Conformal aspects of Spinor–Vector duality

Duality and conformal structure

In four dimensions, two metrics that are conformally related define the same Hodge dual operator on the space of two-forms. The converse, namely, that two metrics that have the same Hodge dual are conformally related, is established. This is true for metrics of arbitrary (nondegenerate) signature. For Euclidean signature a stronger result, namely, that the conformal class of the metric is compl...

Local Langlands Duality and a Duality of Conformal Field Theories

We show that the numerical local Langlands duality for GLn and the T-duality of twodimensional quantum gravity arise from one and the same symmetry principle. The unifying theme is that the local Fourier transform in both its `-adic and complex incarnation gives rise to symmetries of arithmetic and geometric local Langlands parameters.

Conformal Aspects of QCD∗

Theoretical and phenomenological evidence is now accumulating that the QCD coupling becomes constant at small virtuality; i.e., αs(Q ) develops an infrared fixed point in contradiction to the usual assumption of singular growth in the infrared. For example, the hadronic decays of the τ lepton can be used to determine the effective charge ατ (m 2 τ ′) for a hypothetical τ -lepton with mass in th...

Aspects of Electromagnetic Duality

I briefly try to give a critical assessment of this idea, discussing what it means, the extent to which it is true, and how it relates to other ideas in mathematics and physics. Examples of related physical concepts concern solitons and integrability in space-times of two dimensions, supersymmetry, superstring theory, and so on. Relevant mathematical developments appear to be the Atiyah-Singer ...

Mathematical Aspects of String Duality