Abstract
We compute leading order quantum corrections to the Regge trajectory of a rotating string with massive endpoints using semiclassical methods. We expand the bosonic string action around a classical rotating solution to quadratic order in the fluctuations and perform the canonical quantization of the resulting theory. For a rotating string in D dimensions the intercept receives contributions from D − 3 transverse modes and one mode in the plane of rotation, in addition to a contribution due to the Polchinski-Strominger term of the non-critical effective string action when D ≠ 26. The intercept at leading order is proportional to the expectation value of the worldsheet Hamiltonian of the fluctuations, and this is shown explicitly in several cases. All contributions to the intercept are considered, and we show a simple physical method to renormalize the divergences in them. The intercept converges to known results at the massless limit, and corrections from the masses are explicitly calculated at the long string limit. In the process we also determine the quantum spectrum of the string with massive endpoints, and analyze the asymmetric case of two different endpoint masses.
Highlights
More than four decades have passed since A
We describe the string with massive endpoints by combining the Nambu-Goto string action, Sst = −T
To verify that the corrections coming from the fluctuations are small for long strings, and to quantify what it means for the string to be long in this case, we look at the simplest order terms, which are those of the contribution to the intercept from the transverse modes
Summary
More than four decades have passed since A. In non-critical dimensions one is required to incorporate the Liouville [28] or the Polchinski-Strominger (PS) term of effective string theory [29] in order to render the quantization procedure consistent This was generally not done in previous papers that considered the quantization of a string with massive endpoints. This paper does not offer the answer to this question of the phenomenological intercept, as we only compute the corrections due to the mass to the result a = 1 corresponding to the string without massive endpoints. This section mirrors the section preceding it as we write down the action and Hamiltonian for the fluctuations, the mode expansion, the equation of motion and boundary conditions (corrected by the radial mode living on the boundary), and determine the contribution to the intercept.
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