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We investigate the quantum antiferromagnetism arising from algebraic spinliquid via spontaneous chiral symmetry breaking. We claim that in theantiferromagnet massive Dirac spinons can appear to make broad continuumspectrum at high energies in inelastic neutron scattering. The mechanism ofspinon deconfinement results from the existence of fermion zero modes in singlemonopole potentials. Neel vectors can make a skyrmion configuration around amagnetic monopole of compact U(1) gauge fields. Remarkably, in themonopole-skyrmion composite potential the Dirac fermion is shown to have a zeromode. The emergence of the fermion zero mode forbids the condensation ofmonopoles, resulting in deconfinement of Dirac spinons in the quantumantiferromagnet.Comment: K. -S. Kim is much indebted to Dr. A. Tanaka who pointed out a  mistake in association with the gradient expansion in Eq. (C3) and Eq. (C4

Existence of fermion zero modes and deconfinement of spinons in quantum antiferromagnetism resulting from algebraic spin liquid