This entry is about the notion in particle physics/quantum gravity. For the notion in computer science see at string (computer science).
physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
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Tools
Structural phenomena
Types of quantum field thories
A string or 1-brane is a brane of dimension one higher than an ordinary particle:
where a 1-dimensional sigma-model may be thought of a describing the dynamics of particles propagating of a target space $X$, a 2-dimensional sigma-model is said to described the dynamics of a string on some target space.
Much of traditional quantum field theory on $X$ may be understood in terms of second quantization of 1-dimensional sigma-models with target space $X$. What is called string theory is the corresponding study of what happens to this situation as the 1-dimensional $\sigma$-model is replaced by a 2-dimensional one (for more on this see at worldline formalism).
A key motivation/application for strings is their identification with flux tubes in confined Yang-Mills theory/QCD [Polyakov (1998), Polyakov (1999)], for more on this see at AdS-CFT correspondence and AdS-QCD correspondence.
There is
the superstring of superstring theory
(also called the F1-brane)
$\,$
Table of branes appearing in supergravity/string theory (for classification see at brane scan).
See references at string theory, bosonic string and superstring.
Key ideas underlying what is now known as the holographic duality in string theory and specifically holographic QCD (see notably also at holographic light front QCD) were preconceived by Alexander Polyakov in efforts to understand confined QCD (the mass gap problem) by regarding color-flux tubes between quarks as dynamical strings:
Early suggestion that confined QCD is described by regarding the color-flux tubes as string-like dynamical degrees of freedoms:
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$]$
$[$old personal page$]$: 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.
Early suggestion (due to the Liouville field see in the quantization of the bosonic string via the Polyakov action) that such flux tubes regarded as confinig strings are to be thought of a probing higher dimensional spacetime, exhibiting a holographic principle in which actual spacetime appears as a brane:
Alexander Polyakov, String Theory and Quark Confinement, talk at Strings’97, 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 culminating in the formulation of the dictionary for 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 the suggestion of finding the string-QCD correspondence:
in the strong coupling limit of a lattice gauge theory the elementary excitations are represented by closed strings formed by the color-electric fluxes. In the presence of quarks these strings open up and end on the quarks, thus guaranteeing quark confinement. Moreover, in the $SU(N)$ gauge theory the strings interaction is weak at large $N$. This fact makes it reasonable to expect that also in the physically interesting continuous limit (not accessible by the strong coupling approximation) the best description of the theory should involve the flux lines (strings) and not fields, thus returning us from Maxwell to Faraday. In other words it is natural to expect an exact duality between gauge fields and strings. The challenge is to build a precise theory on the string side of this duality.
Historical review:
Already in 1974, in his famous large $N$ paper, ‘t Hooft already tried to find the string-gauge connections. His idea was that the lines of Feynman’s diagrams become dense in a certain sense and could be described as a 2d surface. This is, however, very different from the picture of strings as flux lines. Interestingly, even now people often don’t distinguish between these approaches. In fact, for the usual amplitudes Feynman’s diagrams don’t become dense and the flux lines picture is an appropriate one. However there are cases in which t’Hooft’s mechanism is really working.
Last revised on December 21, 2022 at 11:14:18. See the history of this page for a list of all contributions to it.