We show that the two branches of collective modes discovered recently in underdoped cuprates with a large spectral weight are a necessary consequence of the loop-current state. Such a state has been shown in earlier experiments to be consistent with the symmetry of the order parameter competing with superconductivity in four families of cuprates. We also predict a third branch of excitations which cannot be discovered by neutron scattering but may be discovered by other techniques. Using parameters to fit the observed modes, we show that quantum fluctuations change the direction of the effective moments in the ground state to lie at an angle to the c axis as observed in experiments.