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Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

Ryuichi Nakayama·Toshiya Suzuki
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Abstract

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.

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Ryuichi Nakayama, Toshiya Suzuki. 1996-04-15. Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory. https://doi.org/10.1103/physrevd.54.3985

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