old personal page at Princeton
My main interests this year [1993?] were directed towards string theory of quark confinement. The problem is to find the string Lagrangian for the Faraday’s “lines of force”,which would reproduce perturbative corrections from the Yang-Mills theory to the Coulomb law at small distances and would give permanent confinement of quarks at large distances.
Introducing the Polyakov action (and via Liouville theory in the non-critical case) for the bosonic string:
Introducing conformal field theory:
Proposing the identification of flux tubes in confined QCD with the strings of string theory, hence of the holographic principle in what came to be known as the AdS-QCD correspondence:
Alexander Polyakov, String representations and hidden symmetries for gauge fields, Physics Letters B 82 2 (1979) 247-250 [doi:10.1016/0370-2693(79)90747-0]
Alexander Polyakov, Gauge fields as rings of glue, Nuclear Physics B 164 (1980) 171-188 [doi:10.1016/0550-3213(80)90507-6]
Alexander Polyakov, Gauge Fields and Strings, Routledge, Taylor and Francis (1987, 2021) [doi:10.1201/9780203755082, oapen:20.500.12657/50871]
Alexander Polyakov, String Theory and Quark Confinement, Nucl. Phys. Proc. Suppl. 68 (1998) 1-8 [arXiv:hep-th/9711002, doi:10.1016/S0920-5632(98)00135-2]
Alexander Polyakov, The wall of the cave, Int. J. Mod. Phys. A 14 (1999) 645-658 [arXiv:hep-th/9809057, doi:10.1142/S0217751X99000324]
eventually leading to the rules of the AdS-CFT correspondence:
Relations between gauge fields and strings present an old, fascinating and unanswered question. The full answer to this question is of great importance for theoretical physics. It will provide us with a theory of quark confinement by explaining the dynamics of color-electric fluxes.
and specifically between single trace operators and superstring-excitations:
The picture which slowly arises from the above considerations is that of the space-time gradually disappearing in the regions of large curvature. The natural description in this case is provided by a gauge theory in which the basic objects are the texts formed from the gauge-invariant words. The theory provides us with the expectation values assigned to the various texts, words and sentences.
These expectation values can be calculated either from the gauge theory or from the strongly coupled 2d sigma model. The coupling in this model is proportional to the target space curvature. This target space can be interpreted as a usual continuous space-time only when the curvature is small. As we increase the coupling, this interpretation becomes more and more fuzzy and finally completely meaningless.
Historical review:
Last revised on December 21, 2022 at 11:21:49. See the history of this page for a list of all contributions to it.