scholarly journals Equivariant differential cohomology

2018 ◽  
Vol 370 (11) ◽  
pp. 8237-8283 ◽  
Author(s):  
Andreas Kübel ◽  
Andreas Thom
Keyword(s):  
Differential Cohomology

scholarly journals Twisted differential cohomology

2019 ◽  
Vol 19 (4) ◽  
pp. 1631-1710 ◽  
Author(s):  
Ulrich Bunke ◽  
Thomas Nikolaus
Keyword(s):  
Differential Cohomology

First cohomology of 𝔞𝔣𝔣(1) and 𝔞𝔣𝔣(1|1) acting on linear differential operators

2016 ◽  
Vol 13 (01) ◽  
pp. 1550130 ◽  
Author(s):  
Imed Basdouri ◽  
Maha Boujelben ◽  
Ammar Derbali
Keyword(s):  
Differential Operators ◽  
Lie Superalgebra ◽  
Module Structure ◽  
Differential Cohomology ◽  
Linear Differential Operators ◽  
Linear Differential

We consider the [Formula: see text]-module structure on the spaces of differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra [Formula: see text] with coefficients in differential operators acting on the spaces of weighted densities. We study also the super analogue of this problem getting the same results.

Cohomology of orthosymplectic Lie superalgebra acting on λ-densities on ℝ1|n

2016 ◽  
Vol 14 (01) ◽  
pp. 1750016
Author(s):  
Nabila El Gomdi ◽  
Rim Messaoud
Keyword(s):  
Lie Superalgebra ◽  
Acta Math ◽  
Differential Cohomology ◽  
Orthosymplectic Superalgebra ◽  
Orthosymplectic Lie Superalgebra

We compute the first differential cohomology of the orthosymplectic Lie superalgebra [Formula: see text] with coefficients in the superspace of weighted densities [Formula: see text] on the (1, 2)-dimensional real superspace. We explicitly give 1-cocycles spanning these cohomologies. This work is the simplest generalization of a result by Basdouri and Essayari [On cohomology of the orthosymplectic superalgebra, Acta Math. Hungar. 130(1–2) (2011) 155–166].

scholarly journals Differential cohomology theories as sheaves of spectra

2014 ◽  
Vol 11 (1) ◽  
pp. 1-66 ◽  
Author(s):  
Ulrich Bunke ◽  
Thomas Nikolaus ◽  
Michael Völkl
Keyword(s):  
Differential Cohomology

scholarly journals Super-Lie n-algebra extensions, higher WZW models and super-p-branes with tensor multiplet fields

2015 ◽  
Vol 12 (02) ◽  
pp. 1550018 ◽  
Author(s):  
Domenico Fiorenza ◽  
Hisham Sati ◽  
Urs Schreiber
Keyword(s):  
Homotopy Theory ◽  
Symmetry Algebra ◽  
Formal Proof ◽  
Differential Cohomology ◽  
Higher Symmetry ◽  
Higher Dimensional ◽  
Tensor Multiplet ◽  
Type Iib String Theory ◽  
Super Lie Algebra ◽  
M Theory

We formalize higher-dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type σ-model branes (open brane ending on background brane) are encoded precisely in (super-)L∞-extension theory and how the resulting "extended (super-)space-times" formalize spacetimes containing σ-model brane condensates. As an application we prove in Lie n-algebra homotopy theory that the complete super-p-brane spectrum of superstring/M-theory is realized this way, including the pure σ-model branes (the "old brane scan") but also the branes with tensor multiplet worldvolume fields, notably the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional (11D) spacetime with an M2-brane condensate turns out to be the "M-theory super-Lie algebra". We also observe that in this formulation there is a simple formal proof of the fact that type IIA spacetime with a D0-brane condensate is the 11D sugra/M-theory spacetime, and of (prequantum) S-duality for type IIB string theory. Finally we give the non-perturbative description of all this by higher WZW-type σ-models on higher super-orbispaces with higher WZW terms in stacky differential cohomology.

scholarly journals Primary operations in differential cohomology

2018 ◽  
Vol 335 ◽  
pp. 519-562 ◽  
Author(s):  
Daniel Grady ◽  
Hisham Sati
Keyword(s):  
Differential Cohomology

Cohomology and deformation of 𝔞𝔣𝔣(1|1) acting on differential operators

2018 ◽  
Vol 15 (05) ◽  
pp. 1850072
Author(s):  
Khaled Basdouri ◽  
Salem Omri
Keyword(s):  
Differential Operators ◽  
Lie Superalgebra ◽  
Module Structure ◽  
Infinitesimal Deformation ◽  
Differential Cohomology ◽  
Linear Differential Operators ◽  
Formal Deformation ◽  
Pseudo Differential Operators ◽  
Linear Differential

We consider the [Formula: see text]-module structure on the spaces of differential operators acting on the spaces of weighted densities. We compute the second differential cohomology of the Lie superalgebra [Formula: see text] with coefficients in differential operators acting on the spaces of weighted densities. We classify formal deformations of the [Formula: see text]-module structure on the superspaces of symbols of differential operators. We prove that any formal deformation of a given infinitesimal deformation of this structure is equivalent to its infinitesimal part. This work is the simplest superization of a result by Basdouri [Deformation of [Formula: see text]-modules of pseudo-differential operators and symbols, J. Pseudo-differ. Oper. Appl. 7(2) (2016) 157–179] and application of work by Basdouri et al. [First cohomology of [Formula: see text] and [Formula: see text] acting on linear differential operators, Int. J. Geom. Methods Mod. Phys. 13(1) (2016)].

Differential Cohomology

2010 ◽  
pp. 19-70 ◽  
Author(s):  
André Haefliger
Keyword(s):  
Differential Cohomology
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