Related papers: Bad fields with torsion
For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…
We provide a vast class of counterexamples to the chain rule for the divergence of bounded vector fields in three space dimensions. Our convex integration approach allows us to produce renormalization defects of various kinds, which in a…
We are considering iterative derivations on the function field L of abelian schemes in positive characteristic p>0, and give conditions when the torsion group schemes of this abelian scheme occur as ID-automorphism groups, i.e. are the…
As put forward in [arXiv:1907.12339] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An…
We explore higher-dimensional conformal field theories (CFTs) in the presence of a conformal defect that itself hosts another sub-dimensional defect. We refer to this new kind of conformal defect as the composite defect. We elaborate on the…
It is outlined how deformations of field theoretical rigid symmetries can be constructed and classified by cohomological means in the extended antifield formalism. Special attention is devoted to deformations referring only to a subset of…
Several notions of multiplicativity are introduced for forms of degree $d\geq 3$ over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multiplicative forms of higher degree are given. Conditions…
In this paper, by using the trace map of Frobenius, we consider problems on extending sections for positive characteristic threefolds.
We show that the height of a variety over a finitely generated field of characteristic zero can be written as an integral of local heights over the set of places of the field. This allows us to apply our previous work on toric varieties and…
We explore spacetime torsion in a two-dimensional setting, wherein it corresponds to a vector field. Without invoking field equations of a particular gravitational theory, we develop visualization techniques for such torsion fields,…
We consider axial torsion fields which appear in higher derivative quantum gravity. It is shown, in general, that the torsion field possesses states with two spins, one and zero, with different masses. The first-order formulation of torsion…
Recent works have revealed that the recipe for field-antifield quantization of Lagrangian gauge theories can be considerably relaxed when it comes to choosing a path integral measure \rho if a zero-order term \nu_{\rho} is added to the…
We determine a strong form of the decomposition theorem for proper toric maps over finite fields.
We formulate extensions of Wilking's Jacobi field splitting theorem to uniformly positive sectional curvature and also to positive and nonnegative intermediate Ricci curvatures.
We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form a group with respect to the matrix product and the functional composition. These…
A construction of massive free fields with arbitrary spin and reversed spin-statistics relation is presented. The main idea of the construction is to consider fields that transform according to representations of the Lorentz group that are…
In this paper we investigate the possible supersymmetric extensions for the massive (bi)gravity theories in the lowest non-trivial order. For this purpose we construct the cubic interaction vertices for massive spin-2 and one or two massive…
We discuss variations of mixed Hodge structure arising from projective morphisms of complex analytic spaces. Then we treat generalizations of Koll\'ar's torsion-free theorem, vanishing theorem, and so on, for reducible complex analytic…
We construct analytic solutions of open superstring field theory for any exactly marginal deformation in any boundary superconformal field theory when properly renormalized operator products of the marginal operator are given. Our…
We give a geometric construction of tilting perverse sheaves using stratified Morse theory, torus actions, and nearby cycles.