The impact of Friedmann's work on cosmology
We present a brief review of Friedmann's impact on cosmology from a historical and a physical perspective.
gr-qc↗
arXiv subjects
Hermann Nicolai
Publications and source records attributed to Hermann Nicolai.
Perturbative linearization of super-Yang-Mills theories in general gauges
Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.
hep-th↗
Supermassive gravitinos and giant primordial black holes
We argue that the stable (color singlet) supermassive gravitinos proposed in our previous work can serve as seeds for giant primordial black holes. These seeds are hypothesized to start out as tightly bound states of fractionally charged gravitinos in the radiation dominated era, whose formation is supported by the universally attractive combination of gravitational and electric forces between the gravitinos and anti-gravitinos (reflecting their `almost BPS-like' nature). When lumps of such bound states coalesce and undergo gravitational collapse, the resulting mini-black holes can escape Hawking evaporation if the radiation temperature exceeds the Hawking temperature. Subsequently the black holes evolve according to an exact solution of Einstein's equations, to emerge as macroscopic black holes in the transition to the matter dominated era, with masses on the order of the solar mass or larger. The presence of these seeds at such an early time provides ample time for further accretion of matter and radiation, and would imply the existence of black holes of almost any size in the universe, up to the observed maximum.
astro-ph.HE↗
Perturbative linearization of supersymmetric Yang-Mills theory
Supersymmetric gauge theories are characterized by the existence of a transformation of the bosonic fields (Nicolai map) such that the Jacobi determinant of the transformation equals the product of the Matthews-Salam-Seiler and Faddeev-Popov determinants. This transformation had been worked out to second order in the coupling constant. In this paper, we extend this result (and the framework itself) to third order in the coupling constant. A diagrammatic approach in terms of tree diagrams, aiming to extend this map to arbitrary orders, is outlined. This formalism bypasses entirely the use of anti-commuting variables, as well as issues concerning the (non-)existence of off-shell formulations for these theories. It thus offers a fresh perspective on supersymmetric gauge theories and, in particular, the ubiquitous $\mathcal N{=}\,4$ theory.
hep-th↗
Tachyonic Kaluza-Klein modes and the AdS swampland conjecture
We compute the Kaluza-Klein spectrum of the non-supersymmetric SO(3)$\,\times\,$SO(3)-invariant AdS$_4$ vacuum of 11-dimensional supergravity, whose lowest-lying Kaluza-Klein modes belong to a consistent truncation to 4-dimensional ${\cal N}=8$ supergravity and are stable. We show that, nonetheless, the higher Kaluza-Klein modes become tachyonic so that this non-supersymmetric AdS$_4$ vacuum is perturbatively unstable within 11-dimensional supergravity. This represents the first example of unstable higher Kaluza-Klein modes and provides further evidence for the AdS swampland conjecture, which states that there are no stable non-supersymmetric AdS vacua within string theory. We also find 27 infinitesimal moduli amongst the Kaluza-Klein modes, which hints at the existence of a family of non-supersymmetric AdS$_4$ vacua.
hep-th↗
N=4 super Yang-Mills correlators without anti-commuting variables
Quantum correlators of pure supersymmetric Yang-Mills theories in D=3,4,6 and 10 dimensions can be reformulated via the non-linear and non-local transformation (`Nicolai map') that maps the full functional measure of the interacting theory to that of a free bosonic theory. As a special application we show that for the maximally extended N=4 theory in four dimensions, and up to order O(g^2), all known results for scalar correlators can be recovered in this way without any use of anti-commuting variables, in terms of a purely bosonic and ghost free functional measure for the gauge fields. This includes in particular the dilatation operator yielding the anomalous dimensions of composite operators. The formalism is thus competitive with more standard perturbative techniques.
hep-th↗
Supersymmetric Yang-Mills Theories: not quite the usual perspective
In this paper, we take up an old thread of development concerning the characterization of supersymmetric theories without any use of anticommuting variables that goes back to one of the authors' very early work [1]. Our special focus here will be on the formulation of supersymmetric Yang-Mills theories, extending previous results beyond $D=4$ dimensions. This perspective is likely to provide new insights into these theories, and in particular the maximally extended $N=4$ theory. As a new result we present a novel derivation of the admissible dimensions for interacting (pure) super-Yang-Mills theories to exist. This article is dedicated to the memory of Peter Freund, amongst many other things an early contributor to supersymmetry, and an author of one of the very first papers on superconformal gauge theories [2]. The final section contains some personal reminiscences of H.N.'s encounters with Peter Freund.
hep-th↗
Superheavy Gravitinos and Ultra-High Energy Cosmic Rays
We argue that the superheavy gravitinos that we had previously proposed as candidates for Dark Matter can offer a possible explanation for the ultra-high energy cosmic ray (UHECR) events observed at the Pierre Auger Observatory, via gravitino anti-gravitino annihilation in the `skin' of neutron stars. The large mass and strong interactions of these particles, together with their stability against decays into standard matter are essential for the proposed explanation to work. In particular, it ensues that UHECR events can be understood to originate from neutron stars inside a GKZ horizon of $\sim$ 50 Mpc. The composition of neutron stars near their surface could play a crucial role in explaining the presence of heavy ions in these events. If confirmed, this new mechanism can be taken as evidence for the fundamental ansatz towards unification on which it is based.
astro-ph.HE↗
Planck Mass Charged Gravitino Dark Matter
Following up on our earlier work predicting fractionally charged supermassive gravitinos, we explain their potential relevance as novel candidates for Dark Matter and discuss possible signatures and ways to detect them.
hep-ph↗
On spinorial representations of involutory subalgebras of Kac-Moody algebras
The representation theory of involutory (or 'maximal compact') subalgebras of infinite-dimensional Kac-Moody algebras is largely terra incognita, especially with regard to fermionic (double-valued) representations. Nevertheless, certain distinguished such representations feature prominently in proposals of possible symmetries underlying M theory, both at the classical and the quantum level. Here we summarise recent efforts to study spinorial representations systematically, most notably for the case of the hyperbolic Kac-Moody algebra $E_{10}$ where spinors of the involutory subalgebra $K(E_{10})$ are expected to play a role in describing algebraically the fermionic sector of $D=11$ supergravity and M theory. Although these results remain very incomplete, they also point towards the beginning of a possible explanation of the fermion structure observed in the Standard Model of Particle Physics.
hep-th↗
Softly broken conformal symmetry with quantum gravitational corrections
We show that a previously proposed new mechanism to eliminate quadratic divergences for scalar masses is self-consistently compatible with corrections induced by perturbative quantum gravity, provided the theory embeds consistently into a UV completion at the Planck scale.
hep-th↗
Conformal Anomaly for Non-Conformal Scalar Fields
We give a general definition of the conformal anomaly for theories that are not classically Weyl invariant and show that this definition yields a quantity that is both finite and local. As an example we study the conformal anomaly for a non-minimally coupled massless scalar and show that our definition coincides with results obtained using the heat kernel method.
hep-th↗
Corrigendum to "Coupling the SO(2) supergravity through dimensional reduction" [Phys. Lett. B 96 (1-2) (1980) 89-93]
Due to renewed interest in D=5 supergravity and its quartic fermionic terms, fuelled by very recent work on supersymmetric quantum cosmology we correct an error in eq.(4) of the paper cited in the title. We also give the Lagrangian in second order formalism which was not explicitly written out before.
hep-th↗
Standard Model Fermions and Infinite-Dimensional R-Symmetries
Following up on our earlier work where we showed how to amend a scheme originally proposed by M. Gell-Mann to identify the 48 spin 1/2 fermions of N=8 supergravity that remain after complete breaking of N=8 supersymmetry with the 3x16 quarks and leptons of the Standard Model, we further generalize the construction to account for the full SU(3)_c x SU(2)_w x U(1)_Y assignments, with an additional family symmetry SU(3)_f. Our proposal relies in an essential way on embedding the SU(8) R-symmetry of N=8 supergravity into the (infinite-dimensional) `maximal compact' subgroup K(E10) of the conjectured maximal duality symmetry E10. As a by-product, it predicts fractionally charged and possibly strongly interacting massive gravitinos. It also indicates how E10 and K(E10) can supersede supersymmetry as a guiding principle for unification.
hep-th↗
On quantum compatibility of counterterm deformations and duality symmetries in ${\cal N}\geq 5$ supergravities
In ${\cal N}=5, 6, 8$ supergravities there are hidden symmetries of equations of motion, described by duality groups $SU(1,5), \, SO^*(12), \, E_{7(7)}$ respectively. UV divergences and known candidate counterterms violate the deformed duality symmetry current conservation. Extra higher derivative terms in the action are required to restore duality. We study the effect of a two-vector part of the counterterm for ${\cal N}\geq 5$ supergravities using the universality of the symplectic structure of extended supergravities. We construct a compact form of a deformed action with infinite number of higher derivative terms and restored duality symmetry with deformation parameter $λ$. We find, in $λ^2$ approximation, that the $SU({\cal N})$ symmetry of the deformed theory is restored on shell.
hep-th↗
Conformal Standard Model, Leptogenesis and Dark Matter
The Conformal Standard Model (CSM) is a minimal extension of the Standard Model of Particle Physics based on the assumed absence of large intermediate scales between the TeV scale and the Planck scale, which incorporates only right-chiral neutrinos and a new complex scalar in addition to the usual SM degrees of freedom, but no other features such as supersymmetric partners. In this paper, we present a comprehensive quantitative analysis of this model, and show that all outstanding issues of particle physics proper can in principle be solved `in one go' within this framework. This includes in particular the stabilization of the electroweak scale, `minimal' leptogenesis and the explanation of Dark Matter, with a small mass and very weakly interacting Majoron as the Dark Matter candidate (for which we propose to use the name `minoron'). The main testable prediction of the model is a new and almost sterile scalar boson that would manifest itself as a narrow resonance in the TeV region. We give a representative range of parameter values consistent with our assumptions and with observation.
hep-ph↗
A rederivation of the conformal anomaly for spin-1/2
We rederive the conformal anomaly for spin-1/2 fermions by a genuine Feynman graph calculation, which has not been available so far. Although our calculation merely confirms a result that has been known for a long time, the derivation is new, and thus furnishes a method to investigate more complicated cases (in particular concerning the significance of the quantum trace of the stress tensor in non-conformal theories) where there remain several outstanding and unresolved issues.
hep-th↗
Hyperbolic Weyl groups and the four normed division algebras
We study the Weyl groups of hyperbolic Kac-Moody algebras of `over-extended' type and ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K=R,C,H,O, respectively. A crucial role is played by integral lattices of the division algebras and associated discrete matrix groups. Our findings can be summarized by saying that the even subgroups, W^+, of the Kac-Moody Weyl groups, W, are isomorphic to generalized modular groups over K for the simply laced algebras, and to certain finite extensions thereof for the non-simply laced algebras. This hints at an extended theory of modular forms and functions.
math.RT↗