nLab
string bit model

Contents

Contents

Idea

A kind of analogue of lattice gauge theory for worldsheet computations in perturbative string theory/string scattering amplitudes.

Properties

Via single trace observables under AdS/CFT

From the point of view of AdS/CFT-duality, string bit observables are the incarnation of single trace observables on the CFT-side Berenstein-Maldacena-Nastase 02, p. 13.

More in detail:

The single trace operators/observables in conformal field theories such as super Yang-Mills theories play a special role in the AdS-CFT correspondence: They correspond to single string excitations on the AdS-supergravity side of the correspondence, where, curiously, the “string of characters/letters” in the argument of the trace gets literally mapped to a superstring in spacetime (see the references below).

From Polyakov 02, referring to gauge fields and their single trace operators as letter and words, respectively:

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.

From Berenstein-Maldacena-Nastase 02, who write ZZ for the elementary field observables (“letters”) Φ\mathbf{\Phi} above:

In summary, the “string of ZZs” becomes the physical string and that each ZZ carries one unit of JJ which is one unit of p +p_+. Locality along the worldsheet of the string comes from the fact that planar diagrams allow only contractions of neighboring operators. So the Yang Mills theory gives a string bit model where each bit is a ZZ operator.

On the CFT side these BMN operators of fixed length (of “letters”) are usefully identified as spin chains which, with the dilatation operator regarded as their Hamiltonian, are integrable systems (Minahan-Zarembo 02, Beisert-Staudacher 03).

This integrability allows a detailed matching between

under AdS/CFT duality (Beisert-Frolov-Staudacher-Tseytlin 03, …). For review see BBGK 04, Beisert et al. 10.

References

The idea originates with

It is made explicit in

Review includes

Further developments include the following:

Last revised on December 8, 2019 at 13:07:20. See the history of this page for a list of all contributions to it.