Abstract
Quantum state wave functionals are constructed in exact form for the graviton-like field theory obtained by breaking down the topological symmetry of the string action related with the Euler characteristic of the world-surface; their continuous and discrete symmetries are discussed. The comparison with the so-called Chern–Simons state, which may be inappropriate as quantum state, allows us to conclude that the found wave functionals will give a plausible approximation to the ground state for the considered field theory.
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