High energy physics signatures from inflation and conformal symmetry of de Sitter

During inflation, the geometry of spacetime is described by a (quasi‐)de Sitter phase. Inflationary observables are determined by the underlying (softly broken) de Sitter isometry group which acts like a conformal group on : when the fluctuations are on super‐Hubble scales, the correlators of the scalar fields are constrained by conformal invariance. Heavy fields with mass m larger than the Hubble rate H correspond to operators with imaginary dimensions in the dual Euclidean three‐dimensional conformal field theory. By making use of the dS/CFT correspondence we show that, besides the Boltzmann suppression expected from the thermal properties of de Sitter space, the generic effect of heavy fields in the inflationary correlators of the light fields is to introduce power‐law suppressed corrections of the form . This can be seen, for instance, at the level of the four‐point correlator for which we provide the correction due to a massive scalar field exchange.     

On the hidden maxwell superalgebra underlying supergravity

In this work, we expand the hidden ‐Lorentz superalgebra underlying supergravity, reaching a (hidden) Maxwell superalgebra. The latter can be viewed as an extension involving cosmological constant of the superalgebra underlying supergravity in flat spacetime. We write the Maurer‐Cartan equations in this context and we find some interesting extensions of the antisymmetric 3‐form A ⁽³⁾ appearing in the Free Differential Algebra in Minkowski space. The structure of Free Differential Algebras is obtained by considering the zero curvature equations. We write the parametrization of A ⁽³⁾ in terms of 1‐forms and we rend the topological features of its extensions manifest. We interestingly find out that the structure of these extensions, and consequently the structure of the corresponding boundary contribution , strongly depends on the form of the extra fermionic generator appearing in the hidden Maxwell superalgebra. The model we develop in this work is defined in an enlarged superspace with respect to the ordinary one, and the extra bosonic and fermionic 1‐forms required for the closure of the hidden Maxwell superalgebra must be considered as physical fields in this enlarged superspace.     

Non‐Thermal Corrections to Hawking Radiation Versus the Information Paradox**

We provide a model‐independent argument indicating that for a black hole of entropy N the non‐thermal deviations from Hawking radiation, per each emission time, are of order , as opposed to . This fact abolishes the standard a priory basis for the information paradox.     

Half‐Maximal Supersymmetry from Exceptional Field Theory

We study ‐dimensional half‐maximal flux backgrounds using exceptional field theory. We define the relevant generalised structures and also find the integrability conditions which give warped half‐maximal Minkowski_D and AdS_D vacua. We then show how to obtain consistent truncations of type II / 11‐dimensional SUGRA which break half the supersymmetry. Such truncations can be defined on backgrounds admitting exceptional generalised structures, where , and N is the number of vector multiplets obtained in the lower‐dimensional theory. Our procedure yields the most general embedding tensors satisfying the linear constraint of half‐maximal gauged SUGRA. We use this to prove that all half‐maximal warped AdS_D and Minkowski_D vacua of type II / 11‐dimensional SUGRA admit a consistent truncation keeping only the gravitational supermultiplet. We also show to obtain heterotic double field theory from exceptional field theory and comment on the M‐theory / heterotic duality. In five dimensions, we find a new SO(5, N ) double field theory with a ‐dimensional extended space. Its section condition has one solution corresponding to 10‐dimensional supergravity and another yielding six‐dimensional SUGRA.     

Six open string disk amplitude in pure spinor superspace

The tree-level amplitude of six massless open strings is computed using the pure spinor formalism. The OPE poles among integrated and unintegrated vertices can be efficiently organized according to the cohomology of pure spinor superspace. The identification and use of these BRST structures and their interplay with the system of equations fulfilled by the generalized Euler integrals allow the full supersymmetric six-point amplitude to be written in compact form. Furthermore, the complete set of extended Bern–Carrasco–Johansson relations are derived from the monodromy properties of the disk world-sheet and explicitly verified for the supersymmetric numerator factors.     

Chiral expansion and Macdonald deformation of two‐dimensional Yang‐Mills theory

We derive the analog of the large N Gross‐Taylor holomorphic string expansion for the refinement of q‐deformed Yang‐Mills theory on a compact oriented Riemann surface. The derivation combines Schur‐Weyl duality for quantum groups with the Etingof‐Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of q‐deformed Yang‐Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit , the expansion defines a new β‐deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and β‐ensembles of matrix models arising in refined topological string theory.     

Nilpotent orbits in real symmetric pairs and stationary black holes

In the study of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In this paper we discuss two approaches to determine the nilpotent orbits of a real symmetric pair. We apply our methods to an explicit example, and thereby classify the nilpotent orbits of acting on the fourth tensor power of the natural 2‐dimensional ‐module. This makes it possible to classify all stationary solutions of the so‐called STU‐supergravity model.     

Aspects of quadratic gravity

We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure R² theory is indeed ghost free. Then we point out that for flat backgrounds the pure R² theory propagates only a scalar massless mode and no spin‐two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti‐de Sitter, or by changing the long‐distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string‐ or M‐theory. We demonstrate that string theory on non‐compact manifolds, like a line bundle over , may indeed lead to gravity dynamics determined by a higher curvature action.     

The Flux‐Scaling scenario: De sitter uplift and axion inflation

Non‐geometric flux‐scaling vacua provide promising starting points to realize axion monodromy inflation via the F‐term scalar potential. We show that these vacua can be uplifted to Minkowski and de Sitter by adding an ‐brane or a D‐term containing geometric and non‐geometric fluxes. These uplifted non‐supersymmetric models are analyzed with respect to their potential to realize axion monodromy inflation self‐consistently. Admitting rational values of the fluxes, we construct examples with the required hierarchy of mass scales.     

Higher‐Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions

We first review the Coset Space Dimensional Reduction (CSDR) programme and present the best model constructed so far based on the , 10‐dimensional E₈ gauge theory reduced over the nearly‐Kähler manifold with the additional use of the Wilson flux mechanism. Then we present the corresponding programme in the case that the extra dimensions are considered to be fuzzy coset spaces and the best model that has been constructed in this framework too. In both cases the best model appears to be the trinification GUT .     

Exceptional Calabi–Yau spaces: the geometry of backgrounds with flux

In this paper we define the analogue of Calabi–Yau geometry for generic , flux backgrounds in type II supergravity and M‐theory. We show that solutions of the Killing spinor equations are in one‐to‐one correspondence with integrable, globally defined structures in generalised geometry. Such “exceptional Calabi–Yau” geometries are determined by two generalised objects that parametrise hyper‐ and vector‐multiplet degrees of freedom and generalise conventional complex, symplectic and hyper‐Kähler geometries. The integrability conditions for both hyper‐ and vector‐multiplet structures are given by the vanishing of moment maps for the “generalised diffeomorphism group” of diffeomorphisms combined with gauge transformations. We give a number of explicit examples and discuss the structure of the moduli spaces of solutions. We then extend our construction to and flux backgrounds preserving eight supercharges, where similar structures appear, and finally discuss the analogous structures in generalised geometry.     

On heterotic vacua with fermionic expectation values

We study heterotic backgrounds with non‐trivial H‐flux and non‐vanishing expectation values of fermionic bilinears, often referred to as gaugino condensates. The gaugini appear in the low energy action via the gauge‐invariant three‐form bilinear . For Calabi‐Yau compactifications to four dimensions, the gaugino condensate corresponds to an internal three‐form that must be a singlet of the holonomy group. This condition does not hold anymore when an internal H‐flux is turned on and effects are included. In this paper we study flux compactifications to three and four‐dimensions on G‐structure manifolds. We derive the generic conditions for supersymmetric solutions. We use integrability conditions and Lichnerowicz type arguments to derive a set of constraints whose solution, together with supersymmetry, is sufficient for finding backgrounds with gaugino condensate.     

Towards the Standard Model in F‐theory

This article explores possible embeddings of the Standard Model gauge group and its matter representations into F‐theory. To this end we construct elliptic fibrations with gauge group as suitable restrictions of a ‐fibration with rank‐two Mordell‐Weil group. We analyse the five inequivalent toric enhancements to gauge group along two independent divisors W₃ and W₂ in the base. For each of the resulting smooth fibrations, the representation spectrum generically consists of a bifundamental , three types of representations and five types of representations (plus conjugates), in addition to charged singlet states. The precise spectrum of zero‐modes in these representations depends on the 3‐form background. We analyse the geometrically realised Yukawa couplings among all these states and find complete agreement with field theoretic expectations based on their U(1) charges. We classify possible identifications of the found representations with the Standard Model field content extended by right‐handed neutrinos and extra singlets. The linear combination of the two abelian gauge group factors orthogonal to hypercharge acts as a selection rule which, depending on the specific model, can forbid dangerous dimension‐four and ‐five proton decay operators.     

Mass formulae for broken supersymmetry in curved space‐time

We derive the mass formulae for , matter‐coupled Supergravity for broken (and unbroken) Supersymmetry in curved space‐time. These formulae are applicable to De Sitter configurations as is the case for inflation. For unbroken Supersymmetry in anti‐de Sitter (AdS) one gets the mass relations modified by the AdS curvature. We compute the mass relations both for the potential and its derivative non‐vanishing.     

The Spin‐Charge‐Family Theory Offers Understanding of the Triangle Anomalies Cancellation in the Standard Model

The standard model has for massless quarks and leptons “miraculously” no triangle anomalies due to the fact that the sum of all possible traces — where and are the generators of one, of two or of three of the groups and U (1) — over the representations of one family of the left handed fermions and anti‐fermions (and separately of the right handed fermions and anti‐fermions), contributing to the triangle currents, is equal to zero. 1 - 4 It is demonstrated in this paper that this cancellation of the standard model triangle anomaly follows straightforwardly if the and are the subgroups of the orthogonal group , as it is in the spin‐charge‐family theory. 5 - 22 We comment on the anomaly cancellation, which works if handedness and charges are related “by hand”.     

The imaginary Starobinsky model and higher curvature corrections

We elaborate on the predictions of the imaginary Starobinsky model of inflation coupled to matter, where the inflaton is identified with the imaginary part of the inflaton multiplet suggested by the Supergravity embedding of a pure gravity. In particular, we study the impact of higher‐order curvature terms and show that, depending on the parameter range, one may find either a quadratic model of chaotic inflation or monomial models of chaotic inflation with fractional powers between 1 and 2.     

Firewalls as artefacts of inconsistent truncations of quantum geometries

In this paper we argue that a firewall is simply a manifestation of an inconsistent truncation of non‐perturbative effects that unitarize the semiclassical black hole. Namely, we show that a naive truncation of quantum corrections to the Hawking spectrum at order , inexorably leads to a “localised” divergent energy density near the black hole horizon. Nevertheless, in the same approximation, a distant observer only sees a discretised spectrum and concludes that unitarity is achieved by effects. This is due to the fact that instead, the correct quantum corrections to the Hawking spectrum go like . Therefore, while at a distance far away from the horizon, where , quantum corrections are perturbative, they do diverge close to the horizon, where . Nevertheless, these “corrections” nicely re‐sum so that correlations functions are smooth at the would‐be black hole horizon. Thus, we conclude that the appearance of firewalls is just a signal of the breaking of the semiclassical approximation at the Page time, even for large black holes.     

Quantum holonomy theory and hilbert space representations

We present a new formulation of quantum holonomy theory, which is a candidate for a non‐perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the algebra, which is generated by holonomy‐diffeomorphisms on a 3‐dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy‐diffeomorphisms form a non‐commutative ‐algebra. A proof that the state that generates the representation exist is left for later publications.     

Supersymmetric M2‐branes with Englert fluxes,and the simple group PSL(2, 7)

A new class is introduced of M2‐branes solutions of d=11 supergravity that include internal fluxes obeying Englert equation in 7‐dimensions. A simple criterion for the existence of Killing spinors in such backgrounds is established. Englert equation is viewed as the generalization to d=7 of Beltrami equation defined in d=3 and it is treated accordingly. All 2‐brane solutions of minimal d=7 supergracity can be uplifted to d=11 and have supersymmetry. It is shown that the simple group PSL(2, 7) is crystallographic in d=7 having an integral action on the A7 root lattice. By means of this point‐group and of the T⁷ torus obtained quotiening with the A7 root lattice we were able to construct new M2 branes with Englert fluxes and . In particular we exhibit here an solution depending on 4‐parameters and admitting a large non abelian discrete symmetry, namely . The dual field theories have the same symmetries and have complicated non linear interactions.     

Hodge numbers for CICYs with symmetries of order divisible by 4

We compute the Hodge numbers for the quotients of complete intersection Calabi‐Yau three‐folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant Kähler classes. The quotients studied here have been obtained in the automated classification of V. Braun. Although the computer search found the freely acting groups, the Hodge numbers of the quotients were not calculated. The freely acting groups, G, that arise in the classification are either or contain , , or as a subgroup. The Hodge numbers for the quotients for which the group G contains or have been computed previously. This paper deals with the remaining cases, for which or . We also compute the Hodge numbers for 99 of the 166 CICY's which have quotients.