Superconformal 6D (2,0) theories in superspace (original) (raw)
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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 supertwistors and conformal supergravity in six dimensions
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
The local supertwistor formalism, which involves a superconformal connection acting on the bundle of such objects over superspace, is used to investigate superconformal geometry in six dimensions. The geometry corresponding to (1, 0) and (2, 0) off-shell conformal supergravity multiplets, as well the associated finite super-Weyl transformations, are derived.
(2, 0) tensor multiplets and conformal supergravity in D= 6
We construct the supercurrent multiplet that contains the energy-momentum tensor of the (2, 0) tensor multiplet. By coupling this multiplet of currents to the fields of conformal supergravity, we first construct the linearized superconformal transformations rules of the (2, 0) Weyl multiplet. Next, we construct the full non-linear transformation rules by gauging the superconformal algebra OSp(8 * |4). We then use this result to construct the full equations of motion of the tensor multiplet in a conformal supergravity background. Coupling N + 5 copies of the tensor multiplet to conformal supergravity and imposing a geometrical constraint on the scalar fields which fixes the conformal symmetry, we obtain the coupling of (2, 0) Poincaré supergravity to N tensor multiplets in which the physical scalars parametrize the coset SO(N, 5)/(SO(N) × SO(5)).
Six-dimensional (1,0) superconformal models and higher gauge theory
Journal of Mathematical Physics, 2013
We analyze the gauge structure of a recently proposed superconformal field theory in six dimensions. We find that this structure amounts to a weak Courant-Dorfman algebra, which, in turn, can be interpreted as a strong homotopy Lie algebra. This suggests that the superconformal field theory is closely related to higher gauge theory, describing the parallel transport of extended objects. Indeed we find that, under certain restrictions, the field content and gauge transformations reduce to those of higher gauge theory. We also present a number of interesting examples of admissible gauge structures such as the structure Lie 2-algebra of an abelian gerbe, differential crossed modules, the 3-algebras of M2-brane models and string Lie 2-algebras.
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 ‘supersingletons’ 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 ‘massless bulk’ representations are particular cases.
Manifestly supersymmetric extensions of (curvature)2-terms in six-dimensional N = 2 supergravity
Physics Letters B, 1986
A systematic and manifestly supersymmetric procedure for supersymmetrization of general (curvature)2-terms in N 2 supergravity in six dimensions (D = 6) is presented in superspace. The general form of new terms for the supersymmetrization in supertranslation rules is given. As a by-product, the superspace structure of quaternionic K~thler manifolds is elucidated. Our method is the D = 6 application of our previously established formulation for the D = 10. N-1 supergravity with the O(a') superstring corrections.
Using superconformal tensor calculus we construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. We start from the superconformal algebra which we realize on a 40+40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40+40 version of the Weyl multiplet. We also obtain a 48+48 off-shell formulation of Poincar6 supergravity coupled to a tensor multiplet.
Superconformal tensor calculus and matter couplings in six dimensions
Nuclear Physics B, 1986
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