Global spinors and orientable five-branes | Zendy

Jussi Kalkkinen | Zendy

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Global spinors and orientable five-branes

Author(s) -

Jussi Kalkkinen

Publication year - 2006

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2006/09/028

Subject(s) - tangent bundle , spinor , spin (aerodynamics) , mathematics , cohomology , manifold (fluid mechanics) , brane , spin structure , normal bundle , brane cosmology , pure mathematics , twist , modulo , physics , theoretical physics , mathematical physics , tangent space , vector bundle , geometry , quantum mechanics , combinatorics , mechanical engineering , antiferromagnetism , engineering , thermodynamics

Fermion fields on an M-theory five-brane carry a representation of the doublecover of the structure group of the normal bundle. It is shown that, on anarbitrary oriented Lorentzian six-manifold, there is always an Sp(2) twist thatallows such spinors to be defined globally. The vanishing of the arisingpotential obstructions does not depend on spin structure in the bulk, nor doesthe six-manifold need to be spin or spin-C. Lifting the tangent bundle to sucha generalised spin bundle requires picking a generalised spin structure interms of certain elements in the integral and modulo-two cohomology of thefive-brane world-volume in degrees four and five, respectively.Comment: 18 pages, LaTeX; v2: version to appear in JHE

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