The effective theory of strings. (English) Zbl 1292.81107
The starting point of string theory was a model described by the Nambu-Goto action. Even though this action has a physical interpretation as the area of the string world sheet, its quantization turned out to be awkward in the past. As it turned out later, the bosonic strings in a given ambient target space can be consistently quantized when its dimension is 26. The present article shows that the Nambu-Goto string can be quantized in any dimension of the target space as an effective theory, although there have been indications in the past that there exist quantization schemes which do not require the dimension of the ambient space to be fixed. Here the authors use tools from perturbative algebraic QFT, also tools from curved space-time and the Batalin-Vilkovisky formalism. Whether there is a correspondence between the Lüscher-Weisz string theory and the present model remains an open question. The present model may also be related to the effective string theory of Polchinski and Strominger, but in the present approach, in contrast to Pohlmeyer’s approach, the observables are compactly supported and local.
Reviewer: Gert Roepstorff (Aachen)
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83E30 | String and superstring theories in gravitational theory |
| 81T70 | Quantization in field theory; cohomological methods |
Keywords:
string theory; Nambu-Goto action; perturbative algebraic QFT; quantization in any dimension; Batalin-Vilkovisky formalismReferences:
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