$W$-Infinity Ward Identities and Correlation Functions in the $C=1$ Matrix Model

Abstract

We explore consequences of $W$-infinity symmetry in the fermionic field theory of the $c=1$ matrix model. We derive exact Ward identities relating correlation functions of the bilocal operator. These identities can be expressed as equations satisfied by the effective action of a {\it three} dimensional theory and contain non-perturbative information about the model. We use these identities to calculate the two point function of the bilocal operator in the double scaling limit. We extract the operator whose two point correlator has a {\it single} pole at an (imaginary) integer value of the energy. We then rewrite the \winf~ charges in terms of operators in the matrix model and use this derive constraints satisfied by the partition function of the matrix model with a general time dependent potential.

17 pages

Cited by in corpus (16)

• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• Black Hole Non-Formation in the Matrix Model
• W_{\infty} Gauge Transformations and the Electromagnetic Interactions of Electrons in the Lowest Landau Level
• On The Problem of Particle Production in c=1 Matrix Model
• Black hole formation in $c=1$ String Field Theory
• Two Dimensional String Theory and the Topological Torus
• Correlation functions from two-dimensional string Ward identities
• $W_{\infty }$ Algebras, Hawking Radiation and Information Retention by Stringy Black Holes
• Spacetime Diffeomorphisms and Topological W-Infinity Symmetry in Two Dimensional Topological String Theory
• W_\infty and w_\infty Gauge Theories and Contraction
• Open String Descriptions of Space-like Singularities in Two Dimensional String Theory
• Two-Dimensional String Theory, Topological Field Theories and the Deformed Matrix Model
• Phase space holography with no strings attached
• Coupling of Tachyons and Discrete States in $c=1$ 2-D Gravity
• A Study of Two Dimensional String Theory (PhD Thesis)
• c = 1 Two Dimensional Quantum Gravity