Time-dependent backgrounds of two dimensional string theory from the c=1c=1 matrix model

The aim of this paper is to use correspondence between solutions in the $c=1$ matrix model collective field theory and coupled dilaton-gravity to a massless scalar field. First, we obtain the incoming and outgoing fluctuations for the time-dependent backgrounds with the lightlike and spacelike boundaries. In the case of spacelike boundaries, we have done here for the first time. Then by using the leg-pole transformations we find corresponding tachyon field in two dimensional string theory for lightlikes and spacelikes boundary.Comment: 10 page

Collective Field Description of Matrix Cosmologies

We study the Das-Jevicki collective field description of arbitrary classical solutions in the c=1 matrix model, which are believed to describe nontrivial spacetime backgrounds in 2d string theory. Our analysis naturally includes the case of a Fermi droplet cosmology: a finite size droplet of Fermi fluid, made up of a finite number of eigenvalues. We analyze properties of the coordinates in which the metric in the collective field theory is trivial, and comment on the form of the interaction terms in these coordinates.Comment: 16 pages, 1 figure. v2: Typos corrected, JHEP styl

Tachyon Backgrounds in 2D String Theory

We consider the construction of tachyonic backgrounds in two-dimensional string theory, focusing on the Sine-Liouville background. This can be studied in two different ways, one within the context of collective field theory and the other via the formalism of Toda integrable systems. The two approaches are seemingly different. The latter involves a deformation of the original inverted oscillator potential while the former does not. We perform a comparison by explicitly constructing the Fermi surface in each case, and demonstrate that the two apparently different approaches are in fact equivalent.Comment: 25 pages, no figure

Areas and entropies in BFSS/gravity duality

The BFSS matrix model provides an example of gauge-theory / gravity duality where the gauge theory is a model of ordinary quantum mechanics with no spatial subsystems. If there exists a general connection between areas and entropies in this model similar to the Ryu-Takayanagi formula, the entropies must be more general than the usual subsystem entanglement entropies. In this note, we first investigate the extremal surfaces in the geometries dual to the BFSS model at zero and finite temperature. We describe a method to associate regulated areas to these surfaces and calculate the areas explicitly for a family of surfaces preserving $SO(8)$ symmetry, both at zero and finite temperature. We then discuss possible entropic quantities in the matrix model that could be dual to these regulated areas.Comment: 29 pages, 3 figures. v2 Examples in section 6 moved to appendix. Minor comments adde

Energy Quantisation in Bulk Bouncing Tachyon

We argue that the closed string energy in the bulk bouncing tachyon background is to be quantised in a simple manner as if strings were trapped in a finite time interval. We discuss it from three different viewpoints; (1) the timelike continuation of the sinh-Gordon model, (2) the dual matrix model description of the (1+1)-dimensional string theory with the bulk bouncing tachyon condensate, (3) the c_L=1 limit of the timelike Liouville theory with the dual Liouville potential turned on. There appears to be a parallel between the bulk bouncing tachyon and the full S-brane of D-brane decay. We find the critical value \lambda_c of the bulk bouncing tachyon coupling which is analogous to \lambda_o=1/2 of the full S-brane coupling, at which the system is thought to be at the bottom of the tachyon potential.Comment: 25 pages, minor changes, one reference adde

Large Representation Recurrences in Large N Random Unitary Matrix Models

In a random unitary matrix model at large N, we study the properties of the expectation value of the character of the unitary matrix in the rank k symmetric tensor representation. We address the problem of whether the standard semiclassical technique for solving the model in the large N limit can be applied when the representation is very large, with k of order N. We find that the eigenvalues do indeed localize on an extremum of the effective potential; however, for finite but sufficiently large k/N, it is not possible to replace the discrete eigenvalue density with a continuous one. Nonetheless, the expectation value of the character has a well-defined large N limit, and when the discreteness of the eigenvalues is properly accounted for, it shows an intriguing approximate periodicity as a function of k/N.Comment: 24 pages, 11 figure