Bojko Bakalov et al 2008 J. Phys. A: Math. Theor. 41 194002 doi:10.1088/1751-8113/41/19/194002
Infinite-dimensional Lie algebras in 4D conformal quantum field theory*
Bojko Bakalov1, Nikolay M Nikolov2, Karl-Henning Rehren2,3 and Ivan Todorov2
Show affiliationsThe concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of two-dimensional chiral conformal field theory, to a higher (even) dimensional spacetime. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, VM(x, y), where the M span a finite dimensional real matrix algebra 
closed under transposition. The associative algebra 
is irreducible iff its commutant 
coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite-dimensional Lie algebra: a central extension of 
corresponding to the field 
of reals, of u(∞, ∞) associated with the field 
of complex numbers, and of so*(4∞) related to the algebra 
of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups O(N), U(N) and 
, respectively.
- Footnote
- PACS
- MSC
-
17B65 Infinite-dimensional Lie (super)algebras (See also 22E65)
81T40 Two-dimensional field theories, conformal field theories, etc.
- Subjects
- Dates
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Issue 19 (16 May 2008)
Received 9 November 2007, in final form 12 February 2008
Published 29 April 2008
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Infinite-dimensional Lie algebras in 4D conformal quantum field theory
Bojko Bakalov et al 2008 J. Phys. A: Math. Theor. 41 194002
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