A Nonrelativistic Tour of String Theory

Nonrelativistic theories have always attracted a lot of attention in different fields of physics. However, nonrelativistic string theory remains largely unexplored. Whether or not nonrelativistic string theory helps to provide deep insights into string theory itself is an interesting question. This thesis is motivated mainly by the prospect that the nonrelativistic string theory as a unitary and ultraviolet theory promises to provide intriguing applications. It has long been known that one can construct a procedure, the so-called nonrelativistic limit, to obtain a nonrelativistic theory from a relativistic one. However, there is no unique way of taking the limit of a theory.

We begin with an overview of the groundwork for the rest of the thesis, including a detailed discussion of the nonrelativistic particle limit. We then generalize the particle limit to a nonrelativistic string limit and take as a toy model the nonrelativistic string limit of the Einstein-Palatini action, supplemented with a term containing a vector field and a two-form field.
We subsequently focus on nonrelativistic string theory, which can be obtained as a particular limit of relativistic string theory. Its field equations that govern the dynamics of the target space fields and the underlying geometry have been established. This non-Lorentzian geometry is now known as torsional string Newton–Cartan geometry. This geometry is quite analogous to Newton-Cartan geometry, which has been studied for a longer period of time. The new insights we obtained contribute to the current discussion and pave the way for applications of nonrelativistic string theory.