An Infinite Dimensional Symmetry Algebra in String Theory

Details An Infinite Dimensional Symmetry Algebra in String Theory An Infinite Dimensional Symmetry Algebra in String Theory

1994-01-15

arxiv.org/abs/hep-th/9401075v1

Phys.Rev.D50:4022-4031,1994

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, Plain TeX, report RU93-8, CTP-TAMU-2/94, CERN-TH.7022/93

Scientific paper

10.1103/PhysRevD.50.4022

Symmetry transformations of the space-time fields of string theory are generated by certain similarity transformations of the stress-tensor of the associated conformal field theories. This observation is complicated by the fact that, as we explain, many of the operators we habitually use in string theory (such as vertices and currents) have ill-defined commutators. However, we identify an infinite-dimensional subalgebra whose commutators are not singular, and explicitly calculate its structure constants. This constitutes a subalgebra of the gauge symmetry of string theory, although it may act on auxiliary as well as propagating fields. We term this object a {\it weighted tensor algebra}, and, while it appears to be a distant cousin of the $W$-algebras, it has not, to our knowledge, appeared in the literature before.

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