Description

One of the first succesful attempts for unification of forces was Maxwell's theory of electromagnetism. Maxwell managed to put on equal footing the electric and magnetic fields. Kaluza (1921) and Klein (1926) proposed that electromagnetism in four space-time dimensions was in fact nothing but the interpretation of a gravitational force that lived in a five dimensional world. The only assumption is that the extra dimension should be compact, a circle. It was later shown that indeed, the four dimensional electromagnetic and gravitational fields can be cast as components of a five dimensional gravitational field. However, consistency of the five dimensional theory predicted the existence of an extra scalar field in four dimensions.

In more recent years, after the discovery of superstring and M theory in ten and eleven space-time dimensions, Kaluza-Klein theory was revived. With string theory viewed as the fundamental theory, four dimensional theories are built by essentially applying the ideas Kaluza and Klein on six dimensional manifolds. At a more fundamental level, the same set of ideas has helped us understand a big web of dualities between the seemingly different five superstring theories and M theory.

The students involved in the project will have the opportunity to learn the general concepts of Kaluza-Klein theory and at the same time explore some of its applications in string theory and supergravity.

Prerequisites:

• Mathematical Physics II
• Differential Geometry III is recommended but not required

Corequisites:

• General Relativity IV

Resources:

• For a brief introduction to the concepts see the Wiki pages
• A nice overview article on the history of Kaluza-Klein theory by E. Witten
• An excellent set of notes by C. Pope

• T. Appelquist, A. Chodos, and P. G. O. Freund, eds., Modern Kaluza-Klein Theories (Addison-Wesley, 1987)