Unitary and Complex Matrix Models as 1-d Type 0 Strings

We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to < 1 matter coupled to super-Liouville theory. We examine in detail the = 0 or pure supergravity case, which is related to the double scaling limit around the Gross-Witten transition, and find that reversing the sign of the Liouville superpotential interchanges the 0A and 0B theories. We also find smooth transitions between weakly coupled string backgrounds with D-branes, and backgrounds with Ramond-Ramond fluxes only. Finally, we discuss matrix models with multicritical potentials that are conjectured to correspond to 0A/0B string theories based on (2,4k) super-minimal models.Dedicated to Freeman Dyson, a pioneer of large N matrix models, on the occasion of his eightieth birthdayAcknowledgement We would like to thank E. Martinec and E. Witten for useful discussions, and C. Johnson for correspondence. IRK is grateful to the Institute for Advanced Study for hospitality during his work on this paper. The research of JM and NS is supported in part by DOE grant DE-FG02-90ER40542. The research of IRK is supported in part by NSF grant PHY-0243680. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.