Six-dimensional (1,0) superconformal models and higher gauge theory (original) (raw)
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š© = 8 superconformal gauge theories and M 2 branes
Journal of High Energy Physics, 2009
Based on recent developments, in this letter we find 2 + 1 dimensional gauge theories with scale invariance and N = 8 supersymmetry. The gauge theories are defined by a lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. The theories are parity invariant and do not admit any tunable coupling constant. In the case of SU(N) the moduli space of vacua contains a branch of the form (R 8) N /S N. These properties are expected for the field theory living on a stack of M2 branes.
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Script N = 8 superconformal gauge theories and M2 branes
Journal of High Energy Physics, 2009
Based on recent developments, in this letter we find 2+1 dimensional gauge theories with scale invariance and N=8 supersymmetry. The gauge theories are defined by a Lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. The theories are parity invariant and do not admit any tunable coupling constant. In the case of SU(N) the moduli space of vacua contains a branch of the form (R^8)^N/S_N. These properties are expected for the field theory living on a stack of M2 branes.
Letters in Mathematical Physics - LETT MATH PHYS, 2000
We construct unitary representations of (1,0) and (2,0) superconformal algebras in six dimensions by using superfields defined on harmonic superspaces with coset manifolds USp(2n)/[U(1)]n, n=1, 2. In the spirit of the AdS7/CFT6 correspondence, massless conformal fields correspond to āsupersingletonsā in AdS7. By tensoring them we produce all short representations corresponding to 1/2 and 1/4 BPS anti-de Sitter bulk states of which āmassless bulkā representations are particular cases.
Aspects of superconformal field theories in six dimensions
Journal of High Energy Physics, 2004
We introduce the analytic superspace formalism for six-dimensional (N, 0) superconformal field theories. Concentrating on the (2, 0) theory we write down the Ward identities for correlation functions in the theory and show how to solve them. We then consider the four-point function of four energy momentum multiplets in detail, explicitly solving the Ward identities in this case. We expand the four-point function using both Schur polynomials, which lead to a simple formula in terms of a single function of two variables, and (a supersymmetric generalisation of) Jack polynomials, which allow a conformal partial wave expansion. We then perform a complete conformal partial wave analysis of both the free theory four-point function and the AdS dual four-point function. We also discuss certain operators at the threshold of the series a) unitary bound, and prove that some such operators can not develop anomalous dimensions, by finding selection rules for certain three-point functions. For those operators which are not protected, we find representations with which they may combine to become long.
(1,0) superconformal models in six dimensions
Journal of High Energy Physics, 2011
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.
Local supersymmetry, superconformal algebra in two dimensions and strings in background fields
Physics Letters B, 1989
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Supersymmetric gauge theories in five and six dimensions
Physics Letters B, 1997
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