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Extreme 5-dimensional black holes with SU(2)-symmetric horizons

Journal of High Energy Physics
We show that the near horizon geometry of 5-dimensional extreme (i.e., degenerate) stationary vacuum black holes, with or without cosmological constant, whose event horizons exhibit SU(2) symmetry must be that of a Berger sphere.
Eric Bahuaud, Sharmila Gunasekaran, Hari K Kunduri, Eric Woolgar   +3 more
doaj   +1 more source

Developments in noncommutative differential geometry [PDF]

, 2002
One of the great outstanding problems of theoretical physics is the quantisation of gravity, and an associated description of quantum spacetime. It is often argued that, at short distances, the manifold structure of spacetime breaks down and is replaced ...
Hale, Mark
core  

Schubert problems, positivity and symbol letters

Journal of High Energy Physics, 2022
We propose a geometrical approach to generate symbol letters of amplitudes/integrals in planar N $$ \mathcal{N} $$ = 4 Super Yang-Mills theory, known as Schubert problems. Beginning with one-loop integrals, we find that intersections of lines in momentum
Qinglin Yang
doaj   +1 more source

Noncommutative Differential Geometry of Generalized Weyl Algebras [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2016
Elements of noncommutative differential geometry of ${\mathbb Z}$-graded generalized Weyl algebras ${\mathcal A}(p;q)$ over the ring of polynomials in two variables and their zero-degree subalgebras ${\mathcal B}(p;q)$, which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed.
openaire   +6 more sources

T-duality of emergent gravities on nilmanifolds

Journal of High Energy Physics
We study the transport of generalized metrics between topological T-dual nil-manifolds through a Lie algebraic point of view. Emergent gravities are generalized metrics with symplectic B-fields.
Raju Roychowdhury, Leonardo Soriani
doaj   +1 more source

Duals of Feynman Integrals. Part II. Generalized unitarity

Journal of High Energy Physics, 2022
The first paper of this series introduced objects (elements of twisted relative cohomology) that are Poincaré dual to Feynman integrals. We show how to use the pairing between these spaces — an algebraic invariant called the intersection number — to ...
Simon Caron-Huot, Andrzej Pokraka
doaj   +1 more source

Algebraic A-hypergeometric functions [PDF]

, 2010
We formulate and prove a combinatorial criterion to decide if an A-hypergeometric system of differential equations has a full set of algebraic solutions or not.
Beukers, F., Sub Algebra,Geometry&Mathem. Logic begr., Algebra & Geometry and Mathematical Locic, Frits Beukers   +3 more
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C* Algebras and Differential Geometry

, 2004
Translated Comptes Rendus Note of March ...
openaire   +2 more sources

Smoothly splitting amplitudes and semi-locality

Journal of High Energy Physics, 2022
In this paper, we study a novel behavior developed by certain tree-level scalar scattering amplitudes, including the biadjoint, NLSM, and special Galileon, when a subset of kinematic invariants vanishes without producing a singularity.
Freddy Cachazo, Nick Early, Bruno Giménez Umbert   +2 more
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Bertini theorems for differential algebraic geometry [PDF]

Proceedings of the American Mathematical Society, 2023
We study intersection theory for differential algebraic varieties. Particularly, we study families of differential hypersurface sections of arbitrary affine differential algebraic varieties over a differential field. We prove the differential analogue of Bertini’s theorem, namely that for an arbitrary geometrically irreducible differential algebraic ...
openaire   +2 more sources