Speaker
Description
We briefly review the c=1 string theory and its dual description by a quantum mechanical model of a single N × N Hermitian matrix, i.e. c=1 Matrix Quantum Mechanics (MQM). The ground state of the c=1 MQM admits a Fermi Sea representation, and in the double scaling limit, the perturbative excitations on the Fermi Sea can be studied by a continuum 2D scalar field theory via collective field approach. In the target space picture, this shows the emergence of a 2D spacetime with the tachyon field that lives on it. We study the operator algebra in a subregion of the emergent spacetime away from the potential wall of the MQM, where the string perturbation theory still works, and shows that it gives a type III_1 factor. We then perform the crossed product via the subregion modular operator, which leads to a type II_infinity algebra. Furthermore, by introducing a projection operator on the spectrum of modular operator, the algebra becomes type II_1 factor. On the other hand, We explicitly construct the type II algebra from the canonical anti-communtation relation (CAR) algebra of the fermions in c=1 MQM and shows that the type III_1 factor can be recovered by a dual crossed product suggested by the Takesaki duality.