From a different perspective, it is known that the DLCQ of string theory arises from a T-duality transformation along a compactified spacelike circle in a genuine NR theory. The infinite boost limit along a spacelike circle can be interpreted as a compactification on a lightlike circle, which leads to nonrelativistic (NR) behavior in the resulting frame (see for example ). Similarly, by taking an infinite boost limit of the compactification of string theory on a spacelike circle, we are led to the discrete light cone quantization (DLCQ) of strings, which has a Matrix string theory description. This notably leads to Matrix theory, which serves as a powerful tool for understanding the full M-theory in a simple system of D0-branes. One nonperturbative approach to M-theory stems from taking a subtle limit of the compactification on a spacelike circle. For example, exploring nonperturbative aspects of string/M-theory is important for understanding the information paradox for black holes, which are fundamentally nonperturbative objects. While the various corners in this web that are described by perturbative string theories are fairly well understood, we are still far from a complete understanding of nonperturbative regimes in the full M-theory. It has long been known that different string theories are limits of M-theory. Finally, we discuss applications of nonrelativistic strings to decoupling limits in the context of the AdS/CFT correspondence. We also give a review of nonrelativistic open strings and effective field theories living on D-branes. This is known as (torsional) string Newton–Cartan geometry, which is neither Lorentzian nor Riemannian. We then give an overview of recent progress, including the appropriate target-space geometry that nonrelativistic strings couple to. In this review, we start with an introduction to the foundations of nonrelativistic string theory in flat spacetime. In recent years, there has been a resurgence of interest in the non-Lorentzian geometries and quantum field theories that arise from nonrelativistic string theory in background fields. This string theory also gives a unitary and ultraviolet complete framework that connects different corners of string theory, including matrix string theory and noncommutative open strings. It has a string spectrum with a Galilean dispersion relation, and a spacetime S-matrix with nonrelativistic symmetry. This theory arises as a self-contained corner of relativistic string theory. In flat spacetime, the theory is defined by a two-dimensional relativistic quantum field theory with nonrelativistic global symmetries acting on the worldsheet fields. We review recent developments on nonrelativistic string theory.
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