String Dualities and M-Theory
The five superstring theories which we have encountered so far will be argued to be different perturbative limits of one underlying theory, connected via a web of perturbative and non-perturbative dualities. We will discuss the concept of dualities and th
- PDF / 1,006,239 Bytes
- 100 Pages / 439.36 x 666.15 pts Page_size
- 69 Downloads / 181 Views
String Dualities and M-Theory
Abstract The five superstring theories which we have encountered so far will be argued to be different perturbative limits of one underlying theory, connected via a web of perturbative and non-perturbative dualities. We will discuss the concept of dualities and the role of BPS states in establishing non-perturbative dualities. We construct brane solutions of supergravity, discuss their BPS properties and identify those carrying R-R charge as D-branes. We discuss the place of eleven-dimensional supergravity in this duality web and the self-consistent evidence for the existence of a so far unknown eleven-dimensional quantum gravity theory, called M-theory. The known facts include that its low-energy effective field theory is given by elevendimensional supergravity and that it contains membranes and five-branes, which upon compactification are related to the branes of string theory. Two examples of the power of dualities will be discussed in the final two sections: F -theory, an interesting class of non-perturbative compactifications of type IIB string theory and the AdS-CFT correspondence. They derive their appeal and usefulness from the fact that non-perturbative effects can be related to simple geometric structures.
18.1 General Remarks A well known example of a duality is the particle-wave duality of quantum mechanics: depending on the experiment, either the particle or the wave aspect of light or matter gives the simpler description. In general, duality means an exact quantum equivalence between two theories T and TQ , which thus really represent only one theory, albeit in different guises. To establish such a duality we must (1) identify the pair of theories which are proposed to be dual to each other and (2) find the duality map T $ TQ . Dualities in quantum field field theory and string theory are very intricate: T and TQ generally have different microscopic degrees of freedom and they have different actions. One of the attractive features of duality symmetries in string and field theory is that what is an emergent phenomenon in T , might be fundamental in TQ , and vice versa. R. Blumenhagen et al., Basic Concepts of String Theory, Theoretical and Mathematical Physics, DOI 10.1007/978-3-642-29497-6 18, © Springer-Verlag Berlin Heidelberg 2013
675
676
18 String Dualities and M-Theory
A field theoretical duality which we have already encountered is the duality between a free complex world-sheet fermion and a chiral boson . The twodimensional world-sheet actions of these two theories indeed look very different. The map between the elementary fields appearing R z in the two actions is via bosonization: .z/ DW e i .z/ W and .z/ D i d w W .w/ W . These two relations demonstrate an important feature of a duality: the elementary fields of one theory might be a coherent superposition of the fields of the other theory or the relation might be a non-local one. All calculations of this c D 1 CFT can be done in either representation. They are quantum equivalent and the duali
Data Loading...
