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

Original · EN

New loop equations for all genera in c = 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 W₃ algebra and are equivalent to the W₃ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for c = 1/2 string field theory is considered.