Symmetries of String Theory and Newton Cartan Geometry

Abstract

The string theory has some beautiful properties, which have bewildered researchers since it’s inception. One of such properties is the presence of a duality symmetry, which relates large objects to very small ones. The duality is also called topological or T Duality. T Duality informally says, strings can not differentiate between objects of radii R and that of Radii 1/R. This allows strings to wind the same way around the two said objects, leading to the same winding mode quantum numbers. A symmetry of this nature is obscure in other theories in Physics. There has been extensive research to explore this duality as an explicit symmetry of a field theory. One such attempt is the Double Field Theory. Turning towards another area of research in the subject, these rather complex formulations of double field theory contain the non relativistic Newton Cartan string, which sounds unlikely, but holds true. Newton Cartan geometry is a reformulation of Newton's gravity, to make it a reduction of Einstein's relativity in non relativistic regimes. The Newton Cartan string theory was first written to discover simpler physics, but the surprising nature of string theory brings us to this junction. The thesis begins on the intersection of the two, and we proceed as follows.