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”.     

New Gaugings and Non‐Geometry

We discuss the possible realisation in string/M theory of the recently discovered family of four‐dimensional maximal gauged supergravities, and of an analogous family of seven‐dimensional half‐maximal gauged supergravities. We first prove a no‐go theorem that neither class of gaugings can be realised via a compactification that is locally described by ten‐ or eleven‐dimensional supergravity. In the language of Double Field Theory and its M theory analogue, this implies that the section condition must be violated. Introducing the minimal number of additional coordinates possible, we then show that the standard S ³ and S ⁷ compactifications of ten‐ and eleven‐dimensional supergravity admit a new class of section‐violating generalised frames with a generalised Lie derivative algebra that reproduces the embedding tensor of the and gaugings respectively. The physical meaning, if any, of these constructions is unclear. They highlight a number of the issues that arise when attempting to apply the formalism of Double Field Theory to non‐toroidal backgrounds. Using a naive brane charge quantisation to determine the periodicities of the additional coordinates restricts the gaugings to an infinite discrete set and excludes all the gaugings other than the standard one.     

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.     

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.     

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.     

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.     

algebras and field theory

We review and develop the general properties of algebras focusing on the gauge structure of the associated field theories. Motivated by the homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the structure of general gauge invariant perturbative field theories. We sketch such formulations for non‐abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full algebra for the interacting theory. The analysis suggests that algebras provide a classification of perturbative gauge invariant classical field theories.     

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.     

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.     

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.     

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.     

inflation from scale invariant supergravity and anomaly free superstrings with fluxes

The scale invariant gravity theory coupled to conformally invariant matter is investigated. We show that in the non‐supersymmetric case the conformally coupled scalars belong to an manifold, while in the supersymmetric case the scalar manifold becomes isomorphic to the Kählerian space =. In both cases when the underlying scale symmetry is preserved the vacuum corresponds to de Sitter space. Once the scale symmetry is broken by quantum effects, a transition to flat space becomes possible. We argue that the scale violating terms are induced by anomalies related to a symmetry. The anomaly is resolved via the gauging of a Peccei‐Quinn axion shift symmetry. The theory describes an inflationary transition from de Sitter to flat Minkowski space, very similar to the Starobinsky inflationary model. The extension to metastable de Sitter superstring vacua is also investigated. The scalar manifold is extended to a much richer manifold, but it contains always as a sub‐manifold. In superstrings the metastability is induced by axions that cure the anomalies in chiral (or even ) supersymmetric vacua via a Green‐Schwarz/Peccei‐Quinn mechanism generalized to four dimensions. We present some typical superstring models and discuss the possible stabilization of the no‐scale modulus.     

Can Superconducting Cosmic Strings Piercing Seed Black Holes Generate Supermassive Black Holes in the Early Universe?

The discovery of a large number of supermassive black holes (SMBH) at redshifts , when the Universe was only 900 million years old, raises the question of how such massive compact objects could form in a cosmologically short time interval. Each of the standard scenarios proposed, involving rapid accretion of seed black holes or black hole mergers, faces severe theoretical difficulties in explaining the short‐time formation of supermassive objects. In this work we propose an alternative scenario for the formation of SMBH in the early Universe, in which energy transfer from superconducting cosmic strings piercing small seed black holes is the main physical process leading to rapid mass increase. As a toy model, the accretion rate of a seed black hole pierced by two antipodal strings carrying constant current is considered. Using an effective action approach, which phenomenologically incorporates a large class of superconducting string models, we estimate the minimum current required to form SMBH with masses of order by . This corresponds to the mass of the central black hole powering the quasar ULAS J112001.48+064124.3 and is taken as a test case scenario for early‐epoch SMBH formation. For GUT scale strings, the required fractional increase in the string energy density, due to the presence of the current, is of order 10⁻⁷, so that their existence remains consistent with current observational bounds on the string tension. In addition, we consider an “exotic” scenario, in which an SMBH is generated when a small seed black hole is pierced by a higher‐dimensional string, predicted by string theory. We find that both topological defect strings and fundamental strings are able to carry currents large enough to generate early‐epoch SMBH via our proposed mechanism.     

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.     

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 .     

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.     

Diving into traversable wormholes

We study various aspects of wormholes that are made traversable by an interaction beween the two asymptotic boundaries. We concentrate on the case of nearly‐ gravity and discuss a very simple mechanical picture for the gravitational dynamics. We derive a formula for the two sided correlators that includes the effect of gravitational backreaction, which limits the amount of information we can send through the wormhole. We emphasize that the process can be viewed as a teleportation protocol where the teleportee feels nothing special as he/she goes through the wormhole. We discuss some applications to the cloning paradox for old black holes. We point out that the same formula we derived for gravity is also valid for the simple SYK quantum mechanical theory, around the thermofield double state. We present a heuristic picture for this phenomenon in terms of an operator growth model. Finally, we show that a similar effect is present in a completely classical chaotic system with a large number of degrees of freedom.     

Abelian scalar theory at large global charge

We elaborate on Abelian complex scalar models, which are dictated by natural actions (all couplings are of order one), at fixed and large global U (1) charge in an arbitrary number of dimensions. The ground state is coherently constructed by the zero modes and the appearance of a centrifugal potential is quantum mechanically verified. Using the path integral formulation we systematically analyze the quantum fluctuations around in order to derive an effective action for the Goldstone mode, which becomes perturbatively meaningful when the charge is large. In this regime we explicitly show, by computing the first few loop corrections, that the whole construction is stable against quantum effects, in the sense that any higher derivative couplings to Goldstone's tree‐level action are suppressed by appropriate powers of the large charge.     

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.