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Register a new userNoether identities in Einstein--Dirac theory and the Lie derivative of spinor fields
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We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restrictions on the Lie derivative of fields.
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We derive both {em local} and {em global} generalized {em Bianchi identities} for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the {em a priori} introduction of a connection. The proof is based on a {em global} decomposition of the {em variational Lie derivative} of the generalized Euler--Lagrange morphism and the representation of the corresponding generalized Jacobi morphism on gauge-natural bundles. In particular, we show that {em within} a gauge-natural invariant Lagrangian variational principle, the gauge-natural lift of infinitesimal principal automorphism {em is not} intrinsically arbitrary. As a consequence the existence of {em canonical} global superpotentials for gauge-natural Noether conserved currents is proved without resorting to additional structures.
For six dimensional nilmanifolds we build a module $mathcal{H}$ of an affine Kac Moody vertex algebras. Then, we associate some logarithmic fields for the module $mathcal{H}$ and we study their singularities. We also presented a physics motivation behind this construction. We study a particular case, we show that when the nilmanifold $N$ is a $k$ degree $S^1$--fibration over the two torus and a choice of $l in mathbb{Z} simeq H^3(N, mathbb{Z})$ the fields associated to the space $mathcal{H}$ have tri-logarithm singularities whenever $kl eq 0$.
In the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes contribute topological terms to the action of worldsheets of both open and closed strings. We show that these terms naturally fit into a 2-dimensional, smooth open-closed functorial field theory (FFT) in the sense of Atiyah, Segal, and Stolz-Teichner. We give a detailed construction of this smooth FFT, based on the definition of a suitable smooth bordism category. In this bordism category, all manifolds are equipped with a smooth map to a spacetime target manifold. Further, the object manifolds are allowed to have boundaries; these are the endpoints of open strings stretched between D-branes. The values of our FFT are obtained from the B-field and its D-branes via transgression. Our construction generalises work of Bunke-Turner-Willerton to include open strings. At the same time, it generalises work of Moore-Segal about open-closed TQFTs to include target spaces. We provide a number of further features of our FFT: we show that it depends functorially on the B-field and the D-branes, we show that it is thin homotopy invariant, and we show that it comes equipped with a positive reflection structure in the sense of Freed-Hopkins. Finally, we describe how our construction is related to the classification of open-closed TQFTs obtained by Lauda-Pfeiffer.
Higgs fields are attributes of classical gauge theory on a principal bundle $Pto X$ whose structure Lie group $G$ if is reducible to a closed subgroup $H$. They are represented by sections of the quotient bundle $P/Hto X$. A problem lies in description of matter fields with an exact symmetry group $H$. They are represented by sections of a composite bundle which is associated to an $H$-principal bundle $Pto P/H$. It is essential that they admit an action of a gauge group $G$.
We construct a specific example of a class of traversable wormholes in Einstein-Dirac-Maxwell theory in four spacetime dimensions, without needing any form of exotic matter. Restricting to a model with two massive fermions in a singlet spinor state, we show the existence of spherically symmetric asymptotically flat configurations which are free of singularities, representing localized states. These solutions satisfy a generalized Smarr relation, being connected with the extremal Reissner-Nordstrom black holes. They also possess a finite mass $M$ and electric charge $Q_e$, with $Q_e/M>1$. An exact wormhole solution with ungauged, massless fermions is also reported.
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