We discuss the propagation of fermions on generic, curved branes in Ishibashi-Kawai-Kitazawa-Tsuchiya-type matrix models. The Dirac operator can be understood either terms a Weitzenb\"ock connection, or Levi-Civita connection with an extra torsion term. detail coupling spin to background geometry using Jeffreys-Wentzel-Kramers-Brillouin approximation. Despite absence local Lorentz invariance un...

We consider the sum of Einstein-Hilbert action and a Pontryagin density (PD) in arbitrary even dimension $D$. All curvatures are functions independent affine (torsionless) connections only. In dimension, not only $D=4n$, these first order PD terms shown to be covariant divergences "Chern-Simons" currents. The field equation for connection leads it being Levi-Civita, metric equations equivalent ...

The proofs of the extreme value theorem, the mean value theorem and the inverse function theorem for analytic functions on the Levi-Civita field will be presented. After reviewing convergence criteria for power series [15], we review their analytical properties [18, 20]. Then we derive necessary and sufficient conditions for the existence of relative extrema for analytic functions and use that ...

1. Seja (Q, 〈, 〉) uma variedade pseudo-Riemanniana e ∇ a conexão de Levi-Civita em Q associada a 〈, 〉. A primeira identidade de Bianchi implica que Rcdab = gceRdab = gce(−Rabd −Rbda) = −Rcabd −Rcbda (1) Uma vez que a conexão ∇ é compat́ıvel com a métrica, o tensor de Riemann satisfaz Rabcd = −Rbacd. Portanto Rcdab = Racbd +Rbcda (2) Usando novamente a primeira identidade de Bianchi, a propriedad...

A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a metric structure, when gravitational models with infinite many couplings reduce to two–loop renormalizable effective actions. We use a key result from our p...

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter. In Part I, we compute the Levi-Civita connection for these metrics. The connection and curvature forms take values in pseudodifferential operators (ΨDOs), and we compute the top symbols of these forms. In Part II, we develop a theory of Chern-Simons classes CS ...

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. In Part I, we compute the Levi-Civita connection for these metrics for s ∈ Z. The connection and curvature forms take values in pseudodifferential operators (ΨDOs), and we compute the top symbols of these forms. In Part II, we develop a theory of Wodzicki-Che...

Because of the disconnectedness of a non-Archimedean ordered field in the topology induced by the order, it is possible to have non-constant functions with zero derivatives everywhere. In fact the solution space of the differential equation y′ = 0 is infinite dimensional. In this paper, we give sufficient conditions for a function on an open subset of the Levi-Civita field to have zero derivati...