We investigate inflation models in Jordan frame supergravity, in which an inflaton non-minimally couples to the scalar curvature. By imposing the condition that an inflaton would have the canonical kinetic term in the Jordan frame, we construct inflation models with asymptotically flat potential through pole inflation technique and discuss their relation to the models based on Einstein frame supergravity. We also show that the model proposed by Ferrara et al. has special position and the relation between the Kähler potential and the frame function is uniquely determined by requiring that scalars take the canonical kinetic terms in the Jordan frame and that a frame function consists only of a holomorphic term (and its anti-holomorphic counterpart) for symmetry breaking terms. Our case corresponds to relaxing the latter condition.
We study various inflation models in the Jordan frame supergravity with a logarithmic Kahler potential. We find that, in a class of inflation models containing an additional singlet in the superpotential, three types of inflation can be realized: the Higgs-type inflation, power-law inflation, and chaotic inflation with/without a running kinetic term. The former two are possible if the holomorphic function dominates over the non-holomorphic one in the frame function, while the chaotic inflation occurs when both are comparable. Interestingly, the fractional-power potential can be realized by the…
We consider the inflationary scenario with non-minimal coupling in 4D Jordan frame supergravity. We find that there occurs a tachyonic instability along the direction of the accompanying non-inflaton field in generic Jordan frame supergravity models. We propose a higher order correction to the Jordan frame function for solving the tachyonic mass problem and show that the necessary correction can be naturally generated by the heavy thresholds without spoiling the slow-roll conditions. We discuss the implication of the result on the Higgs inflation in NMSSM.
This paper provides a systematic study of supergravity contributions relevant for inflationary model building in Jordan frame supergravity. In this framework, canonical kinetic terms in the Jordan frame result in the separation of the Jordan frame scalar potential into a tree-level term and a supergravity contribution, which is potentially dangerous for sustaining inflation. We show that if the vacuum energy necessary for driving inflation originates dominantly from the F-term of an auxiliary field (i.e. not the inflaton), the supergravity corrections to the Jordan frame scalar potential are g…
We present a complete explicit N=1, d=4 supergravity action in an arbitrary Jordan frame with non-minimal scalar-curvature coupling of the form $Φ(z, \bar z)\, R$. The action is derived by suitably gauge-fixing the superconformal action. The theory has a modified Kaehler geometry, and it exhibits a significant dependence on the frame function $Φ(z, \bar z)$ and its derivatives over scalars, in the bosonic as well as in the fermionic part of the action. Under certain simple conditions, the scalar kinetic terms in the Jordan frame have a canonical form. We consider an embedding of the Next-to-Mi…
In string-inspired supergravity theory, Kähler metric of chiral matter fields often has a pole. Such Kähler metric is interesting from the viewpoint of the framework of the pole inflation, where the scalar potential can be stretched out to be flat around the pole for a canonically normalized field and inflation can be realized. However, when Kähler metric has a pole, the scalar potential can also have a pole at the same point in supergravity theory. We study such supergravity models with the pole, and provide numerical analysis of inflationary dynamics and resultant density perturbation. In co…
In the context of six-dimensional supergravity there is a special class of parent models for five-dimensional theories defined by the four Euclidean simple Jordan algebras of degree 3. We extend this result to include six- dimensional parent models for three infinite families of five-dimensional theories defined by Minkowskian Jordan algebras. Connections of the six-dimensional models to F-theory constructions are constrained by anomaly cancellation conditions and the structure of the six-dimensional theory gauge group.
It is known that black hole charge vectors of N=8 and magic N=2 supergravity in four and five dimensions can be represented as elements of Jordan algebras of degree three over the octonions and split-octonions and their Freudenthal triple systems. We show both such Jordan algebras are contained in the exceptional Jordan C*-algebra and construct its corresponding Freudenthal triple system and single variable extension. The transformation groups for these structures give rise to the complex forms of the U-duality groups for N=8 and magic N=2 supergravities in three, four and five dimensions.
In this review, we discuss inflation models based on supergravity. After explaining the difficulties in realizing inflation in the context of supergravity, we show how to evade such difficulties. Depending on types of inflation, we give concrete examples, particularly paying attention to chaotic inflation because the ongoing experiments like Planck might detect the tensor perturbations in near future. We also discuss inflation models in Jordan frame supergravity, motivated by Higgs inflation.
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.
Modulus stabilization of modular flavor models in Jordan frame supergravity
School of Physics, Zhengzhou University（郑州大学物理学院）
本文在 Jordan 标架超引力中，通过非最小标量-曲率耦合形式 $Φ(τ,\barτ)R$，结合模不变性、尺度因子正定性和 Kähler 度规正定性，约束标架函数及 Kähler 势，并研究从 Jordan 标架到 Einstein 标架变换后标量势的形状，发现其与普通单模稳定化机制不同，势能在 $i\infty$ 不动点处可能静止导致逃逸型真空，但可通过典型模 VEV 在大 $\Imτ$ 下稳定，最后数值讨论了简化场景下的模稳定化。
We show how we can implement within Supergravity chaotic inflation in the presence of a pole of order one or two in the kinetic mixing of the inflaton sector. This pole arises due to the selected logarithmic Kahler potentials K, which parameterize hyperbolic manifolds with scalar curvature related to the coefficient -N of the logarithmic term. The associated superpotential W exhibits the same R charge with the inflaton-accompanying superfield and includes all the allowed terms. The role of the inflaton can be played by a gauge singlet or non-singlet superfield. Models with one logarithmic term…
After reviewing the existing results we give an extensive analysis of the critical points of the potentials of the gauged N=2 Yang-Mills/Einstein Supergravity theories coupled to tensor- and hyper multiplets. Our analysis includes all the possible gaugings of all N=2 Maxwell-Einstein supergravity theories whose scalar manifolds are symmetric spaces. In general, the scalar potential gets contributions from R-symmetry gauging, tensor couplings and hyper-couplings. We show that the coupling of a hypermultiplet into a theory whose potential has a non-zero value at its critical point, and gauging a…
We study unified N=2 Maxwell-Einstein supergravity theories (MESGTs) and unified Yang-Mills Einstein supergravity theories (YMESGTs) in four dimensions. As their defining property, these theories admit the action of a global or local symmetry group that is (i) simple, and (ii) acts irreducibly on all the vector fields of the theory, including the ``graviphoton''. Restricting ourselves to the theories that originate from five dimensions via dimensional reduction, we find that the generic Jordan family of MESGTs with the scalar manifolds [SU(1,1)/U(1)] X [SO(2,n)/SO(2)X SO(n)] are all unified in…
We identify a particularly simple class of supergravity models describing superconformal coupling of matter to supergravity. In these models, which we call the canonical superconformal supergravity (CSS) models, the kinetic terms in the Jordan frame are canonical, and the scalar potential is the same as in the global theory. The pure supergravity part of the total action has a local Poincare supersymmetry, whereas the chiral and vector multiplets coupled to supergravity have a larger local superconformal symmetry. The scale-free globally supersymmetric theories, such as the NMSSM with a scale-…
We present a superconformal master action for a class of supergravity models with one arbitrary function defining the Jordan frame. It leads to a gauge-invariant action for a real vector multiplet, which upon gauge fixing describes a massive vector multiplet, or to a dual formulation with a linear multiplet and a massive tensor field. In both cases the models have one real scalar, the inflaton, naturally suited for single-field inflation. Vectors and tensors required by supersymmetry to complement a single real scalar do not acquire vev's during inflation, so there is no need to stabilize the …
We extend the Cecotti-Kallosh model of Starobinsky inflation in supergravity by adding a holomorphic function to the superpotential in order to generate a large peak in the power spectrum of scalar (curvature) perturbations. In our approach, the singular non-canonical kinetic terms are largely responsible for inflation (as an attractor solution), whereas the superpotential is engineered to generate a production of primordial black holes. We study the cases with (i) a linear holomorphic function, (ii) a quadratic holomorphic function, and (iii) an exponential holomorphic function, as regards th…
We present novel realizations of E-model inflation within Supergravity which are largely associated with the existence of a pole of order one in the kinetic term of the (gauge-singlet) inflaton superfield. This pole arises due to the selected logarithmic Kahler potentials K1 and ~K1, which parameterize the same hyperbolic manifold with scalar curvature R=-2/N, where N>0 is the coefficient of a logarithmic term. The associated superpotential W exhibits the same R charge with the inflaton-accompanying superfield and includes all the allowed renormalizable terms. For K=K1, inflation can be attain…
We study a Jordanian deformation of the $AdS_5 \times S^5$ superstring that preserves 12 superisometries. It is an example of homogeneous Yang-Baxter deformations, a class that generalises TsT deformations to the non-abelian case. Many of the attractive features of TsT carry over to this more general class, from the possibility of generating new supergravity solutions to the preservation of worldsheet integrability. In this paper, we exploit the fact that the deformed $σ$-model with periodic boundary conditions can be reformulated as an undeformed one with twisted boundary conditions, to discu…
We present novel realizations of E- and T-model inflation within Supergravity which are largely associated with the existence of a pole of order one and two respectively in the kinetic term of the inflaton superfield. This pole arises due to the selected logarithmic Kahler potentials K, which parameterize hyperbolic manifolds with scalar curvature related to the coefficient (-N)<0 of a logarithmic term. The associated superpotential W exhibits the same R charge with the inflaton-accompanying superfield and includes all the allowed terms. The role of the inflaton can be played by a gauge single…
A second order pole in the scalar kinetic term can lead to a class of inflation models with universal predictions referred to as pole inflation or $α$-attractors. While this kinetic structure is ubiquitous in supergravity effective field theories, realising a consistent UV complete model in e.g. string theory is a non-trivial task. For one, one expects quantum corrections arising in the vicinity of the pole which may spoil the typical attractor dynamics. As a conservative estimate of the range of validity of supergravity models of pole inflation we employ the weak gravity conjecture (WGC). We …
We demonstrate a solution generating technique, modulo some constraints, for a large class of smooth supergravity solutions with the same asymptotic charges as a five dimensional 3-charge BPS black hole or black ring, dual to a D1/D5/P system. These solutions are characterized by a harmonic function with both positive and negative poles, which induces a geometric transition whereby singular sources have disappeared and all of the net charge at infinity is sourced by fluxes through two-cycles joining the poles of the harmonic function.
Single-field D-type inflation in the minimal supergravity in light of Planck-ACT-SPT data
Fudan University（复旦大学）；Tokyo Metropolitan University（东京都立大学）；Tomsk State University（托木斯克国立大学）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study（宇宙物理与数学研究所（WPI），东京大学高等研究院）
In a series of recent papers Kallosh, Linde, and collaborators have provided a unified description of single-field inflation with several types of potentials, ranging from power law to supergravity, in terms of just one parameter $α$. These so-called $α$-attractors predict a spectral index $n_{s}$ and a tensor-to-scalar ratio $r$, which are fully compatible with the latest Planck data. The only common feature of all $α$-attractors is a non-canonical kinetic term with a pole, and a potential analytic around the pole. In this paper, starting from the same Einstein frame with a non-canonical scal…
We derive an on-shell diagram recursion for tree-level scattering amplitudes in $\mathcal{N}=7$ supergravity. The diagrams are evaluated in terms of Grassmannian integrals and momentum twistors, generalising previous results of Hodges in momentum twistor space to non-MHV amplitudes. In particular, we recast five and six-point NMHV amplitudes in terms of $\mathcal{N}=7$ R-invariants analogous to those of $\mathcal{N}=4$ super-Yang-Mills, which makes cancellation of spurious poles more transparent. Above 5-points, this requires defining momentum twistors with respect to different orderings of th…
We present novel realizations of Higgs inflation within Supergravity which are largely tied to the existence of a pole of order two in the kinetic term of the inflaton field. This pole arises due to the selected Kaehler potentials which parameterize the (SU(1,1)/U(1))^2 or SU(2,1)/(SU(2)xU(1)) manifolds with scalar curvatures R_{(11)^2}=-4/N or R_{21}=-3/N respectively. The associated superpotential includes, in addition to the Higgs superfields, a stabilizer superfield, respects the gauge and an R symmetries and contains the first allowed nonrenormalizable term. If the coefficient of this ter…
We study both the "large" and "small" U-duality charge orbits of extremal black holes appearing in D = 5 and D = 4 Maxwell-Einstein supergravity theories with symmetric scalar manifolds. We exploit a formalism based on cubic Jordan algebras and their associated Freudenthal triple systems, in order to derive the minimal charge representatives, their stabilizers and the associated "moduli spaces". After recalling N = 8 maximal supergravity, we consider N = 2 and N = 4 theories coupled to an arbitrary number of vector multiplets, as well as N = 2 magic, STU, ST^2 and T^3 models. While the STU mod…
We analyze the polynomial part of the Iwasawa realization of the coset representative of non compact symmetric Riemannian spaces. We start by studying the role of Kostant's principal SU(2)_P subalgebra of simple Lie algebras, and how it determines the structure of the nilpotent subalgebras. This allows us to compute the maximal degree of the polynomials for all faithful representations of Lie algebras. In particular the metric coefficients are related to the scalar kinetic terms while the representation of electric and magnetic charges is related to the coupling of scalars to vector field stre…
In this paper we consider the degrees of freedom beyond the graviton present in the effective field theory for quantum gravity. We point out that the position of the poles due to $R^2$ and $R_{μν}R^{μν}$ cannot be affected by operators that are higher order in curvature. On the other hand, operators of the type $R\Box R$ will lead to new poles while shifting the positions of the poles found at second order in curvature. New degrees of freedom can be identified either, as just described, by looking at the poles of the graviton propagator corrected by quantum gravity or by mapping the Jordan fra…
In this paper we study half-BPS type IIB supergravity solutions with multiple $AdS_3\times S^3\times M_4$ asymptotic regions, where $M_4$ is either $T^4$ or $K_3$. These solutions were first constructed in [1] and have geometries given by the warped product of $AdS_2 \times S^2 \times M_4 $ over $Σ$, where $Σ$ is a Riemann surface. We show that the holographic boundary has the structure of a star graph, i.e. $n$ half-lines joined at a point. The attractor mechanism and the relation of the solutions to junctions of self-dual strings in six-dimensional supergravity are discussed. The solutions o…
We present a realization of Higgs inflation within Supergravity which is largely tied to the existence of a pole of order two in the kinetic term of the inflaton field. This pole arises due to the selected Kaehler potential which parameterizes the SU(2,1) / (SU(2) x U(1)) manifold with scalar curvature R_{21}=-6/N. The associated superpotential includes, in addition to the Higgs superfields, a stabilizer superfield, respects a B-L gauge and an R symmetries and contains the first allowed nonrenormalizable term. If the coefficient of this term is almost equal to that of the others within about 1…
The set of double-logarithmic (DL) contributions $(α\, t \ln^2 {s})^n$ to the 4-graviton amplitude in ${\cal N}$$=$ 8 supergravity (SUGRA), with $α$ being the gravitational coupling and $(s,t)$ the Mandelstam invariants, is studied in impact parameter ($ρ$) representation. This sector of the amplitude shows interesting properties which shed light on the nature of quantum corrections in gravity. Besides having a convergent behaviour as $s$ increases, which is not present in ${\cal N}$$<$ 4 SUGRA theories, there exists a critical line $ρ_c(s)$ above which the Born amplitude prevails. The short d…
This paper studies the semiclassical approximation of simple supergravity in Riemannian four-manifolds with boundary, within the framework of $ζ$-function regularization. The massless nature of gravitinos, jointly with the presence of a boundary and a local description in terms of potentials for spin ${3\over 2}$, force the background to be totally flat. First, nonlocal boundary conditions of the spectral type are imposed on spin-${3\over 2}$ potentials, jointly with boundary conditions on metric perturbations which are completely invariant under infinitesimal diffeomorphisms. The axial gauge-…
We point out that a model with scalar fields with a large nonminimal coupling to the Ricci scalar, such as Higgs inflation, can be regarded as a nonlinear sigma model (NLSM). With the inclusion of not only the scalar fields but also the conformal mode of the metric, our definition of the target space of the NLSM is invariant under the frame transformation. We show that the $σ$-meson that linearizes this NLSM to be a linear sigma model (LSM) corresponds to the scalaron, the degree of freedom associated to the $R^2$ term in the Jordan frame. We demonstrate that quantum corrections inevitably ind…
Hybrid inflation, driven by a Fayet-Iliopoulos (FI) D term, is an intriguing inflationary model. In its usual formulation, it however suffers from several shortcomings. These pertain to the origin of the FI mass scale, the stability of scalar fields during inflation, gravitational corrections in supergravity, as well as to the latest constraints from the cosmic microwave background. We demonstrate that these issues can be remedied if D-term inflation is realized in the context of strongly coupled supersymmetric gauge theories. We suppose that the D term is generated in consequence of dynamical…
We study a new model of quintessential inflation which is inspired by supergravity and string theory. The model features a kinetic pole, which gives rise to the inflationary plateau, and a runaway quintessential tail. We envisage a coupling between the inflaton and the Peccei-Quinn (PQ) field which terminates the roll of the runaway inflaton and traps the latter at an enhanced symmetry point (ESP), thereby breaking the PQ symmetry. The kinetic density of the inflaton is transferred to the newly created thermal bath of the hot big bang due to the decay of PQ particles. The model successfully ac…
Spin interactions beteween two moving Dp-branes are analyzed using the Green-Schwarz formalism of boundary states. This approach turns out to be extremely efficient to compute all the spin effects related by supersymmetry to the leading v^4/r^7-p term. All these terms are shown to be scale invariant, supporting a matrix model description of supergravity interactions. By employing the LSZ reduction formula for matrix theory and the mentioned supersymmetric effective potential for D0-branes, we compute the t-pole of graviton-graviton and three form-three form scattering in matrix theory. The res…
