A NEW HAT FOR THE c = 1 MATRIX MODEL

Abstract

We consider two dimensional supergravity coupled toĉ = 1 matter. This system can also be interpreted as noncritical type 0 string theory in a two dimensional target space. After reviewing and extending the traditional descriptions of this class of theories, we provide a matrix model description. The 0B theory is similar to the realization of two dimensional bosonic string theory via matrix quantum mechanics in an inverted harmonic oscillator potential; the difference is that we expand around a non-perturbatively stable vacuum, where the matrix eigenvalues are equally distributed on both sides of the potential. The 0A theory is described by a quiver matrix model. July 2003 made in [7].2 Equivalently, this model can be described as quantum mechanics of a unitary matrix U with potential Tr(U + U † ). After the double scaling limit is taken, both models are described by fermions in an upside down harmonic oscillator potential filling both sides of the potential to Fermi level −µ.3 The spectrum of D-branes in 10-d type 0 theories was studied in [21][22][23][24][25].3 the boundary states of the full quantum theory, and their relation to the minisuperspace wavefunctions. The annulus partition function is also considered. Section 8 discusses some aspects of the worldvolume dynamics of D-branes and their interactions with closed string fields. 4The precise nature of our proposal for a type 0B matrix model is presented in section 9, where we check the torus worldsheet calculation against a computation of the finite temperature matrix model free energy. Section 10 introduces the type 0A matrix model and performs the analogous check. In section 11 we study the relation of tachyon condensation and rolling matrix eigenvalues [7-9] through a calculation of the disk expectation value of the ground ring generators. We also explore the radiation of closed strings produced by the decay. Three appendices contain useful technical results.It is also possible to show thatĉ < 1 superconformal minimal models coupled to 2d supergravity are dual to unitary matrix models, 5 as one might expect on the basis of gravitational RG flow [30][31][32]. These matrix models were solved in the planar limit in [33], and in the double scaling limit in [34][35][36]. These models will be the subject of a separate publication.Note Added: While completing this manuscript, we learned of work by T. Takayanagi and N. Toumbas [37] where the matrix model for 2d type 0 strings is also proposed. The 2d Fermionic StringFermionic strings are described by N = 1 supersymmetric world sheet field theories coupled to worldsheet supergravity. The construction of type II string theories requires the existence of a non-anomalous chiral (−1) F L symmetry of the worldsheet theory. The generic background may only admit a nonchiral (−1) F ; the use of this class of (GSO) projection gives type 0 string theory (see [38] for a review).4 Sections 2-8 review known material but also describe many new results. The reader who is impatient to get to the matrix model can move directly to...

Matrix models, 4D black holes and topological strings on non-compact Calabi-Yau manifolds

“…In the original relation between 2D string theory and c = 1 matrix models, the removal of half of the states corresponds, for example, on the space-time side to projecting the RR-scalar away [1,2], thus leaving the tachyon as the only propagating degree of freedom. It would be interesting to see if something similar happens on the 4D space-time side.…”

Two-dimensional superstrings and the supersymmetric matrix model

“…This proposal reinterprets the matrix-model/string-theory correspondence as a holographic open-string/closed-string duality, and suggests a search algorithm for more examples. It has been clarified [3,4,5,6] and very recently extended to type 0 strings [7,8]. In this note, we apply this perspective to shed some new light on the physical identification of the supersymmetric matrix model of Marinari and Parisi [9].…”

Two-Dimensional Unoriented Strings And Matrix Models

“…The only difference in solving this model compared to its bosonic string analog is that when constructing the quasi-Fermi sea for the dual of the Type 0B orientifold one fills the states symmetrically with respect to the tachyon maximum, due to the Z 2 symmetry of the open string tachyon potential [10] [11] . Therefore the free energy in this case should be twice that of the bosonic string, in agreement with the computation in section 4.…”

“…As in [11], we will study a collection of N D0-branes and N + m D0-branes. As usual, After gauge-fixing, the problem reduces to studying the dynamics of N non-interacting fermions moving in a plane with angular momentum m and subject to an inverted harmonic oscillator potential [11].…”