Integrability of Schwinger-Dyson Equations in 2D Quantum Gravity and c < 1 Non-critical String Field Theory

Abstract

We investigate the integrability of the Schwinger-Dyson equations in $c=1-\frac{6}{m(m+1)}$ string field theory which were proposed by Ikehara et al as the continuum limit of the Schwinger-Dyson equations of the matrix chain model. We show the continuum Schwinger-Dyson equations generate a closed algebra. This algebra contains Virasoro algebra but does not coincide with $W_{\infty }$ algebra. We include in the Schwinger-Dyson equations a new process of removing from the loop boundaries the operator $\mathcal{H}(\sigma )$ which locally changes the spin configuration. We also derive the string field Hamiltonian from the continuum Schwinger-Dyson equations. Its form is universal for all $c=1-\frac{6}{m(m+1)}$ string theories.

15 pages, Latex, 4 figures

References in corpus (9)

• String Field Theory of $c\le 1$ Noncritical Strings
• 2D Quantum Gravity in the Proper-Time Gauge
• Loop Space Hamiltonians And Field Theory Of Non-Critical Strings
• String Field Theory in the Temporal Gauge
• Two-Dimensional Quantum Gravity in Temporal Gauge
• A Note on String Field Theory in the Temporal Gauge
• LOOP SPACE HAMILTONIAN FOR $c\le 1$ OPEN STRINGS
• The Continuum Limit of the Schwinger-Dyson Equations of the One and Two Matrix Model with Finite Loop Length
• Recent Developments in D=2 String Field Theory

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• The Hausdorff Dimension of Surfaces in Two-Dimensional Quantum Gravity Coupled to Ising Minimal Matter
• Stochastic Hamiltonian for Non-Critical String Field Theories from Double-Scaled Matrix Models
• Boundary operators and touching of loops in 2d gravity
• Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory