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Register a new userSuper-Weyl invariance in 5D supergravity
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Gabriele Tartaglino-Mazzucchelli
Publication date
2008
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English
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We propose a superspace formulation for the Weyl multiplet of N=1 conformal supergravity in five dimensions. The corresponding superspace constraints are invariant under super-Weyl transformations generated by a real scalar parameter. The minimal supergravity multiplet, which was introduced by Howe in 1981, emerges if one couples the Weyl multiplet to an Abelian vector multiplet and then breaks the super-Weyl invariance by imposing the gauge condition W=1, with W the field strength of the vector multiplet. The geometry of superspace is shown to allow the existence of a large family of off-shell supermultiplets that possess uniquely determined super-Weyl transformation laws and can be used to describe supersymmetric matter. Many of these supermultiplets have not appeared within the superconformal tensor calculus. We formulate a manifestly locally supersymmetric and super-Weyl invariant action principle. In the super-Weyl gauge W=1, this action reduces to that constructed in arXiv:0712.3102. We also present a superspace formulation for the dilaton Weyl multiplet.
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In both ${cal N}=1$ and ${cal N}=2$ supersymmetry, it is known that $mathsf{Sp}(2n, {mathbb R})$ is the maximal duality group of $n$ vector multiplets coupled to chiral scalar multiplets $tau (x,theta) $ that parametrise the Hermitian symmetric space $mathsf{Sp}(2n, {mathbb R})/ mathsf{U}(n)$. If the coupling to $tau$ is introduced for $n$ superconformal gauge multiplets in a supergravity background, the action is also invariant under super-Weyl transformations. Computing the path integral over the gauge prepotentials in curved superspace leads to an effective action $Gamma [tau, bar tau]$ with the following properties: (i) its logarithmically divergent part is invariant under super-Weyl and rigid $mathsf{Sp}(2n, {mathbb R})$ transformations; (ii) the super-Weyl transformations are anomalous upon renormalisation. In this paper we describe the ${cal N}=1$ and ${cal N}=2$ locally supersymmetric induced actions which determine the logarithmically divergent parts of the corresponding effective actions. In the ${cal N}=1$ case, superfield heat kernel techniques are used to compute the induced action of a single vector multiplet $(n=1)$ coupled to a chiral dilaton-axion multiplet. We also describe the general structure of ${cal N}=1$ super-Weyl anomalies that contain weight-zero chiral scalar multiplets $Phi^I$ taking values in a Kahler manifold. Explicit anomaly calculations are carried out in the $n=1$ case.
This paper is a companion to our earlier work arXiv:0710.3440 in which the projective superspace formulation for matter-coupled simple supergravity in five dimensions was presented. For the minimal multiplet of 5D N=1 supergravity introduced by Howe in 1981, we give a complete solution of the Bianchi identities. The geometry of curved superspace is shown to allow the existence of a large family of off-shell supermultiplets that can be used to describe supersymmetric matter, including vector multiplets and hypermultiplets. We formulate a manifestly locally supersymmetric action principle. Its natural property turns out to be the invariance under so-called projective transformations of the auxiliary isotwistor variables. We then demonstrate that the projective invariance allows one to uniquely restore the action functional in a Wess-Zumino gauge. The latter action is well-suited for reducing the supergravity-matter systems to components.
We revisit supersymmetric solutions to five dimensional ungauged N=1 supergravity with dynamic hypermultiplets. In particular we focus on a truncation to the axion-dilaton contained in the universal hypermultiplet. The relevant solutions are fibrations over a four-dimensional Kahler base with a holomorphic axion-dilaton. We focus on solutions with additional symmetries and classify Killing vectors which preserve the additional structure imposed by supersymmetry; in particular we extend the existing classification of solutions with a space-like U(1) isometry to the case where the Killing vector is rotational. We elaborate on general geometrical aspects which we illustrate in some simple examples. We especially discuss solutions describing the backreaction of M2-branes, which for example play a role in the black hole deconstruction proposal for microstate geometries.
The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse) diffeomorphisms, linearized Weyl rescalings, and conformal transformations.
We study 5-dimensional supergravity on S^1/Z_2 with a physical Z_2-odd vector multiplet, which yields an additional modulus other than the radion. We derive 4-dimensional effective theory and find additional terms in the Kahler potential that are peculiar to the multi moduli case. Such terms can avoid tachyonic soft scalar masses at tree-level, which are problematic in the single modulus case. We also show that the flavor structure of the soft terms are different from that in the single modulus case when hierarchical Yukawa couplings are generated by wavefunction localization in the fifth dimension. We present a concrete model that stabilizes the moduli at a supersymmetry breaking Minkowski minimum, and show the low energy sparticle spectrum.
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