Non-critical string theory: Difference between revisions

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The '''non-critical string theory''' describes the relativistic string without enforcing the critical dimension. Although this allows the construction of a string theory in 4 spacetime dimensions, such a theory usually does not describe a Lorentz invariant background. However, there are recent developments which make possible

[[Non-critical_string_theorycritical string theory:_Lorentz_invariance Lorentz invariance|Lorentz invariant quantization]]

of string theory in 4-dimensional Minkowski space-time.

There are several applications of the non-critical string. Through the [[AdS/CFT correspondence]] it provides a holographic description of gauge theories which are asymptotically free.{{FactCitation needed|date=February 2007}} It may then have applications to the study of the [[Quantum chromodynamics|QCD]], the theory of strong interactions between [[quarks]]. Another area of much research is two-dimensional string theory which provides simple [[toy model]]s of [[string theory]]. There also exists a [[string duality|duality]] to the 3-dimensional [[Ising model]].{{FactCitation needed|date=February 2007}}

== The critical dimension and central charge ==

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== Two-dimensional string theory ==

Perhaps the most studied example of non-critical string theory is that with two-dimensional target space. While clearly not of phenomenological interest, string theories in two dimensions serve as important toy models. They allow one to probe interesting concepts which would be computationally intractable in a more realistic scenario.

These models often have fully non-perturbative descriptions in the form of the quantum mechanics of large matrices. Such a description known as the c=1 matrix model captures the dynamics of [[bosonic string theory]] in two dimensions. Of much recent interest are matrix models of the two-dimensional [[Type 0 string theory|Type 0 string theories]]. These "matrix models" are understood as describing the dynamics of [[open string (physics)|open string]]s lying on [[D-branes]] in these theories. Degrees of freedom associated with [[closed string]]s, and [[spacetime]] itself, appear as emergent phenomena, providing an important example of open string [[tachyon condensation]] in string theory.

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** Vol. 1: An introduction to the bosonic string. ISBN 0-521-63303-6.

** Vol. 2: Superstring theory and beyond. ISBN 0-521-63304-4.

* A. M. Polyakov, Phys. Lett. B 103 (1981) 207, Phys. Lett. B 103 (1981) 211.

* T. L. Curtright and C. B. Thorn, Phys. Rev. Lett. 48 (1982) 1309 [Erratum-ibid. 48 (1982) 1768].