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On models of cosmic inflation in D=4 supergravity and the -attractor mechanism & the -problem resolution: (See also at Starobinsky model of cosmic inflation the references on its embedding into supergravity). Dimitri V. Nanopoulos, Keith A. Olive, Mark Srednicki, K. Tamvakis: Primordial inflation in simple supergravity, Phys. Lett. B 123 (1983) 41–44 [doi:10.1016/0370-2693(83)90954-1] R. Holman, …

superalgebra and (synthetic ) supergeometry algebraic quantum field theory (perturbative, on curved spacetimes, homotopical) quantum mechanical system, quantum probability interacting field quantization In globally supersymmetric field theory, the superpotential is a strictly holomorphic function of the chiral superfields that controls the theory’s non-gauge interaction. It appears in the action …

Planck Collaboration, Planck 2013 results. XXII. Constraints on inflation (arXiv:1303.5082) Planck Collaboration, BICEP2 A Joint Analysis of BICEP2/Keck Array and Planck Data (arXiv:1502.00612) Planck Collaboration, Planck 2015, Overview of results (arXiv:1502.01582) Planck Collaboration, Planck 2015 results. XIII. Cosmological parameters (arXiv:1502.01589) Planck Collaboration, Planck 2015 resul…

Formulation of (Lagrangian densities for) type II supergravity with “democratic”/“pregeometric” RR-fields subject to self-duality: On gauged supergravity in view of U-duality and M-theory: On supergravity models of cosmic inflation: Renata Kallosh, Andrei Linde, Diederik Roest: Superconformal Inflationary -Attractors, J. High Energ. Phys. 2013 198 (2013) [doi:10.1007/JHEP11(2013)198, arXiv:1311.0…

On simplicial de Rham cohomology?: Johan Louis Dupont: Simplicial de Rham Cohomology and characteristic classes of flat bundles, Topology 15 3 (1976) 233–245 [doi:10.1016/0040-9383(76)90038-0] Johan Louis Dupont: A dual simplicial de Rham complex, in: Algebraic Topology, Rational Homotopy, Lecture Notes in Mathematics 1318 (1988) [doi:10.1007/BFb0077796] On regulators and characteristic classes o…

physics, mathematical physics, philosophy of physics theory (physics), model (physics) experiment, measurement, computable physics Axiomatizations Tools Structural phenomena Types of quantum field thories examples superalgebra and (synthetic ) supergeometry supergravity in dimension 4. The maximally supersymmetric -version arises from type II supergravity in 10 dimension by compactification on a …

nLab Vladimir P. Akulov Selected writings Selected writings Precursor discussion of what became supergravity: and early formulation on superspace: Created on June 16, 2026 at 10:30:21. See the history of this page for a list of all contributions to it.

Raoul Bott (1923–2005) was one of the great 20th century topologists and geometers. Among his famous works, one should mention the Bott periodicity theorem (of importance in K-theory), studies in Morse theory (including the study of Bott–Morse functions), the Borel–Weil–Bott theorem in geometric representation theory, the study of fixed point (localization) formulas (the Atiyah–Bott fixed point t…

This entry is about the concept in supergeometry. For the concept in gravity/cosmology see at Wheeler superspace. superalgebra and (synthetic ) supergeometry Physicists often refer to spaces in supergeometry, such as supermanifolds or super schemes, as superspaces. Hence a superspace can be an affine superspace (the affine counterpart of the super vector space over real or complex numbers), super…

On the simplicial de Rham complex and equivariant de Rham cohomology:

nLab Yevsey Nisnevich Selected writings Selected writings Introducing what came to be known as the Nisnevich site: - Yevsey Nisnevich: The completely decomposed topology on schemes and associated descent spectral sequences in algebraic K-theory, in: Algebraic K-Theory: Connections with Geometry and Topology (Lake Louise, AB, 1987), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 279 Kl…

∞-Lie theory (higher geometry) Background Smooth structure Higher groupoids Lie theory ∞-Lie groupoids ∞-Lie algebroids Formal Lie groupoids Cohomology Homotopy Related topics Examples -Lie groupoids -Lie groups -Lie algebroids -Lie algebras superalgebra and (synthetic ) supergeometry A super Lie algebra which is a polyvector extension of the super Poincaré Lie algebra (supersymmetry) in for supe…

symmetric monoidal (∞,1)-category of spectra Let and be algebraic theories. The category of -bimodels and their homomorphisms is the category of -models and homomorphisms in . An alternative description is that it is a co--model in . Each such bimodel determines and is determined by a pair of adjoint functors Composition of such adjoint pairs yields a functor The category has a unit object – it w…

A morphism of sites is, unsurprisingly, the appropriate sort of morphism between sites. It is defined exactly so as to induce a geometric morphism between toposes of sheaves (or, more generally, exact completions). Let and be sites. A functor is a morphism of sites if is covering-flat, and preserves covering families, i.e. for every covering of an object , the family is a covering of . If has fin…

The term torsion is used for different concepts in different fields: In algebra, the torsion subgroup of a group is the group of elements of finite order (meaning: elements such that there is such that (with factors in the product)); similarly in ring theory an element of a module over a ring is a torsion element if it is annihilated by a nonzero element of the ring. A module is torsion (resp. to…

The Nisnevich topology, also called the completely decomposed topology, is a certain Grothendieck topology on the category of schemes which is finer than the Zariski topology but coarser than the étale topology. It retains many desirable properties from both topologies: The Nisnevich cohomological dimension (and even the homotopy dimension) of a scheme is bounded by its Krull dimension (like Zari…

homotopy theory, (∞,1)-category theory, homotopy type theory flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed… models: topological, simplicial, localic, … see also algebraic topology Introductions Definitions Paths and cylinders Homotopy groups Basic facts Theorems representation, 2-representation, ∞-representation Grothendieck group, lambda-ring, symmetric fu…

A quasicoherent sheaf of modules (often just “quasicoherent sheaf”, for short) is a sheaf of modules over the structure sheaf of a ringed space that is locally presentable in that it is locally the cokernel of a morphism of free modules. For comparison, by the Serre-Swan theorem a vector bundle on a suitable ringed space is equivalently encoded in its sheaf of sections which is even locally free …

On hypercovers in simplicial presheaves: On quasicoherent sheaves over stacks: On the homotopy theory of stacks via localization of a model structure on simplicial presheaves:

The “fundamental theorem” of topos theory (in the terminology of McLarty 1992) asserts that for any topos and any object, also the slice category is a topos: the slice topos. If is a category of sheaves, hence a Grothendieck topos, then so its its slice: (SGA4.1, p. 295). The analogous statement holds for slice -categories of -toposes: slice -toposes (Lurie 2009, Prop. 6.3.5.1). The archetypical …