Abstract
Quantization of the bosonic string around the classical, perturbative vacuum is not consistent for spacetime dimensions 2<d<26. Recently we have showed that at large d there is another so-called mean-field vacuum. Here we extend this mean-field calculation to finite d and show that the corresponding mean-field vacuum is stable under quadratic fluctuations for 2<d<26. We point out the analogy with the two-dimensional O(N)-symmetric sigma-model, where the 1/N-vacuum is very close to the real vacuum state even for finite N, in contrast to the perturbative vacuum.
Highlights
The action of the Nambu–Goto string is the area of the string world sheet
It is highly nonlinear in the embedding-space coordinates
The action is quadratic in the embedding-space coordinates and in the path integral one can in principle perform the integration over these coordinates
Summary
The action of the Nambu–Goto string is the area of the string world sheet. It is highly nonlinear in the embedding-space coordinates. The action is quadratic in the embedding-space coordinates and in the path integral one can in principle perform the integration over these coordinates The dependence of this part of the path integral on the world sheet metric is determined by the conformal anomaly. In the work [3] we constructed another vacuum state of the Nambu–Goto string by introducing an independent intrinsic metric ρab and the corresponding Lagrange multiplier λab and integrating over the d target-space coordinates Xμ. This approach is quite similar to the well-known introduction of a Lagrange multiplier field in the two-dimensional O (N) sigmamodel. We show that it is positive definite for 2 < d < 26, but becomes unstable in the stringy scaling limit for d > 26
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