4,120 research outputs found
THE UNIVERSAL DE RHAM / SPENCER DOUBLE COMPLEX ON A SUPERMANIFOLD
No full textThe universal Spencer and de Rham complexes of sheaves over a smooth or analytical manifold are well known to play a basic role in the theory of D-modules. In this article we consider a double complex of sheaves generalizing both complexes for an arbitrary supermanifold, and we use it to unify the notions of differential and integral forms on real, complex and algebraic supermanifolds. The associated spectral sequences give the de Rham complex of differential forms and the complex of integral forms at page one. For real and complex supermanifolds both spectral sequences converge at page two to the locally constant sheaf. We use this fact to show that the cohomology of differential forms is isomorphic to the cohomology of integral forms, and they both compute the de Rham cohomology of the reduced manifold. Furthermore, we show that, in contrast with the case of ordinary complex manifolds, the Hodge-to-de Rham (or Frolicher) spectral sequence of supermanifolds with Kahler reduced manifold does not converge in general at page one
Conformal structure of the Schwarzschild black hole.
No full textWe show that the scalar wave equation at low frequencies in the Schwarzschild geometry enjoys a hidden SL(2,R) invariance, which is not inherited from an underlying symmetry of the spacetime itself. Contrary to what happens for Kerr black holes, the vector fields generating the SL(2,R) are globally defined. Furthermore, it turns out that under an SU(2,1) Kinnersley transformation, which maps the Schwarzschild solution into the near horizon limit AdS_2 x S^2 of the extremal Reissner-Nordstr"om black hole (with the same entropy), the Schwarzschild hidden symmetry generators become exactly the isometries of the AdS_2 factor. Finally, we use the SL(2,R) symmetry to determine algebraically the quasinormal frequencies of the Schwarzschild black hole, and show that this yields the correct leading behaviour for large damping
One-dimensional super Calabi-Yau manifolds and their mirrors
No full textWe apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCYâs having reduced manifold equal to â 1, namely the projective super space â 1 | 2 and the weighted projective super space Wâ(2)1|1. Then we compute the corresponding sheaf cohomology of superforms, showing that the cohomology with picture number one is infinite dimensional, while the de Rham cohomology, which is what matters from a physical point of view, remains finite dimensional. Moreover., we provide the complete real and holomorphic de Rham cohomology for generic projective super spaces â n|m. We also determine the automorphism groups: these always match the dimension of the projective super group with the only exception of â 1 | 2, whose automorphism group turns out to be larger than the projective super group. By considering the cohomology of the super tangent sheaf, we compute the deformations of â 1|m, discovering that the presence of a fermionic structure allows for deformations even if the reduced manifold is rigid. Finally., we show that â 1 | 2 is self-mirror, whereas Wâ(2)1|1 has a zero dimensional mirror. Also., the mirror map for â 1 | 2 naturally endows it with a structure of N = 2 super Riemann surface
Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity
No full textWe consider various models of three-dimensional gravity with torsion or nonmetricity (metric affine gravity), and show that they can be written as Chern-Simons theories with suitable gauge groups. Using the groups ISO(2,1), SL(2,C) and SL(2,R)xSL(2,R), and the fact that they admit two independent coupling constants, we obtain the Mielke-Baekler model for zero, positive and negative effective cosmological constant respectively. Choosing SO(3,2) as the gauge group, one gets a generalization of conformal gravity that has zero torsion and only the trace part of the nonmetricity. This characterizes a Weyl structure. Finally, we present a new topological model of metric affine gravity in three dimensions arising from an SL(4,R) Chern-Simons theory
Multi-Centered Invariants, Plethysm and Grassmannians
No full textMotivated by multi-centered black hole solutions of Maxwell-Einstein theories of (super)gravity in D=4 space-time dimensions, we develop some general methods, that can be used to determine all homogeneous invariant polynomials on the irreducible (SL_h(p,R) x G4)-representation (p,R), where p denotes the number of centers, and SL_h(p,R) is the "horizontal" symmetry of the system, acting upon the indices labelling the centers. The black hole electric and magnetic charges sit in the symplectic representation R of the generalized electric-magnetic (U-)duality group G4. We start with an algebraic approach based on classical invariant theory, using Schur polynomials and the Cauchy formula. Then, we perform a geometric analysis, involving Grassmannians, Pluecker coordinates, and exploiting Bott's Theorem. We focus on non-degenerate groups G4 "of type E7" relevant for (super)gravities whose (vector multiplets') scalar manifold is a symmetric space. In the triality-symmetric stu model of N=2 supergravity, we explicitly construct a basis for the 10 linearly independent degree-12 invariant polynomials of 3-centered black holes.Motivated by multi-centered black hole solutions of Maxwell-Einstein theories of (super)gravity in D = 4 space-time dimensions, we develop some general methods, that can be used to determine all homogeneous invariant polynomials on the irreducible (SL ( )h( )(p, ) ⊗ G (4))-representation (p , R), where p denotes the number of centers, and SL ( )h( )(p, ) is the “horizontal” symmetry of the system, acting upon the indices labelling the centers. The black hole electric and magnetic charges sit in the symplectic representation R of the generalized electric-magnetic (U -)duality group G (4).Motivated by multi-centered black hole solutions of Maxwell-Einstein theories of (super)gravity in D=4 space-time dimensions, we develop some general methods, that can be used to determine all homogeneous invariant polynomials on the irreducible (SL_h(p,R) x G4)-representation (p,R), where p denotes the number of centers, and SL_h(p,R) is the "horizontal" symmetry of the system, acting upon the indices labelling the centers. The black hole electric and magnetic charges sit in the symplectic representation R of the generalized electric-magnetic (U-)duality group G4. We start with an algebraic approach based on classical invariant theory, using Schur polynomials and the Cauchy formula. Then, we perform a geometric analysis, involving Grassmannians, Pluecker coordinates, and exploiting Bott's Theorem. We focus on non-degenerate groups G4 "of type E7" relevant for (super)gravities whose (vector multiplets') scalar manifold is a symmetric space. In the triality-symmetric stu model of N=2 supergravity, we explicitly construct a basis for the 10 linearly independent degree-12 invariant polynomials of 3-centered black holes
Adams-Iwasawa N=8 Black Holes
No full textWe study some of the properties of the geometry of the exceptional Lie group E7(7), which describes the U-duality of the N=8, d=4 supergravity. In particular, based on a symplectic construction of the Lie algebra e7(7) due to Adams, we compute the Iwasawa decomposition of the symmetric space M=E7(7)/(SU(8)/Z_2), which gives the vector multiplets' scalar manifold of the corresponding supergravity theory. The explicit expression of the Lie algebra is then used to analyze the origin of M as scalar configuration of the "large" 1/8-BPS extremal black hole attractors. In this framework it turns out that the U(1) symmetry spanning such attractors is broken down to a discrete subgroup Z_4, spoiling their dyonic nature near the origin of the scalar manifold. This is a consequence of the fact that the maximal manifest off-shell symmetry of the Iwasawa parametrization is determined by a completely non-compact Cartan subalgebra of the maximal subgroup SL(8,R) of E7(7), which breaks down the maximal possible covariance SL(8,R) to a smaller SL(7,R) subgroup. These results are compared with the ones obtained in other known bases, such as the Sezgin-van Nieuwenhuizen and the Cremmer-Julia /de Wit-Nicolai frames.We study some of the properties of the geometry of the exceptional Lie group E7(7), which describes the U-duality of the N=8, d=4 supergravity. In particular, based on a symplectic construction of the Lie algebra e7(7) due to Adams, we compute the Iwasawa decomposition of the symmetric space M=E7(7)/(SU(8)/Z_2), which gives the vector multiplets' scalar manifold of the corresponding supergravity theory. The explicit expression of the Lie algebra is then used to analyze the origin of M as scalar configuration of the "large" 1/8-BPS extremal black hole attractors. In this framework it turns out that the U(1) symmetry spanning such attractors is broken down to a discrete subgroup Z_4, spoiling their dyonic nature near the origin of the scalar manifold. This is a consequence of the fact that the maximal manifest off-shell symmetry of the Iwasawa parametrization is determined by a completely non-compact Cartan subalgebra of the maximal subgroup SL(8,R) of E7(7), which breaks down the maximal possible covariance SL(8,R) to a smaller SL(7,R) subgroup. These results are compared with the ones obtained in other known bases, such as the Sezgin-van Nieuwenhuizen and the Cremmer-Julia /de Wit-Nicolai frames
CR1 Knops blood group alleles are not associated with severe malaria in the Gambia
No full textThe Knops blood group antigen erythrocyte polymorphisms have been associated with reduced falciparum malaria-based in vitro rosette formation (putative malaria virulence factor). Having previously identified single-nucleotide polymorphisms (SNPs) in the human complement receptor 1 (CR1/CD35) gene underlying the Knops antithetical antigens Sl1/Sl2 and McC(a)/McC(b), we have now performed genotype comparisons to test associations between these two molecular variants and severe malaria in West African children living in the Gambia. While SNPs associated with Sl:2 and McC(b+) were equally distributed among malaria-infected children with severe malaria and control children not infected with malaria parasites, high allele frequencies for Sl 2 (0.800, 1,365/1,706) and McC(b) (0.385, 658/1706) were observed. Further, when compared to the Sl 1/McC(a) allele observed in all populations, the African Sl 2/McC(b) allele appears to have evolved as a result of positive selection (modified Nei-Gojobori test Ka-Ks/s.e.=1.77, P-valu
Quantum and its irreducible representations
No full textWe define for real a unital -algebra
quantizing the universal enveloping
-algebra of . The -algebra
is realized as a -subalgebra of the
Drinfeld double of and its dual Hopf -algebra
, generated by the equatorial Podle\'s sphere coideal
-subalgebra of and
its associated orthogonal coideal -subalgebra . We then classify all the irreducible
-representations of .Comment: 22 pages; author accepted manuscrip
On the sheaf-theoretic SL(2, C) Casson–Lin invariant
No full textWe prove that the (τ-weighted, sheaf-theoretic) SL(2, C) Casson–Lin invariant introduced by Manolescu and the first author is generically independent of the parameter τ and additive under connected sums of knots in integral homology 3-spheres. This addresses two questions asked by Manolescu and the first author. Our arguments involve a mix of topology and algebraic geometry, and rely crucially on the fact that the SL(2, C) Casson–Lin invariant admits an alternative interpretation via the theory of Behrend functions.</p
Candidatus Rhetoricae (or Novus Candidatus).
No full textThis little book is a find whatever it finally turns out to be! For now it seems to be a Jesuit collegium text in rhetoric following the Progymnasmata of Aphthonius. If one works from the back of the book, there is an apparently independent 48-page work, Angelus Pacis by Nicolas Caussini (Latinized name), S.J. The rest of the book seems to be a commentary on or presentation of Aphthonius' Progymnasmata in 3 parts covering 435 pages, followed by a T of C and an AI, which is often one page off. Pars II is titled Rhetoricae Praecepta, Pars III De Panegyrico seu Laudatione. Pars I seems to be Apparatus ad Fabulam et Narrationem. Fable is handled on 15-31. After the famous Greek definition of Theion done into Latin ( sermo falsus veritatem effingens ), the author distinguishes rational (human) and moral (animal) fables, with mixed fables including both. He holds (19) that the sense of the fable generally needs to be expressed; otherwise people often miss the point of a fable. His Latin for promythium is praefabulatio, for epimythium affabulatio. Apologus and parabola are identical for him with fabula. After describing the qualities and uses of fables, the author presents some nine fables that exemplify various levels of style, twice telling the same stories on two levels (WL and FC). The last example is of the florid style: The Silkworm and the Spider takes four pages to tell! I found this book sitting in a box of disparate, unmarked, old books. It pays to look!This is a hardbound book (hard cover)Language note: Bilingual: Greek/LatinElzevers
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