  We study the bosonic sector of a decoupling limit of type IIA superstring
theory, where a background Ramond-Ramond one-form is fined tuned to its
critical value, such that it cancels the associated background D0-brane
tension. The light excitations in this critical limit are D0-branes, whose
dynamics is described by the Banks-Fischler-Shenker-Susskind (BFSS) Matrix
theory that corresponds to M-theory in the Discrete Light-Cone Quantization
(DLCQ). We develop the worldsheet formalism for the fundamental string in the
same critical limit of type IIA superstring theory. We show that the
fundamental string develops singularities on its worldsheet, whose topology is
described by nodal Riemann spheres as in ambitwistor string theory. We study
the T-duality transformations of this string sigma model and provide a
worldsheet derivation for the recently revived and expanded duality web that
unifies a zoo of decoupling limits in type II superstring theories. By matching
the string worldsheet actions, we demonstrate how some of these decoupling
limits are related to tensionless (and ambitwistor) string theory, Carrollian
string theory, the Spin Matrix limits of the AdS/CFT correspondence, and more.
