Dynamical Symmetry and String Theory

Abstract

Dynamical symmetries and spectrum genererating algebras have found applications in many branches of physics. Franco Iachello has championed their applications in Nuclear Physics and has explored several other areas of physics by using ingenious schemes. One of the most effective methods for constructing solvable models of string theory can be viewed in the same light. The so called coset method for affine (KacMoody) algebras is, in fact, a “dynamical symmetry” in the spirit of Iachello’s work. After describing the method, I show how to use it to construct models of strings propagating in curved spacetime. Furthermore, as is known from Iachello’s work in Nuclear Physics, there is a relation between the geometry of the nucleus and the dynamical symmetry chain. Similarly in string theory there is an explicit relation between the geometry of spacetime and the algebraic coset chain, as I describe in this paper.