Supergravity-matter actions in three dimensions and Chern-Simons terms

We study off-shell N-extended Yang-Mills multiplets coupled to conformal supergravity in three spacetime dimensions. Superform formulations are presented for the non-Abelian Chern-Simons actions in the cases N=1, 2, 3, and the corresponding component actions are explicitly worked out. Such a Chern-Simons action does not exist for N=4. In the latter case, a superform formulation is given for the BF term that describes the coupling of two Abelian vector multiplets with self-dual and anti-self-dual superfield strengths respectively. The superform results obtained are used to construct linear multiplet action principles in the cases N=2, 3, 4. The N=3 and N=4 actions are demonstrated to be universal in the sense that all known off-shell supergravity-matter systems (with the exception of pure conformal supergravity) may be described using such an action. Starting from the N=3 and N=4 Abelian vector multiplets, we also construct composite O(2) multiplets which are analogues of the four-dimensional construction of an N=2 reduced chiral scalar engineered from the improved tensor multiplet. Using these composites, we present the superfield equations of motion for N=3 and N=4 anti-de Sitter and topologically massive supergravity theories. We also sketch the construction of a large family of higher derivative couplings for N=3 and N=4 vector multiplets.Comment: 64 pages; V3: published versio

On curvature squared terms in N = 2 supergravity

We present the N = 2 supersymmetric completion of a scalar curvature squared term in a completely gauge independent form. We also elaborate on its component structure.Comment: 15 pages; V2: 17 pages, typos corrected, discussion comments and acknowledgement added; V3: published versio

On supersymmetric Chern-Simons-type theories in five dimensions

We present a closed-form expression for the supersymmetric non-Abelian Chern-Simons action in conventional five-dimensional N=1 superspace. Our construction makes use of the superform formalism to generate supersymmetric invariants. Similar ideas are applied to construct supersymmetric actions for off-shell supermultiplets with an intrinsic central charge. In particular, the large tensor multiplet is described in superspace for the first time.Comment: 26 pages; V2: comments added and typos corrected, published versio

New superconformal multiplets and higher derivative invariants in six dimensions

Within the framework of six-dimensional ${\cal N}=(1,0)$ conformal supergravity, we introduce new off-shell multiplets ${\cal O}{}^{*}(n)$, where $n=3,4,\dots,$ and use them to construct higher-rank extensions of the linear multiplet action. The ${\cal O}{}^{*}(n)$ multiplets may be viewed as being dual to well-known superconformal ${\cal O}(n)$ multiplets. We provide prepotential formulations for the ${\cal O}(n)$ and ${\cal O}{}^{*}(n)$ multiplets coupled to conformal supergravity. For every ${\cal O}{}^{*}(n)$ multiplet, we construct a higher derivative invariant which is superconformal on arbitrary superconformally flat backgrounds. We also show how our results can be used to construct new higher derivative actions in supergravity.Comment: 17 pages; V2: comments and reference adde

Symmetries of curved superspace in five dimensions

We develop a formalism to construct supersymmetric backgrounds within the superspace formulation for five-dimensional (5D) conformal supergravity given in arXiv:0802.3953. Our approach is applicable to any off-shell formulation for 5D minimal Poincare and anti-de Sitter supergravity theories realized as the Weyl multiplet coupled with two compensators. For those superspace backgrounds which obey the equations of motion for (gauged) supergravity, we naturally reproduce the supersymmetric solutions constructed a decade ago by Gauntlett et al. For certain supersymmetric backgrounds with eight supercharges, we construct a large family of off-shell supersymmetric sigma models such that the superfield Lagrangian is given in terms of the Kahler potential of a real analytic Kahler manifold.Comment: 47 pages; V2: references added, minor modifications, published versio

Aristotle\u27s Topics and informal reasoning

The modern tradition of informal logic has relied heavily on accepting, modifying, or criticizing the patterns of reasoning mentioned in Aristotle\u27s Sophistical Refutations. However, already in 1971, Stachowiak focussed his attention on the muc h neglected Topics and enumerated in his work, Rationalismus im Ursprung some of the Aristotelian rules governing the formation of definitions and principles for correct reasoning. The paper will try to examine how these principles might ap ply to informal arguments today

Higher derivative couplings and massive supergravity in three dimensions

We develop geometric superspace settings to construct arbitrary higher derivative couplings (including R^n terms) in three-dimensional supergravity theories with N=1,2,3 by realising them as conformal supergravity coupled to certain compensators. For all known off-shell supergravity formulations, we construct supersymmetric invariants with up to and including four derivatives. As a warming-up exercise, we first give a new and completely geometric derivation of such invariants in N=1 supergravity. Upon reduction to components, they agree with those given in arXiv:0907.4658 and arXiv:1005.3952. We then carry out a similar construction in the case of N=2 supergravity for which there exist two minimal formulations that differ by the choice of compensating multiplet: (i) a chiral scalar multipet; (ii) a vector multiplet. For these formulations all four derivative invariants are constructed in completely general and gauge independent form. For a general supergravity model (in the N=1 and minimal N=2 cases) with curvature-squared and lower order terms, we derive the superfield equations of motion, linearise them about maximally supersymmetric backgrounds and obtain restrictions on the parameters that lead to models for massive supergravity. We use the non-minimal formulation for N = 2 supergravity (which corresponds to a complex linear compensator) to construct a novel consistent theory of massive supergravity. In the case of N = 3 supergravity, we employ the off-shell formulation with a vector multiplet as compensator to construct for the first time various higher derivative invariants. These invariants may be used to derive models for N = 3 massive supergravity. As a bi-product of our analysis, we also present superfield equations for massive higher spin multiplets in (1,0), (1,1) and (2,0) anti-de Sitter superspaces.Comment: 84 pages; V3: references added, minor modifications, published versio

The anomalous current multiplet in 6D minimal supersymmetry

For supersymmetric gauge theories with eight supercharges in four, five and six dimensions, a conserved current belongs to the linear multiplet. In the case of six-dimensional $\cal N=(1,0)$ Poincar\'e supersymmetry, we present a consistent deformation of the linear multiplet which describes chiral anomalies. This is achieved by developing a superform formulation for the deformed linear multiplet. In the abelian case, we compute a nonlocal effective action generating the gauge anomaly.Comment: 27 pages; V2: published versio

Chiral anomalies in six dimensions from harmonic superspace

We develop a superfield approach to compute chiral anomalies in general ${\cal N}=(1,0)$ supersymmetric gauge theories in six dimensions. Within the harmonic-superspace formulation for these gauge theories, the anomalous contributions to the effective action only come from matter and ghost hypermultiplets. By studying the short-distance behaviour of the propagator for the hypermultiplet coupled to a background vector multiplet, we compute the covariant and consistent chiral anomalies. We also provide a superform formulation for the non-abelian anomalous current multiplet in general ${\cal N}=(1,0)$ supersymmetric gauge theories.Comment: 33 page