Could someone tell about the physical meaning of these SO(32) groups in superstring theory? I am under the impression that it is a symmetry of the quantum superstring, but that it is not a symmetry of any underlying classical model, is it? Because if it is so, it is very different of the GUT groups, which are also symmetries of the field Lagrangian.
You are right, the gauge degrees of freedom in string theory appear only on the quantum level. But in a sense, it is not much different from that in particle physics. Namely, you can view a classical gauge field as a first quantized wave function, so you can say that the gauge degrees of freedom of particles also appear only at the quantum (first quantized) level. By the way, most of the results in string theory are expressed in the first quantized language, while second quantization of string theory (string field theory) is not well understood and there are even indications that string field theory is not the correct approach.
Yep, I though, while writing the question that this was the answer. But I asked anyway because I am not sure. One gets the feeling that gauge fields, or at least abelian gauge fields, can be recovered in a classical level, while the SO(32) etc of string theory seem to be intrinsically quantum. Part of the answer seems to lie in N. Marcus and A. Sagnotti, “Group Theory From ’Quarks’ At The Ends Of Strings,” Phys. Lett. B188 (1987) 58. http://www.slac.stanford.edu/spires/find/hep/www?j=PHLTA,B188,58 Further references: http://www.roma2.infn.it/stringaperta/berlin.ps http://motls.blogspot.com/2007/08/answering-few-string-related-questions.html http://arxiv.org/abs/hep-th/0208020 http://arxiv.org/abs/hep-th/0204089 http://arxiv.org/abs/hep-th/0203098v1