Actions for (2,1) sigma models and strings

Hull, C.M.

doi:10.1016/S0550-3213(97)00492-6

Actions for (2,1) sigma models and strings

C.M. Hull
(
- Queen Mary, U. of London and
- Newton Inst. Math. Sci., Cambridge
)

Feb, 1997

32 pages

Published in:

Nucl.Phys.B 509 (1998) 252-272

e-Print:

hep-th/9702067 [hep-th]

DOI:

10.1016/S0550-3213(97)00492-6

Report number:

QMW-97-2,
NI-97005

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Abstract:

Effective actions are derived for (2,0) and (2,1) superstrings by studying the corresponding sigma-models. The geometry is a generalisation of Kahler geometry involving torsion and the field equations imply that the curvature with torsion is self-dual in four dimensions, or has SU(n,m) holonomy in other dimensions. The Yang-Mills fields are self-dual in four dimensions and satisfy a form of the Uhlenbeck-Yau equation in higher dimensions. In four dimensions with Euclidean signature, there is a hyperkahler structure and the sigma-model has (4,1) supersymmetry, while for signature (2,2) there is a hypersymplectic structure consisting of a complex structure squaring to -1 and two real structures squaring to 1. The theory is invariant under a twisted form of the (4,1) superconformal algebra which includes an SL(2,R) Kac-Moody algebra instead of an SU(2) Kac-Moody algebra. Kahler and related geometries are generalised to ones involving real structures.

Note:

32 pages, phyzzx macro Report-no: QMW-97-2. NI97005

sigma model: nonlinear
dimension: 2
supersymmetry: superspace
field theory: Kaehler
torsion
gauge field theory: Yang-Mills
string model

References(23)

Figures(0)

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