry. This is done by studying
a Polyakov-type action obtained by performing a dimensional reduction of a 1-dimension
higher relativistic background along a null Killing vector field. The constraints that arise
from this construction then act as additional fields of the theory which have to be taken
into account when deriving the symmetries of the non-relativistic bosonic string action. I
confirm that the resulting symmetries form a closed group with the resulting Bargmann
algebra- the central extension of the Galilean algebra, which correctly describes nonrelativistic motion of objects.