Abstract :
We study the origins of the five ten-dimensional “matrix superstring” theories, supplementing old results with new ones, and find that they all fit into a unified framework. In all cases the matrix definition of the string in the limit of vanishingly small coupling is a trivial 1+1-dimensional infrared fixed point (an orbifold conformal field theory) characterized uniquely by matrix versions of the appropriate Green-Schwarz action. The Fock space of the matrix string is built out of winding T-dual strings. There is an associated dual supergravity description in terms of the near-horizon geometry of the fundamental string solution of those T-dual strings. The singularity at their core is related to the orbifold target space in the matrix theory. At intermediate coupling, for the IIB and SO(32) systems, the matrix string description is in terms of non-trivial 2 + 1-dimensional fixed points. Their supergravity duals involve anti de-Sitter space (or an orbifold thereof) and are well defined everywhere, providing a complete description of the fixed point theory. In the case of the type IIB system, the two extra organizational dimensions normally found in F-theory appear here as well. The fact that they are non-dynamical has a natural interpretation in terms of holography.
