We relate the Lounesto classification of regular and singular spinors to the orbits of the Spin(3,1) group in the space of Dirac spinors. We find that regular spinors are associated with the ...principal orbits of the spin group while singular spinors are associated with special orbits whose isotropy group is C. We use this to clarify some aspects of the classical and quantum theory of spinors restricted to a class in this classification. In particular, we show that the degrees of freedom of an ELKO field, which has been proposed as a candidate for dark matter, can be reexpressed as a Dirac field preserving locality. Alternatively after introducing the ELKO dual, it can be re-interpreted as four anticommuting Lorentz scalar fields with internal symmetry the spin representation of the Lorentz group. We also propose an interacting Lagrangian which can consistently describe all 6 classes of regular and singular spinors.
The lightcone singularity at the origin is resolved by blowing up the singular point to CP1. The Lorentz group acts on the resolved lightcone and has CP1 as a special orbit. Using Wigner's method of ...associating unitary irreducible representations of the Poincaré group to particle states, we find that the special orbit gives rise to new vacuum states. These vacuum states are labeled by the principal series representations of SL(2,C). Some remarks are included on the applications of these results to gauge theories and asymptotically flat spacetimes.
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We show that the Killing spinor equations of all supergravity theories which may include higher order corrections on a (r,s)-signature spacetime are associated with twisted covariant form ...hierarchies. These hierarchies are characterized by a connection on the space of forms which may not be degree preserving. As a consequence we demonstrate that the form Killing spinor bi-linears of all supersymmetric backgrounds satisfy a suitable generalization of conformal Killing-Yano equation with respect to this connection. To illustrate the general proof the twisted covariant form hierarchies of some supergravity theories in 4, 5, 6, 10 and 11 dimensions are also presented.
Abstract
We present a systematic construction of the Penrose coordinates and plane wave limits of spacetimes for which both the null Hamilton–Jacobi and geodesic equations separate. The method is ...applied to Kerr-NUT-(A)dS four-dimensional black holes. The plane wave limits of the near horizon geometry of the extreme Kerr black hole are also explored. All near horizon geometries of extreme black holes with a regular Killing horizon admit Minkowski spacetime as a plane wave limit.
We present a definition of null G-structures on Lorentzian manifolds and investigate their geometric properties. This definition includes the Robinson structure on 4-dimensional black holes as well ...as the null structures that appear in all supersymmetric solutions of supergravity theories. We also identify the induced geometry on some null hypersurfaces and that on the orbit spaces of null geodesic congruences in such Lorentzian manifolds. We give the algebra of diffeomorphisms that preserves a null G-structure and demonstrate that in some cases it interpolates between the BMS algebra of an asymptotically flat spacetime and the Lorentz symmetry algebra of a Killing horizon.
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Based on the Baikov representation, we present a systematic approach to compute cuts of Feynman Integrals, appropriately defined in
d
dimensions. The information provided by these ...computations may be used to determine the class of functions needed to analytically express the full integrals.
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We investigate the patching of double and exceptional field theories. In double field theory the patching conditions imposed on the spacetime after solving the strong section condition ...imply that the 3-form field strength
H
is exact. A similar conclusion can be reached for the form field strengths of exceptional field theories after some plausive assumptions are made on the relation between the transition functions of the additional coordinates and the patching data of the form field strengths. We illustrate the issues that arise, and explore several alternative options which include the introduction of C-folds and of the topological geometrisation condition.
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A simplified differential equations approach for Master Integrals is presented. It allows to express them, straightforwardly, in terms of Goncharov Polylogarithms. As a proof-of-concept of ...the proposed method, results at one and two loops are presented, including the massless one-loop pentagon with up to one off-shell leg at order epsilon.
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We construct a C-space associated with every closed 3-form on a spacetime
M
and show that it depends on the class of the form in
H
3
M
ℤ
. We also demonstrate that C-spaces have a relation ...to generalized geometry and to gerbes. C-spaces are constructed after introducing additional coordinates at the open sets and at their double overlaps of a spacetime generalizing the standard construction of Kaluza-Klein spaces for 2-forms. C-spaces may not be manifolds and satisfy the topological geometrization condition. Double spaces arise as local subspaces of C-spaces that cannot be globally extended. This indicates that for the global definition of double field theories additional coordinates are needed. We explore several other aspect of C-spaces like their topology and relation to Whitehead towers, and also describe the construction of C-spaces for closed k-forms.
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