2,375 research outputs found
Spin and abelian electromagnetic duality on four-manifolds
We investigate the electromagnetic duality properties of an abelian gauge
theory on a compact oriented four-manifold by analysing the behaviour of a
generalised partition function under modular transformations of the
dimensionless coupling constants. The true partition function is invariant
under the full modular group but the generalised partition function exhibits
more complicated behaviour depending on topological properties of the
four-manifold concerned. It is already known that there may be "modular
weights" which are linear combinations of the Euler number and Hirzebruch
signature of the four-manifold. But sometimes the partition function transforms
only under a subgroup of the modular group (the Hecke subgroup). In this case
it is impossible to define real spinor wave functions on the four-manifold. But
complex spinors are possible provided the background magnetic fluxes are
appropriately fractional rather that integral. This gives rise to a second
partition function which enables the full modular group to be realised by
permuting the two partition functions, together with a third. Thus the full
modular group is realised in all cases. The demonstration makes use of various
constructions concerning integral lattices and theta functions that seem to be
of intrinsic interest.Comment: 29 pages, Plain Te
Orthogonal Decomposition of Some Affine Lie Algebras in Terms of their Heisenberg Subalgebras
In the present note we suggest an affinization of a theorem by Kostrikin
et.al. about the decomposition of some complex simple Lie algebras
into the algebraic sum of pairwise orthogonal Cartan subalgebras. We point out
that the untwisted affine Kac-Moody algebras of types ( prime,
), can be decomposed into
the algebraic sum of pairwise or\-tho\-go\-nal Heisenberg subalgebras. The
and cases are discussed in great detail. Some possible
applications of such decompositions are also discussed.Comment: 16 pages, LaTeX, no figure
Exact electromagnetic duality
This talk, given at several conferences and meetings, explains the background leading to the formulation of the exact electromagnetic duality conjecture believed to be valid in N=4 supersymmetric SU(2) gauge theory
Affine Toda Solitons and Vertex Operators
Affine Toda theories with imaginary couplings associate with any simple Lie
algebra generalisations of Sine Gordon theory which are likewise
integrable and possess soliton solutions. The solitons are \lq\lq created" by
exponentials of quantities which lie in the untwisted affine
Kac-Moody algebra and ad-diagonalise the principal Heisenberg
subalgebra. When is simply-laced and highest weight irreducible
representations at level one are considered, can be expressed as
a vertex operator whose square vanishes. This nilpotency property is extended
to all highest weight representations of all affine untwisted Kac-Moody
algebras in the sense that the highest non vanishing power becomes proportional
to the level. As a consequence, the exponential series mentioned terminates and
the soliton solutions have a relatively simple algebraic expression whose
properties can be studied in a general way. This means that various physical
properties of the soliton solutions can be directly related to the algebraic
structure. For example, a classical version of Dorey's fusing rule follows from
the operator product expansion of two 's, at least when is
simply laced. This adds to the list of resemblances of the solitons with
respect to the particles which are the quantum excitations of the fields.Comment: Imperial/TP/92-93/29 SWAT/92-93/5 PU-PH-93/1392, requires newma
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