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

Ryuichi Nakayama·Toshiya Suzuki
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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 ${\cal H}(σ)$ 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.

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Ryuichi Nakayama, Toshiya Suzuki. 1995-03-28. Integrability of Schwinger-Dyson Equations in 2D Quantum Gravity and c < 1 Non-critical String Field Theory. https://doi.org/10.1016/0370-2693(95)00615-r

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