Sergio Ferrara, Alex Kehagias, Dieter Lust
In these lectures we discuss N-extended conformal supergravity and its spectrum in four dimensions. These theories can be considered as the massless limit of Einstein-Weyl supergravity and by taking into account their enhanced gauge symmetries, we derive their massless spectrum, which in general contains a dipole-ghost graviton multiplet and an N-fold tripole-ghost gravitino multiplet.
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We construct an effective N=1 superfield description of five-dimensional conformal supergravity. By the use of this description, we reinterpret some physical systems such as Scherk-Schwarz supersymmetry breaking from the conformal supergravity viewpoint. We also show how to introduce a radion fluctuation mode in this framework.
We show that the anomaly-mediated supersymmetry breaking via the Kahler and sigma-model anomalies is suppressed by conformal dynamics in the supersymmetry breaking sector.
We reinterpret the Scherk-Schwarz (SS) boundary condition for SU(2)_R in a compactified five-dimensional (5D) Poincare supergravity in terms of the twisted SU(2)_U gauge fixing in 5D conformal supergravity. In such translation, only the compensator hypermultiplet is relevant to the SS twist, and various properties of the SS mechanism can be easily understood. Especially, we show the correspondence between the SS twist and constant superpotentials within our framework.
We consider the supergravity dual descriptions of non-conformal super Yang-Mills theories realized on the world-volume of Dp-branes. We use the dual description to compute stress-energy tensor and current correlators. We apply the results to the study of dilatonic brane-worlds described by non-conformal field theories coupled to gravity. We find that brane-worlds based on D4 and D5 branes exhibit a localization of gauge and gravitational fields. We calculate the corrections to the Newton and Coulomb laws in these theories.
In the context of a conformal Supergravity (SUGRA) model in the Einstein frame, in which the (next to) minimal supersymmetric standard model can embedded naturally to produce chaotic inflation scenarios, we study properties of gravitino in the cases where it is stable or unstable. In the latter case, we demonstrate that for large dilaton scale factors there is an enhanced magnitude of the gravitino width, when it decays to neutralino dark matter, as compared with the standard SUGRA case. In this context, we discuss the associated consequences as far as Big Bang Nucleosynthesis constraints and …
We discuss $N=2\to N=1$ reduction in four dimensional conformal supergravity. In particular, we keep the off-shell structure of supermultiplets (except hypermultiplets). As we will show, starting with (almost) off-shell conformal supergravity makes the procedure simpler than that from $N=2$ Poincaré supergravity, which makes it easier to show the correspondence to the standard $N=1$ conformal supergravity. We find that the $N=1$ superconformal symmetry is simply realized by truncating the gravitino multiplet. We also discuss the consistency with the original $N=2$ system and show the reduced $…
N=6 conformal supergravity in three dimensions is studied in an off-shell component field formulation. We obtain local symmetry transformation laws and a Lagrangian of the conformal supergravity multiplet. We then couple it to the ABJM theory and obtain local transformation laws and a Lagrangian of the coupled theory.
The conformal compensator formalism is a convenient and versatile representation of supergravity (SUGRA) obtained by gauge fixing conformal SUGRA. Unfortunately, practical calculations often require cumbersome manipulations of component field terms involving the full gravity multiplet. In this paper, we derive an alternative gauge fixing for conformal SUGRA which decouples these gravity complications from SUGRA computations. This yields a simplified tree-level action for the matter fields in SUGRA which can be expressed compactly in terms of superfields and a modified conformal compensator. Ph…
Effective superpotentials obtained by integrating out matter in super Yang-Mills and conformal supergravity backgrounds in N=1 SUSY theories are considered. The pure gauge and supergravity contributions (generalizing Veneziano-Yankielowicz terms) are derived by considering the case with matter fields in the fundamental representation of the gauge group. These contributions represent quantum corrections to the tree-level Yang-Mills and conformal supergravity actions. The classical equations of motion following from the conformal supergravity action require the background to be (super)conformall…
We develop a new off-shell formulation for six-dimensional conformal supergravity obtained by gauging the 6D ${\cal N} = (1, 0)$ superconformal algebra in superspace. This formulation is employed to construct two invariants for 6D ${\cal N} = (1, 0)$ conformal supergravity, which contain $C^3$ and $C\Box C$ terms at the component level. Using a conformal supercurrent analysis, we prove that these exhaust all such invariants in minimal conformal supergravity. Finally, we show how to construct the supersymmetric $F \Box F$ invariant in curved superspace.
Conformal supergravity arises in presently known formulations of twistor-string theory either via closed strings or via gauge-singlet open strings. We explore this sector of twistor-string theory, relating the relevant string modes to the particles and fields of conformal supergravity. We also use the twistor-string theory to compute some tree level scattering amplitudes with supergravitons, and compare to expectations from conformal supergravity. Since the supergravitons interact with the same coupling constant as the Yang-Mills fields, conformal supergravity states will contribute to loop am…
We construct the Dirac-Born-Infeld (DBI) action of a real linear multiplet in 4D $\mathcal{N}=1$ supergravity. Based on conformal supergravity, we derive the general condition under which the DBI action can be realized, and show that it can be constructed in the new minimal supergravity. We also generalize it to the matter coupled system.
Construction of a five dimensional conformal supergravity (D=5 CSG) is attempted by applying the AdS/CFT correspondence to the F(4) AdS supergravity in six dimensions. As a first step, local transformation laws of D=5 CSG have been established, from which the Weyl weights of the various fields in D=5 can be predicted.
We consider the role of N=4 conformal supergravity in the relation between N=4 SYM theory and D=5 gauged supergravity expanded near the Anti de Sitter background. We discuss the structure of the SYM effective action in conformal supergravity background, in particular, terms related to conformal anomaly. Solving the leading-order Dirichlet problem for the metric perturbation in AdS background we explicitly compute the bilinear graviton term in the D=5 Einstein action, demonstrating its equivalence to the linearized Weyl tensor squared part of the gravitational effective action induced by SYM th…
The physical states of N=4 conformal supergravity in four dimensions occur in twistor-string theory by Berkovits and Witten(hep-th/0406051). We study two alternative versions of twistor-string theory based on the B-model of weighted projective space WCP^{3|2} and based on a certain construction involving open strings. The spacetime fields described by the twistor superfields contain the physical states of N=1 conformal supergravity from above N=4 superspace approach.
The Bagger-Lambert-Gustavsson theory is coupled to an off-shell D=3, N=8 conformal supergravity background. Local transformation laws of the conformal supergravity multiplet are obtained from those of the D=4, N=8 SO(8) gauged supergravity. The complete Lagrangian and local transformation laws of the coupled theory are obtained. As an application the supercurrent multiplet in a flat background is obtained.
We consider conformal defect solutions in four dimensional $N=2$ gauged supergravity. These solutions are constructed as a warped product of $AdS_2\times S^1$ over an interval with non-trivial electric and magnetic fields. We show for minimal gauged supergravity and for gauged supergravity with vector multiplets and abelian gauging that supersymmetric defect solutions are only possible when the geometry has a conical defect in either the bulk or the boundary metric.
An off-shell formulation of two distinct tensor multiplets,a massive tensor multiplet and a tensor gauge multiplet, is presented in superconformal tensor calculus in five-dimensional space-time. Both contain a rank 2 antisymmetric tensor field, but there is no gauge symmetry in the former, while it is a gauge field in the latter. Both multiplets commonly have 4 bosonic and 4 fermionic {\em on-shell} modes, but the former consists of 16(boson)+16(fermion) component fields while the latter consists of 8(boson)+8(fermion) component fields.
We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plane-wave limit thereof. We then show how to define Yang-Mills theory with rigid supersymmetry on any supersymmetric conformal supergravity background and, in particular, on the maximally supersymmetric backgrounds. We conclude by commenting on a striking resemblance between the sup…
We consider an abelian N=4 super Yang-Mills theory coupled to background N=4 conformal supergravity fields. At the classical level, this coupling is invariant under global SU(1,1) transformation of the complex ("dilaton-axion") supergravity scalar combined with an on-shell vector-vector duality. We compute the divergent part of the corresponding quantum effective action found by integrating over the super Yang-Mills fields and demonstrate its SU(1,1) invariance. This divergent part related to the conformal anomaly is one-loop exact and should be given by the N=4 conformal supergravity action c…
The most general class of 4D N=4 conformal supergravity actions depends on a holomorphic function of the scalar fields that parametrize an SU(1,1)/U(1) coset space. The bosonic sector of these actions was presented in a letter [arXiv:1609.09083]. Here we provide the complete actions to all orders in the fermion fields. They rely upon a new N=4 density formula, which permits a direct but involved construction. This density formula also recovers the on-shell action for vector multiplets coupled to conformal supergravity. Applications of these results in the context of Poincaré supergravity are b…
We review the question of quantum consistency of N=4 conformal supergravity in 4 dimensions. The UV divergences and anomalies of the standard ("minimal") conformal supergravity where the complex scalar $ϕ$ is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to N=4 super Yang-Mills with gauge group of dimension 4. The same turns out to be true also for the "non-minimal" N=4 conformal supergravity with the action (recently constructed in arXiv:1609.09083) depending on an arbitrary holomorphic function $f(ϕ)$. The special case of the "non-minimal" conformal s…
We will use the covariant superform approach to develop a new density formula for $\mathcal{N}=2$ conformal supergravity which is based on a fermionic multiplet whose lowest component is a dimension-5/2 spinor. We will show that this density formula admits an embedding of the real scalar multiplet of [arXiv:1712.02309]. Upon using the embedding of the tensor multiplet into the real scalar multiplet, we will construct a new higher derivative action of the tensor multiplet in $\mathcal{N}=2$ conformal supergravity.
The superspace formulation of N=1 conformal supergravity in four dimensions is demonstrated to be equivalent to the conventional component field approach based on the superconformal tensor calculus. The detailed correspondence between two approaches is explicitly given for various quantities; superconformal gauge fields, curvatures and curvature constraints, general conformal multiplets and their transformation laws, and so on. In particular, we carefully analyze the curvature constraints leading to the superconformal algebra and also the superconformal gauge fixing leading to Poincare supergr…
We obtain three and four dimensional conformal field theories with less than maximal supersymmetry by using their supergravity duals. These supergravity theories are type II on $AdS_5 \times CP^2$, IIA on $AdS_4 \times CP^3$, IIB on $AdS_5 \times S^5/Z_k$ and D=11 supergravity on $AdS_4 \times S^7/Z_k$. They are obtained from the spherically compactified ten and eleven dimensional theories by either Hopf reduction or by winding the U(1) fiber over the base.
Exploring the role of conformal theories of gravity in string theory, we show that the minimal (N=2) gauged supergravities in five dimensions induce the multiplets and transformations of N=1 four dimensional conformal supergravity on the spacetime boundary. N=1 Poincare supergravity can be induced by explicitly breaking the conformal invariance via a radial cutoff in the 5d space. The AdS/CFT correspondence relates the maximal gauged supergravity in five dimensions to N=4 super Yang-Mills on the 4d spacetime boundary. In this context we show that the conformal anomaly of the gauge theory induc…
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 supergravit…
Based on the known non-linear transformation rules of the Weyl multiplet fields, the action of $N=4$ conformal supergravity is constructed up to terms quadratic in the fermion fields. The bosonic sector corrects a recent result in the literature.
We expand the generic model involving chiral matter, super Yang-Mills gauge fields, and supergravity to second order in the gravity and gauge prepotentials in a manifestly covariant and conformal way. Such a class of models includes conventional chiral matter coupled to supergravity via a conformal compensator. This is a first step toward calculating one-loop effects in supergravity in a way that does not require a perturbative expansion in the inverse Planck scale or a recourse to component level calculations to handle the coupling of the Kähler potential to the gravity sector. We also consid…
We present the action for a self-dual tensor in six dimensions, coupled to a (2,0) conformal supergravity background. This action gives rise to the expected equations of motion. An alternative look upon one of the gauge symmetries clarifies its role in the supersymmetry transformation rules and the realisation of the algebra.
This paper describes a fully covariant approach to harmonic superspace. It is based on the conformal superspace description of conformal supergravity and involves extending the supermanifold M^{4|8} by the tangent bundle of CP^1. The resulting superspace M^{4|8} x TCP^1 can be identified in a certain gauge with the conventional harmonic superspace M^{4|8} x S^2. This approach not only makes the connection to projective superspace transparent, but simplifies calculations in harmonic superspace significantly by eliminating the need to deal directly with supergravity prepotentials. As an applicat…
We study the rigid limit of 5d conformal supergravity with minimal supersymmetry on Riemannian manifolds. The necessary and sufficient condition for the existence of a solution is the existence of a conformal Killing vector. Whenever a certain $SU(2)$ curvature becomes abelian the backgrounds define a transversally holomorphic foliation. Subsequently we turn to the question under which circumstances these backgrounds admit a kinetic Yang-Mills term in the action of a vector multiplet. Here we find that the conformal Killing vector has to be Killing. We supplement the discussion with various ap…
Projective superspace provides a natural framework for the construction of actions coupling hypermultiplets to conformal supergravity. We review how the off-shell actions are formulated in superspace and then discuss how to eliminate the infinite number of auxiliary fields to produce an on-shell N=2 supersymmetric sigma model, with the target space corresponding to a generic 4n-dimensional hyperkahler cone. We show how the component action coupling the hypermultiplets to conformal supergravity may be constructed starting from curved superspace. The superspace origin of the geometric data -- th…
We construct the Dirac-Born-Infeld action in the context of N=1 conformal supergravity and its possible extensions including matter couplings. We especially focus on the Volkov-Akulov constraint, which is important to avoid ghost modes from the higher derivative terms. In the case with matter couplings, we find the modified D-term potential.
Conformal supergravity amplitudes are obtained from the double-copy construction using gauge-theory amplitudes, and compared to direct calculations starting from conformal supergravity Lagrangians. We consider several different theories: minimal ${\cal N}=4$ conformal supergravity, non-minimal ${\cal N}=4$ Berkovits-Witten conformal supergravity, mass-deformed versions of these theories, as well as supersymmetry truncations thereof. Coupling the theories to a Yang-Mills sector is also considered. For all cases we give the gravity Lagrangians that the double copy implicitly generates. The two m…
Using AdS/CFT correspondence we found the conformal anomaly from d3 and d5 gauged supergravity with single scalar (dilaton) and the arbitrary scalar potential on AdS-like scalar-gravitational background. Such dilatonic gravity action describes the special RG flows in extended gauged SG when scalars lie in one-dimensional submanifold of complete scalars space. This dilaton-dependent conformal anomaly corresponds to dual non-conformal (gauge) QFT (which is classically conformally invariant) with account of radiative corrections. Equations of motion in d5 gauged supergravity put some restrictions…
d3 and d5 maximally SUSY gauged supergravity is considered in the parametrization (flow) of full scalar coset where the kinetic term for scalars takes the standard field theory form and the bulk potential is an arbitrary one subject to consistent parametrization. From such SG duals we calculate d2 and d4 holographic conformal anomaly which depends on bulk scalars potential. AdS/CFT correspondence suggests that such SG side conformal anomaly should be identified with (non-perturbative) QFT conformal anomaly (taking account of radiative corrections) for the theory living on the boundary of AdS s…
In $D=4$, $\cal{N}=1$ conformal superspace, the Yang-Mills matter coupled supergravity system is constructed where the Yang-Mills gauge interaction is introduced by extending the superconformal group to include the Kähler isometry group of chiral matter fields. There are two gauge-fixing procedures to get to the component Poincaré supergravity: one via the superconformal component formalism and the other via the Poincaré superspace formalism. These two types of superconformal gauge-fixing conditions are analyzed in detail and their correspondence is clarified.
A chiral superfield strength in N=2 conformal supergravity at linearized level is obtained by acting two superspace derivatives on N=4 chiral superfield strength which can be described in terms of N=4 twistor superfields. By decomposing SU(4)_R representation of N=4 twistor superfields into the SU(2)_R representation with an invariant U(1)_R charge, the surviving N=2 twistor superfields contain the physical states of N=2 conformal supergravity. These N=2 twistor superfields are functions of homogeneous coordinates of weighted complex projective space WCP^{3|4} where the two weighted fermionic …
We consider Chern-Simons actions of Abelian tensor hierarchy of $p$-form gauge fields in four-dimensional ${\cal N}=1$ supergravity. Using conformal superspace formalism, we solve the constraints on the field strengths of the $p$-form gauge superfields in the presence of the tensor hierarchy. The solutions are expressed by the prepotentials of the $p$-form gauge superfields. We show the internal and superconformal transformation laws of the prepotentials. The descent formalism for the Chern-Simons actions is exhibited.
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.
We consider Abelian tensor hierarchy in four-dimensional ${\cal N}=1$ supergravity in the conformal superspace formalism, where the so-called covariant approach is used to antisymmetric tensor fields. We introduce $p$-form gauge superfields as superforms in the conformal superspace. We solve the Bianchi identities under the constraints for the superforms. As a result, each of form fields is expressed by a single gauge invariant superfield. The action of superforms is shown with the invariant superfields. We also show the relation between the superspace formalism and the superconformal tensor c…
We give an update on recent results about the matching between CFT operators and KK states in the AdS/CFT correspondence, and add some new comments on the realization of the baryonic symmetries from the supergravity point of view.
We use 4d ambitwistor string theory to derive new worldsheet formulae for tree-level conformal supergravity amplitudes supported on refined scattering equations. Unlike the worldsheet formulae for super-Yang-Mills or supergravity, the scattering equations for conformal supergravity are not in general refined by MHV degree. Nevertheless, we obtain a concise worldsheet formula for any number of scalars and gravitons which we lift to a manifestly supersymmetric formula using four types of vertex operators. The theory also contains states with non-plane wave boundary conditions and we show that th…
Using the off-shell formulation for N-extended conformal supergravity in three dimensions, which has recently been presented in arXiv:1305.3132, we construct superspace actions for conformal supergravity theories with N<6. For each of the cases considered, we work out the complete component action as well as the gauge transformation laws of the fields belonging to the Weyl supermultiplet. The N=1 and N=2 component actions derived coincide with those proposed by van Nieuwenhuizen and Rocek in the mid-1980s. The off-shell N=3, N=4 and N=5 supergravity actions are new results. Upon elimination of…
In the recent paper arXiv:1606.02921, the two invariant actions for 6D $N=(1,0)$ conformal supergravity were constructed in superspace, corresponding to the supersymmetrization of $C^3$ and $C\Box C$. In this paper, we provide the translation from superspace to the component formulation of superconformal tensor calculus, and we give the full component actions of these two invariants. As a second application, we build the component form for the supersymmetric $F\Box F$ action coupled to conformal supergravity. Exploiting the fact that the $N=(2,0)$ Weyl multiplet has a consistent truncation to …
N=2 conformal supergravity in five dimensions
本文通过六维 (2,0) 最大共形超引力的离壳约化构造五维 N=2 共形超引力，并解释其与 Nahm 分类不矛盾。
Starting from the 48+48 component multiplet of supercurrents for a rigid N=2 tensor multiplet in four spacetime dimensions, we obtain the transformation of the linearized supergravity multiplet which couples to this supercurrent multiplet. At the linearized level, this 48+48 component supergravity multiplet decouples into the 24+24 component linearized standard Weyl multiplet and a 24+24 component irreducible matter multiplet containing a real scalar field. By a consistent application of the supersymmetry algebra with field dependent structure constants appropriate to N=2 conformal supergravit…
We present a complete solution of the constraints for three-dimensional N=2 conformal supergravity in terms of unconstrained prepotentials. This allows us to develop a prepotential description of the off-shell versions of N=2 Poincare and anti-de Sitter supergravity theories constructed in arXiv:1109.0496.
Transmutation of Pure 2-D Supergravity Into Topological 2-D Gravity and Other Conformal Theories
我们考虑了二维超引力鬼作用量的BRST性质和超共形性质。使用背景自旋结构的世界表，我们表明，这个行动可以转化为正则场变换，以达到其他共形模型，如2-D拓扑引力或手征模型的规范变化的行动再现左或右共形异常。我们的方法包括使用引力子和鬼作为基本块，以建立不同的共形权重和统计字段。这特别表明，一个共形模型扭曲成另一个共形模型可以经典地解释为超共形对称性的“场表示”的改变。
We consider super Yang-Mills Theory in $N=1$ conformal supergravity. Using the background field method and the Feddeev-Popov procedure, the quantized action of the theory is presented. Its one-loop effective action is studied using the heat kernel method. We shall develop a non-iterative scheme, generalizing the non-supersymmetric case, to obtain the super heat kernel coefficients. In particular, the first three coefficients, which govern the one-loop divergence, will be calculated. We shall also demonstrate how to schematically derive the higher order coefficients. The method presented here c…
We give a superspace description of D=3, N=8 supergravity. The formulation is off-shell in the sense that the equations of motion are not implied by the superspace constraints (but an action principle is not given). The multiplet structure is unconventional, which we connect to the existence of a "Dragon window", that is modules occurring in the supercurvature but not in the supertorsion. According to Dragon's theorem this cannot happen above three dimensions. We clarify the relevance of this window for going on the conformal shell, and discuss some aspects of coupling to conformal matter.
Torus reduction of maximal conformal supergravity
该研究将六维N=(2,0)共形超引力经二维环面维数约化得到四维N=4共形超引力，首次在四维极大超对称情形下推导出dilaton Weyl多重态，并给出六维与四维场之间的非线性关系。
The projective superspace formulation for four-dimensional N = 2 matter-coupled supergravity presented in arXiv:0805.4683 makes use of the variant superspace realization for the N = 2 Weyl multiplet in which the structure group is SL(2,C) x SU(2) and the super-Weyl transformations are generated by a covariantly chiral parameter. An extension to Howe's realization of N = 2 conformal supergravity in which the tangent space group is SL(2,C) x U(2) and the super-Weyl transformations are generated by a real unconstrained parameter was briefly sketched. Here we give the explicit details of the exten…
Superconformal matter multiplets play a crucial role in the construction of Poincare supergravity invariants. Off-shell multiplets allow for construction of general matter couplings in supergravity. In Nucl. Phys. B214 (1983) 519-531, relaxed hypermultiplet was constructed in rigid supersymmetry which on coupling with the real scalar multiplet allowed for an off-shell formulation of the rigid hypermultiplet. In this paper, we extend the relaxed hypermultiplet to conformal supergravity. For consistency with the superconformal algebra, we find that the fields have to be allowed to transform in a…
Bosonic sector of d5 gauged supergravity with specific parametrization of full scalar coset is considered (multi-dilaton gravity). Using holographic RG in the form suggested by de Boer-Verlinde-Verlinde the holographic d4 conformal anomaly (in the sector of curvature invariants) is found when bulk potential is not constant. Its comparison with the earlier calculation done in the scheme where expansion of metric and dilaton over radial coordinate of AdS space is used demonstrates scheme dependence of holographic conformal anomaly. In AdS/CFT correspondence where dilatons play role of coupling c…
In this paper we study the relation between six-dimensional supergravity compactified on S^3 X AdS_3 and certain two-dimensional conformal field theories. We compute the Kaluza-Klein spectrum of supergravity using representation theory; these methods are quite general and can also be applied to other compactifications involving anti-de Sitter spaces. A detailed comparison between the spectrum of the two-dimensional conformal field theory and supergravity is made, and we find complete agreement. This applies even at the level of certain non-chiral primaries, and we propose a resolution to the p…
We study holographic dual descriptions of very special conformal field theories with the T(2) symmetry. After constructing solutions in effective five dimensional Einstein gravity coupled with massive two-form fields, we uplift them to the ten dimensional type IIB supergravity, via a consistent truncation ansatz, to derive new analytical solutions in string theory. From the Kaluza-Klein ansatz in terms of the internal Sasaki-Einstein space, we obtain their field theory interpretation with concrete realizations in a large class of holographic $\mathcal{N}=1$ supersymmetric conformal field theor…
We report our recent results concerning d5 gauged supergravity (dilatonic gravity) considered on AdS background. The finite action on such background as well as d4 holographic conformal anomaly (via AdS/CFT correspondence) are found. In such formalism the bulk potential is kept to be arbitrary, dilaton dependent function. Holographic RG in such theory is briefly discussed. d5 AdS brane-world Universe induced by quantum effects of brane CFT is constructed. Such brane is spherical, hyperbolic or flat one. Hence, the possibility of quantum creation of inflationary brane-world Universe is shown.
We embed general $f(R)$ inflationary models in minimal supergravity plus matter, a single chiral superfield $Φ$, with or without another superfield $S$, via a Jordan frame Einstein+scalar description. In particular, inflationary models like a generalized Starobinsky one are analyzed and constraints on them are found. We also embed the related models of conformal inflation, also described as Jordan frame Einstein+scalar models, in particular the conformal inflation from the Higgs model, and analyze the inflationary constraints on them.
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