We study the infra-red dynamics of D1-branes at the conifold. We show using
methods developed to study the infra-red dynamics of (4,4) theories, the
infra-red degrees of freedom of the (2,2) theory of a single D1-brane at the
conifold is that of a linear dilaton with background charge of 2β and a
compact scalar. The gauge theory of N D1-branes at the conifold is used to
formulate the matrix string in the conifold background.Comment: 20 pages, latex, some clarifications added, version to appear in JHE