(1,0) superconformal models in six dimensions

Journal of High Energy Physics (Impact Factor: 5.62). 08/2011; DOI: 10.1007/JHEP12(2011)062
Source: arXiv

ABSTRACT We construct six-dimensional (1,0) superconformal models with non-abelian
gauge couplings for multiple tensor multiplets. A crucial ingredient in the
construction is the introduction of three-form gauge potentials which
communicate degrees of freedom between the tensor multiplets and the Yang-Mills
multiplet, but do not introduce additional degrees of freedom. Generically
these models provide only equations of motions. For a subclass also a
Lagrangian formulation exists, however it appears to exhibit indefinite metrics
in the kinetic sector. We discuss several examples and analyze the excitation
spectra in their supersymmetric vacua. In general, the models are
perturbatively defined only in the spontaneously broken phase with the vev of
the tensor multiplet scalars serving as the inverse coupling constants of the
Yang-Mills multiplet. We briefly discuss the inclusion of hypermultiplets which
complete the field content to that of superconformal (2,0) theories.

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    ABSTRACT: We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0) supersymmetric non-Abelian constraint equations containing the tensor multiplet. We also demonstrate how this construction leads to constraint equations for non-Abelian supersymmetric self-dual strings.
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    ABSTRACT: We first review self-dual (chiral) gauge field theories by studying their Lorentz non-covariant and Lorentz covariant formulations. Then, we construct a non-Abelian self-dual two-form gauge theory in six dimensions with a spatial direction compactified on a circle. This model reduces to the Yang-Mills theory in five dimensions for a small compactified radius R. This model also reduces to the Lorentz-invariant Abelian self-dual two-form theory when the gauge group is Abelian. The model is expected to describe multiple 5-branes in M-theory. We will discuss its decompactified limit, covariant formulation, BRST-antifield quantization and other generalizations.
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    ABSTRACT: We present a self-dual non-Abelian N=1 supersymmetric tensor multiplet in D=2+2 space-time dimensions. Our system has three on-shell multiplets: (i) The usual non-Abelian Yang-Mills multiplet (A_\mu{}^I, \lambda{}^I) (ii) A non-Abelian tensor multiplet (B_{\mu\nu}{}^I, \chi^I, \varphi^I), and (iii) An extra compensator vector multiplet (C_\mu{}^I, \rho^I). Here the index I is for the adjoint representation of a non-Abelian gauge group. The duality symmetry relations are G_{\mu\nu\rho}{}^I = - \epsilon_{\mu\nu\rho}{}^\sigma \nabla_\sigma \varphi^I, F_{\mu\nu}{}^I = + (1/2) \epsilon_{\mu\nu}{}^{\rho\sigma} F_{\rho\sigma}{}^I, and H_{\mu\nu}{}^I = +(1/2) \epsilon_{\mu\nu}{\rho\sigma} H_{\rho\sigma}{}^I, where G and H are respectively the field strengths of B and C. The usual problem with the coupling of the non-Abelian tensor is avoided by non-trivial Chern-Simons terms in the field strengths G_{\mu\nu\rho}{}^I and H_{\mu\nu}{}^I. For an independent confirmation, we re-formulate the component results in superspace. As applications of embedding integrable systems, we show how the {\cal N} = 2, r = 3 and {\cal N} = 3, r = 4 flows of generalized Korteweg-de Vries equations are embedded into our system.
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