Unifying Structures in Higher Spin Gauge Symmetry
Abstract:
Consider a set of free gauge fields together with their field equations
and possibly a unifying action integrated over all of them. Then
considering the problem of introducing interactions among such fields,
there has historically been two broad avenues of approach. One approach
entails "gauging" a non-Abelian global symmetry algebra, in the
process making it local. The other approach entails "deforming" an
already local but Abelian gauge algebra, in the process making it
non-Abelian. In cases where both avenues have been explored, such as for
spin 1 and 2 gauge fields, the results agree (barring conceptual and
technical issues) with Yang-Mills theory and Einstein gravity. In the
case of an infinite tower of higher spin gauge fields, the first
approach has been thoroughly developed and explored by M. Vasiliev,
whereas the second approach, after having lain dormant for a long time,
has received new attention by several authors lately. In the present
paper we briefly review some aspects of the history of higher spin gauge
fields as a backdrop to a first attempt at comparing the gauging vs.
deforming approaches. A common unifying structure of strongly homotopy
Lie algebras underlying both approaches will be elicited. The modern
deformation approach, using BRST-BV methods, will be decribed as far as
it is developed at the present time.