We define a general class of superconformal inflationary attractor models studied in our previous papers [1,2], which include, among others, inflationary models of 'induced gravity' which were argued to retain perturbative unitarity up to the Planck scale [3]. The choice of the function $f(ϕ)$ in superconformal attractors for the models introduced in [3] is $f(ϕ)= ϕ^n - ξ^{-1}$. We present both superconformal and supergravity versions of these models, which were derived in [1,2] for arbitrary $f(ϕ)$, together with the universal conditions required for stabilization of the extra three moduli present in the superconformal attractors, in addition to the inflaton.
Recently a broad class of superconformal inflationary models was found leading to a universal observational prediction $n_s=1-2/N$ and $r=12/N^2$. Here we generalize this class of models by introducing a parameter $α$ inversely proportional to the curvature of the inflaton Kahler manifold. In the small curvature (large $α$) limit, the observational predictions of this class of models coincide with the predictions of generic chaotic inflation models. However, for sufficiently large curvature (small $α$), the predictions converge to the universal attractor regime with $n_s=1-2/N$ and $r=12α/N^2$…
We introduce a novel non-minimal coupling between gravity and the inflaton sector. Remarkably, for large values of this coupling all models asymptote to a universal attractor. This behavior is independent of the original scalar potential and generalizes the attractor in the phi^4 theory with non-minimal coupling to gravity. The attractor is located in the `sweet spot' of Planck's recent results.
Once quantum corrections are taken into account, the strong coupling limit of the $ξ$-attractor models (in metric gravity) might depart from the usual Starobinsky solution and move into linear inflation. Furthermore, it is well known that the metric and Palatini formulations of gravity lead to different inflationary predictions in presence of non-minimally couplings between gravity and the inflaton. In this letter we show that for a certain class of non-minimally coupled models, loop corrections will lead to a linear inflation attractor regardless of the adopted gravity formulation.
Recently, Kallosh and Linde have drawn attention to a new family of superconformal inflationary potentials, subsequently called $α$-attractors. The $α$-attractor family can interpolate between a large class of inflationary models. It also has an important theoretical underpinning within the framework of supergravity. We demonstrate that the $α$-attractors have an even wider appeal since they may describe dark matter and perhaps even dark energy. The dark matter associated with the $α$-attractors, which we call $α$-dark matter ($α$DM), shares many of the attractive features of fuzzy dark matter…
In this paper we constrain some aspects of the general postinflationary phase in the context of superconformal $α$-attractor models of inflation. In particular, we provide constraints on the duration of the reheating process, $N_{reh}$, and on the reheating temperature, $T_{reh}$, simulating possible and future results given by the next-generation of cosmological missions. Moreover, we stress what kinds of equation-of-state parameter, $w_{reh}$, are favored for different scenarios. The analysis does not depend on the details of the reheating phase and it is performed assuming different measure…
Configurations of N probe D0-branes in a Calabi-Yau black hole are studied. A large degeneracy of near-horizon bound states are found which can be described as lowest Landau levels tiling the horizon of the black hole. These states preserve some of the enhanced supersymmetry of the near-horizon AdS_2xS^2xCY attractor geometry, but not of the full asymptotically flat solution. Supersymmetric non-abelian configurations are constructed which, via the Myers effect, develop charges associated with higher-dimensional branes wrapping CY cycles. An SU(1,1|2) superconformal quantum mechanics describing…
Recently, several broad classes of inflationary models have been discovered whose cosmological predictions are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a non-minimal coupling to gravity. These models, which we will call $ξ$-attractors, describe universal cosmological attractors (including Higgs inflation) and induced inflation models. Another class describes conformal attractors (including Starobinsky inflation and T-models) and their generalization to $α$-attractors. The aim of this paper is to elucidate the common denomin…
We propose a new broad class of multi-field non-canonical inflationary models as an extension of multi-field conformal cosmological attractors. This also generalizes the recently discovered class of non-canonical conformal attractors for single field inflation. Kinetic terms of this class of models are phenomenologically arising from ${\cal N}=1$ supergravity and from ${\cal N}=1$ superconformal theory, with two conformal scalar compensator fields in the latter. We show that the inflationary dynamics and predictions of this class of models are stable with respect to the significant modificatio…
An effective supersymmetric QCD light-front Hamiltonian for hadrons composed of light quarks, which includes a spin-spin interaction between the hadronic constituents, is constructed by embedding superconformal quantum mechanics into AdS space. A specific breaking of conformal symmetry inside the graded algebra determines a unique effective quark-confining potential for light hadrons, as well as remarkable connections between the meson and baryon spectra. The results are consistent with the empirical features of the light-quark hadron spectra, including a universal mass scale for the slopes of…
We explore preheating in multi-field models of inflation in which the field-space metric is a highly curved hyperbolic manifold. One broad family of such models is called $α$-attractors, whose single-field regimes have been extensively studied in the context of inflation and supergravity. We focus on a simple two-field generalization of the $T$-model, which has received renewed attention in the literature. Krajewski et al. concluded, using lattice simulations, that multi-field effects can dramatically speed-up preheating. We recover their results and further demonstrate that significant analyt…
In this PhD thesis, we investigate generic features of inflation which are strictly related to fundamental aspects of UV-physics scenarios, such as string theory or supergravity. After a short introduction to standard and inflationary cosmology, we present our research findings. On the one hand, we show that focusing on universality properties of inflation can yield surprisingly stringent bounds on its dynamics. This approach allows us to identify the regime where the inflationary field range is uniquely determined by both the tensor-to-scalar ratio and the spectral index. Then, we derive a no…
We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $α$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $α$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there …
We give a general analysis of OPEs of 1/2 BPS superfield operators for the $D=3,4,5,6$ superconformal algebras OSp(8/4,R), PSU(2,2), F${}_4$ and OSp($8^*/4$) which underlie maximal AdS supergravity in $4\leq D+1\leq 7$. \\ The corresponding three-point functions can be formally factorized in a way similar to the decomposition of a generic superconformal UIR into a product of supersingletons. This allows for a simple derivation of branching rules for primary superfields. The operators of protected conformal dimension which may appear in the OPE are classified and are shown to be either 1/2 or 1…
SU(2) gauge fields coupled to an axion field can acquire an isotropic background solution during inflation. We study homogeneous but anisotropic inflationary solutions in the presence of such (massless) gauge fields. A gauge field in the cosmological background may pose a threat to spatial isotropy. We show, however, that such models $\textit{generally}$ isotropize in Bianchi type-I geometry, and the isotropic solution is the attractor. Restricting the setup by adding an axial symmetry, we revisited the numerical analysis presented in Wolfson et.al (2020). We find that the reported numerical b…
Following the set up in arXiv:1408.3393, we study 4d N=1 superconformal field theories in conic spaces. We show that the universal part of supersymmetric Rényi entropy S_q across a spherical entangling surface in the limit q goes to 0 is proportional to a linear combination of central charges, 3c-2a. This is equivalent to a similar statement about the free energy of SCFTs on conic space or hyperbolic space S^1_q*H^3 in the corresponding limit. We first derive the asymptotic formula by the free field computation in the presence of a U(1) R-symmetry background and then provide an independent der…
We discuss the introduction of a non minimal coupling between the inflaton and gravity in terms of the recently proposed $β$-function formalism for inflation\cite{Binetruy:2014zya}. Via a field redefinition we reduce to the case of minimally coupled theories. The universal attractor at strong coupling has a simple explanation in terms of the new field. Generalizations are discussed and the possibility of evading the universal attractor is shown.
Numerical simulations of expanding plasma based on the AdS/CFT correspondence as well as kinetic theory and hydrodynamic models strongly suggest that some observables exhibit universal behaviour even when the system is not close to local equilibrium. This leading behaviour is expected to be corrected by transient, exponentially decaying contributions which carry information about the initial state. Focusing on late times, when the system is already in the hydrodynamic regime, we analyse numerical solutions describing expanding plasma of strongly coupled N=4 supersymmetric Yang-Mills theory and…
We bootstrap ${\cal N}=(1,0)$ superconformal field theories in six dimensions, by analyzing the four-point function of flavor current multiplets. Assuming $E_8$ flavor group, we present universal bounds on the central charge $C_T$ and the flavor central charge $C_J$. Based on the numerical data, we conjecture that the rank-one E-string theory saturates the universal lower bound on $C_J$, and numerically determine the spectrum of long multiplets in the rank-one E-string theory. We comment on the possibility of solving the higher-rank E-string theories by bootstrap and thereby probing M-theory o…
We study the thermalization process in highly occupied non-Abelian plasmas at weak coupling. The non-equilibrium dynamics of such systems is classical in nature and can be simulated with real-time lattice gauge theory techniques. We provide a detailed discussion of this framework and elaborate on the results reported in~\cite{Berges:2013eia} along with novel findings. We demonstrate the emergence of universal attractor solutions, which govern the non-equilibrium evolution on large time scales both for non-expanding and expanding non-Abelian plasmas. The turbulent attractor for a non-expanding …
We describe an induced inflation, which refers to a class of inflationary models with a generalized non-minimal coupling $ξg(ϕ) R$ and a specific scalar potential. The defining property of these models is that the scalar field takes a vev in the vacuum and thus induces an effective Planck mass. We study this model as a function of the coupling parameter $ξ$. At large $ξ$, the predictions of the theory are known to have an attractor behavior, converging to a universal result independent on the choice of the function $g(ϕ)$. We find that at small $ξ$, the theory approaches a second attractor. Th…
We investigate the inflationary attractors in models of inflation inspired from general conformal transformation of general scalar-tensor theories to the Einstein frame. The coefficient of the conformal transformation in our study depends on both the scalar field and its kinetic term. Therefore the relevant scalar-tensor theories display the subset of the class I of the degenerate higher-order scalar-tensor theories in which both the scalar field and its kinetic term can non-minimally couple to gravity. We find that if the conformal coefficient $Ω$ takes a multiplicative form such that $Ω\equi…
We consider thermal plasmas in a large class of superconformal gauge theories described by a holographic dual geometry of the form $AdS_5\times M_5$. In particular, we demonstrate that all of the thermodynamic properties and hydrodynamic transport parameters for a large class of superconformal gauge theories exhibit a certain universality to leading order in the inverse 't Hooft coupling and $1/N_c$. In particular, we show that independent of the compactification geometry, the leading corrections are derived from the same five-dimensional effective supergravity action supplemented by a term qu…
Recently we identified a new class of (super)conformally invariant theories which allow inflation even if the scalar potential is very steep in terms of the original conformal variables. Observational predictions of a broad class of such theories are nearly model-independent. In this paper we consider generalized versions of these models where the inflaton has a non-minimal coupling to gravity with ξ<0 different from its conformal value ξ= -1/6. We show that these models exhibit attractor behavior. With even a slight increase of |ξ| from |ξ| = 0, predictions of these models for n_s and r rapid…
We study a supersymmetric, rotating, electrically charged black hole in AdS$_{4}$ which is a solution of four-dimensional minimal gauged supergravity. Using holography we show that the free energy on $S^3$ and the superconformal index of the dual three-dimensional $\mathcal N=2$ SCFT, in the planar limit, are related in a simple universal way. This result applies to large classes of SCFTs constructed from branes in string and M-theory which we discuss in some detail. For theories of class $\mathcal R$, which arise from $N$ M5-branes wrapped on hyperbolic three-manifolds, we show that the super…
We study $α$-attractor models with both E-model and T-model potential in an extended Non-Minimal Derivative (NMD) inflation where a canonical scalar field and its derivatives are non-minimally coupled to gravity. We calculate the evolution of perturbations during this regime. Then by adopting inflation potentials of the model we show that in the large N and small $α$ limit, value of the scalar spectral index ns and tensor to scalar ratio r are universal. Next, we study reheating after inflation in this formalism. We obtain some constraints on the model's parameter space by adopting the results…
Fundamental aspects of nonperturbative QCD dynamics which are not obvious from its classical Lagrangian, such as the emergence of a mass scale and confinement, the existence of a zero mass bound state, the appearance of universal Regge trajectories and the breaking of chiral symmetry are incorporated from the onset in an effective theory based on superconformal quantum mechanics and its embedding in a higher dimensional gravitational theory. In addition, superconformal quantum mechanics gives remarkable connections between the light meson and nucleon spectra. This new approach to hadron physic…
We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT where one copy of the seed CFT has been excited with a left-moving superconformal primary. Despite being BPS at the orbifold point, such states can `lift' as the theory is deformed away from this point in moduli space. We compute this lifting at second order in the deformation parameter for arbitrary left-moving dimension $h$ of this class of states. This result displays an interesting universality since the lifting does not depend on the details of the superconformal primary; it depends only on the dimension. In the …
After Planck 2013, a broad class of inflationary models called α-attractors was developed which has universal observational predictions. For small values of the parameter α, the models have good consistency with the recent CMB data. In this work, we first calculate analytically (and verify numerically) the predictions of these models for spectral index, n_s and tensor-to-scalar ratio, r and then using BICEP2/Keck 2015 data we impose constraints on α-attractors. Then, we study the reheating in α-attractors. The reheating temperature, T_{re} and the number of e-folds during reheating, N_{re} are…
Inflationary attractors predict the spectral index and tensor-to-scalar ratio to take specific values that are consistent with Planck. An example is the universal attractor for models with a generalised non-minimal coupling, leading to Starobinsky inflation. In this paper we demonstrate that it also predicts a specific relation between the amplitude of the power spectrum and the number of e-folds. The length and height of the inflationary plateau are related via the non-minimal coupling: in a wide variety of examples, the observed power normalisation leads to at least 55 flat e-foldings. Prior…
It is known that the unitary representation of the D=4, N=4 superconformal multiplets and their descendants are constructed as supercoherent states of bosonic and fermionic creation oscillators which covariantly transform under SU(2,2|4). We non-linearly realize those creation oscillators on the coset superspace PSU(2,2|4)/{SO(1,4) x SO(5)} which is reparametrized by the D=10 supercoordinates. We consider a D=2 non-linear sigma model on the coset superspace and set up Poisson brackets for the D=10 supercoordinates on the light-like line. It is then shown that the non-linearly realized creation…
We propose a generalization of the Grover-Sheng-Vishwanath model which, as solved by the density-matrix renormalization group, realizes the emergent supersymmetric criticality in the universality class of the even series of the $\mathcal{N}\!=\!1$ superconformal minimal models characterized by a central charge $5/4$. This chain model describes the topological phase transition of the propagating Majorana edge mode in topological superconductors coupled with the two-flavour Ising magnetic fluctuations (or the $XZ$ type). Using bosonization and perturbative renormalization group, we show that the…
We study the moduli dependence of the chiral ring in N = (4,4) superconformal field theories, with special emphasis on those CFTs that are dual to type IIB string theory on AdS3xS3xX4. The chiral primary operators are sections of vector bundles, whose connection describes the operator mixing under motion on the moduli space. This connection can be exactly computed using the constraints from N = (4,4) supersymmetry. Its curvature can be determined using the tt* equations, for which we give a derivation in the physical theory which does not rely on the topological twisting. We show that for N = …
These notes provide a detailed account of the universal structure of superpotentials defining a large class of superconformal Chern-Simons theories with matter, many of which appear as the low-energy descriptions of multiple M2-brane configurations. The amount of superconformal symmetry in the Chern-Simons-matter theory determines the minimum amount of global symmetry that the associated quartic superpotential must realise, which in turn restricts the matter superfield representations. Our analysis clarifies the necessary representation-theoretic data which guarantees a particular amount of su…
