Abstract
We compute semi-classical corrections to the energy of rotating closed Nambu-Goto strings. We confirm the results obtained by means of the Polchinski-Strominger action. We also show that in this semi-classical approximation, the spectrum of physical excitations contains modes that are unphysical non-perturbatively, i.e., to which no physical excitations of the covariantly quantized Nambu-Goto string correspond.
Highlights
In the covariant quantization scheme, the Regge intercept a of the Nambu-Goto string is a free parameter, only constrained by a ≤ 1 for D ≤ 25 and a 1⁄4 1 for D 1⁄4 26, with D the dimension of the target Minkowski space [1,2]
We show that in this semiclassical approximation, the spectrum of physical excitations contains modes that are unphysical nonperturbatively, i.e., to which no physical excitations of the covariantly quantized Nambu-Goto string correspond
We show that for the closed string the spectrum of excitations in the semi-classical theory is too large, i.e., there are semi-classical excitations that do not correspond to physical excitations of the full nonperturbative covariantly quantized theory
Summary
In the covariant quantization scheme, the Regge intercept a of the Nambu-Goto string is a free parameter, only constrained by a ≤ 1 for D ≤ 25 and a 1⁄4 1 for D 1⁄4 26, with D the dimension of the target Minkowski space [1,2]. The equations of motion for φ only depend on the world sheet geometric data, i.e., the metric and the second fundamental form induced by the classical embedding X It seems natural, in line with the framework of [11], to use methods from quantum field theory on curved space-time [14,15] for the renormalization of the free world sheet Hamiltonian H0. An Appendix contains some intermediate results of our treatment of the elliptic case
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