1,721,018 research outputs found
Odd characteristic classes in entire cyclic homology and equivariant loop space homology
No full textGiven a compact manifoldM and a smooth map g:M → U.(l×l:C) from M to the Lie group of unitary l×l matrices with entries in C, we construct a Chern character Ch-(g) which lives in the odd part of the equivariant (entire) cyclic Chen-normalized cyclic complex Nε(ωT(M × T)) of M, and which is mapped to the odd Bismut-Chern character under the equivariant Chen integral map. It is also shown that the assignment g → Ch-(g) induces a well-defined group homomorphism from the K-1 theory of M to the odd homology group of Nε(ωT(M × T))
Super throats with non trivial scalars
Full text linkWe find new BPS solutions in N = 2 D = 4 Fayet-Iliopoulos gauged super- gravity with STU prepotential. These are stationary solutions carrying a Kerr-Newman throat spacetime geometry and are everywhere regular. One of the three scalar vector fields is non constant. Moreover, they carry non vanishing magnetic fluxes and dipolar electric fields
Erratum: Non canonical polarizations of gravitational waves (The European Physical Journal C, (2023), 83, 4, (310), 10.1140/epjc/s10052-023-11502-1)
No full textIn the original article, a misprint has been introduced in Eq. (3). The correct equation reads as follows: (Formula presented.) The original article has been corrected
Non canonical polarizations of gravitational waves
Full text linkWe hereby propose an alternative and additional angle on the nature of gravitational waves (GWs), postulating the theoretical and experimental possibility that GWs carry a deformation of the time component of spacetime, other than the spatial one. By explicitly working outside of the transverse-traceless gauge, we propose how events with well-defined time duration, when hit by a GW, would consequently be expected to show a difference in their characteristic time, as measured from the rest frame of an outside observer, whose clock is to remain unaffected by the GW. This constitutes a theoretically viable way in the sense of detecting the passing of the wave itself and may prove relevant as a standalone method for GWs detection other than laser interferometers, or as well be implemented as a complementary but independent system of signal triggering, improving the statistical significance of existing methods. A simple but physically realistic scenario in which the appropriate conditions for the generation and detection of GWs with time dilation are met is presented, along with the conceptual design of an experimental detector
De sitter magnetic black hole dipole with a supersymmetric horizon
Full text linkWe find a new non BPS solution in N = 2 D = 4 gauged supergravity coupled to U(1) gauge fields and matter. It consists in a closed universe with two extremal black
holes of equal size, surrounding two singularities. They have opposite magnetic charges (and no electric charges), but stay in static equilibrium thanks to the positive pressure of a cosmological constant. The geometry is perfectly symmetric under the exchange of the black holes and the flip of the sign of the charges. However the scalar field is non constant and non symmetric, with different values at the horizons, which depend on a real modulus. Remarkably we show that it satisfies the attractor mechanism and the entropy indeed depends only on the magnetic charges. At one of the horizons the solution becomes 1/2 -BPS supersymmetric, while at the other one there is no supersymmetry, but the entropy remains independent from the scalar modulus
Concentration of measure for classical Lie groups
No full textWe study the concentration of measure in metric-measurable (mm)-spaces. We define the notion of concentration locus of a flag sequence of metric-measurable (mm)-spaces. Some examples of infinite group action on an infinite dimensional compact and non-compact manifold show the role played by the trajectory of concentration locus. We also provide some applications in physics, which emphasize the role of concentration of measure in gravitational effects
Spectral properties for the Klein-Gordon Hamiltonian in charged black hole backgrounds
Full text linkCharged massive scalar fields on charged black hole backgrounds are investigated through methods of spectral analysis in Krein spaces. We consider, on the three charged black hole backgrounds (Nariai, Reissner-Nordström, ultracold-II) taken into account, a necessary condition for the existence of complex eigenvalues. We show that even if it is satisfied, in two cases (Nariai and ultracold-II), by direct calculation, they actually cannot exist. In both cases, the Klein paradox occurs without restriction on the parameters. In the third case, the condition for their existence is shown to coincide with the condition, allowing the quantum discharge phenomenon associated with the Klein paradox. We also clarify the role of “classical potentials,” which appear in the physical literature on the subject, giving rise to the so-called level-crossing appearing in semiclassical calculations, and we comment on problems occurring in quantum field theory in the presence of complex eigenvalues
The E3∕Z3 orbifold, mirror symmetry, and Hodge structures of Calabi–Yau type
No full textStarting from the Kähler moduli space of the rigid orbifold Z=E3∕Z3 one would expect for the cohomology of the generalized mirror to be a Hodge structure of Calabi–Yau type (1,9,9,1). We show that such a structure arises in a natural way from rational Hodge structures on Λ3Q[ω]6, where ω is a primitive third root of unity. We do not try to identify an underlying mirror geometry, but we show how special geometry arises in our abstract construction. We also show how such Hodge structure can be recovered as a polarized substructure of a bigger Hodge structure given by the third cohomology group of a six-dimensional abelian variety of Weil-type. Moreover, we recover a result of Zheng Zhang on the associates variation of Hodge structure
Non projected calabi-yau supermanifolds over P2
Full text linkWe start a systematic study of non-projected supermanifolds, concentrating on supermanifolds with fermionic dimension 2 and with the reduced manifold a complex projective space. We show that all the non-projected supermanifolds of dimension 2j2 over P2 are completely characterised by a non-zero cohomology class 2 H1(TP2 (3)) and by a locally free sheaf FM of rank 0j2, satisfying Sym2FM = KP2 . Denoting such supermanifolds with P2 (FM ), we show that all of them are Calabi-Yau supermanifolds and, when 6= 0, they are non-projective, that is they cannot be embedded into any projective superspace Pnjm. Instead, we show that every non-projected supermanifold over P2 admits an embedding into a super Grassmannian. By contrast, we give an example of a supermanifold P2 (FM ) that cannot be embedded in any of the projective superspaces Pn introduced by Manin and Deligne. However, we also show that when FM is the cotangent bundle over P2, then the non-projected P2 (FM ) and the -projective plane P2 do coincide
Ultraviolet behavior of conformally reduced quadratic gravity
Full text linkWe study the conformally reduced R+R2 theory of gravity and we show that the theory is asymptotically safe with an ultraviolet critical manifold of dimension three. In particular, we discuss the universality properties of the fixed point and its stability under the use of different regulators with the help of the proper-time flow equation. We find three relevant directions, corresponding to the g, gR, and gR2 operators, whose critical properties are very similar to the ones shared by the full theory. Our result shows that the basic mechanism at the core of the asymptotic safety program is still well described by the conformal sector also beyond the Einstein-Hilbert truncation. Possible consequences for the asymptotic safety program are discussed
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