Abstract
We make some observations connecting non-relativistic limits of string theory with Toverline{T} deformations and TsT transformations.
Highlights
To be unreasonably well-behaved as we go to the UV
As well as the usual Nambu-Goto square root term, we need a non-zero B-field with a component in the longitudinal direction proportional to 1/λ. Both this B-field and the Nambu-Goto square root are naively divergent in the limit λ → 0, but these divergences cancel such that we recover the original undeformed theory
String theory is meant to occupy the position in c, G, space corresponding to relativistic quantum gravity
Summary
For more complicated field theories, described by other geometries, a precise link has been elucidated in [12,13,14,15,16] by describing the T Tdeformation in terms of the well-known TsT transformations which involve T-duality, a geometric shift (either of the coordinates or of the B-field) and a second T-duality We will describe this in more detail later on. (Note that from the point of view of this general approach, one can avoid introducing divergent B-fields — and view the appearance of such in the initial example as an artefact of flat space — while the deformation is most clearly expressed not in static gauge but in uniform light cone gauge.) To connect with this more general picture for our example geometry (1.1), we will change perspective. For an alternative viewpoint on the geometry, we turn to the Hamiltonian formulation of the string
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