Recently, a new type of constant Fayet-Iliopoulos (FI) terms was introduced in N = 1 supergravity, which do not require the gauging of the R-symmetry. We revisit and generalise these constructions, building a new class of Kähler invariant FI terms parametrised by a function of the gravitino mass as functional of the chiral superfields, which is then used to describe new models of inflation. They are based on a no-scale supergravity model of the inflaton chiral multiplet, supplemented by an abelian vector multiplet with the new FI-term. We show that the inflaton potential is compatible with the CMB observational data, with a vacuum energy at the minimum that can be tuned to a tiny positive value. Finally, the axionic shift symmetry can be gauged by the U (1) which becomes massive. These models offer a mechanism for fixing the gravitino mass in no-scale supergravities, that corresponds to a flat direction of the scalar potential in the absence of the new FI-term; its origin in string theory is an interesting open problem.

Scalar tensor theories can be expressed in different frames, such as the commonly-used Einstein and Jordan frames, and it is generally accepted that cosmological observables are the same in these frames. We revisit this by making a detailed side-by-side comparison of the quantities and equations in two conformally related frames, from the actions and fully covariant field equations to the linearised equations in both real and Fourier spaces. This confirms that the field and conservation equations are equivalent in the two frames, in the sense that we can always re-express equations in one frame using relevant transformations of variables to derive the corresponding equations in the other. We show, with both analytical derivation and a numerical example, that the line-of-sight integration to calculate CMB temperature anisotropies can be done using either Einstein frame or Jordan frame quantities, and the results are identical, provided the correct redshift is used in the Einstein frame (1 + z = 1/a).

We compute the 2 → 2 gravitino scattering amplitudes at tree level in supergravity theories where supersymmetry is spontaneously broken. In the unitary gauge, the gravitino becomes massive (of mass m3/2) by absorbing the Goldstino, and the scattering amplitudes of its longitudinal polarisations grow with energy as $$ {\kappa}^2{E}^4/{m}_{3/2}^2 $$ κ 2 E 4 / m 3 / 2 2 , signaling a potential breakdown of unitarity at a scale $$ {\Lambda}^2\sim {m}_{3/2}/\kappa \sim {M}_{\textrm{SUSY}}^2 $$ Λ 2 ∼ m 3 / 2 / κ ∼ M SUSY 2 . As we show explicitly in the Polonyi model, this leading term is cancelled by the contributions coming from the scalar partner of the Goldstino (sgoldstino), restoring perturbative unitarity up to the Planck scale. This is expected since supersymmetry is spontaneously broken, in analogy with the situation occuring in the Standard Model, where massive gauge bosons scattering preserves unitarity at high energy once we consider the contributions from the Higgs boson. However, when supersymmetry is broken by the new Fayet-Iliopoulos D-term, with ungauged R-symmetry, the above cancellation does not occur. In this case, the unbroken phase is singular and there is no contribution able to cancel the quartic divergences of the amplitudes, leading to a cutoff Λ ~ MSUSY where the effective theory breaks down. The same behaviour is obtained when supersymmetry is non-linearly realised.

We revisit the effective action of the Gribov-Zwanziger theory, taking into due account the BRST symmetry and renormalization (group invariance) of the construction. We compute at one loop the effective potential, showing the emergence of BRST-invariant dimension 2 condensates stabilizing the vacuum. This paper sets the stage at zero temperature, and clears the way to studying the Gribov-Zwanziger gap equations, and particularly the horizon condition, at finite temperature in future work. I. INTRODUCTIONUp until now, quark and gluon confinement has not been rigorously proven. It is well known that the perturbative formalism fails for non-Abelian gauge theories at low energy, since the coupling constant g 2 is strong. To get reliable results in the infrared (IR) in the continuum formulation, non-perturbative methods are needed. For an overview of such methods and obtained results, let us refer for example to . Notice that the continuum formulation requires gauge fixing, in which case lattice analogues of dedicated gauge fixings can be a powerful ally giving complementary insights, see for some relevant works in this area.Motivated by this, a number of studies over the past decade have focused on the gluon, quark and also ghost propagator in the infrared region, where color degrees of freedom are confined. Although these objects are unphysical by themselves -being gauge variant -they are nevertheless the basic building blocks, next to the interaction vertices, entering gauge-invariant objects directly linked to physically relevant quantities such as the spectrum, decay constants, critical exponents and temperatures, etc.One particular way to deal with non-perturbative physics at the level of elementary degrees of freedom is by dealing with the Gribov issue [21,80]: the fact that there is no unique way of selecting one representative configuration of a given gauge orbit in covariant gauges [81]. As there is also no rigourous way to deal properly with the existence of gauge copy modes in the path integral quantization procedure, in this paper we will use a well-tested formalism available to deal with the issue, which is known as the Gribov-Zwanziger (GZ) formalism: a restriction of the path integral to a smaller subdomain of gauge fields [80,82,83].This approach was first proposed for the Landau and the Coulomb gauges . It long suffered from a serious drawback: its concrete implementation seemed to be inconsistent with BRST (Becchi-Rouet-Stora-Tyutin [84-86]) invariance of the gauge-fixed theory, which clouded its interpretation as a gauge (fixed) theory. Only more recently was it realized by some of us and colleagues how to overcome this complication to get a BRST-invariant restriction of the gauge path integral . As a bonus, the method also allowed the generalization of the GZ approach to the linear covariant gauges, amongst others [36,37,43,45].Another issue with the original GZ approach was that some of its major leading-order predictions did not match the corresponding lattice output. Indeed, in the case of the...