Victor Lekeu

Chiral Tensors of Mixed Young Symmetry

Chiral tensors of mixed Young symmetry, which exist in the same spacetime dimensions

The action of the (free) (4, 0)-theory

2 + 4n

Deformations of vector-scalar models

where chiral

A note on "gaugings" in four spacetime dimensions and electric-magnetic duality

p

Kac-Moody and Borcherds Symmetries of Six-Dimensional Chiral Supergravity

-forms can be defined, are investigated. Such chiral tensors have been argued to play a central role in exotic formulations of gravity in 6 dimensions and possess intriguing properties. A variational principle that yields the chiral equations of motion is explicitly constructed and related to the action for a non-chiral tensor. The use of prepotentials turns out to be essential in our analysis. We also comment on dimensional reduction.

The action of the (free) Open image in new window theory in six spacetime dimensions

A bstractThe (4, 0) theory in six dimensions is an exotic theory of supergravity that has been argued to emerge as the strong coupling limit of theories having N = 8 supergravity as their low energy effective theory in five spacetime dimensions. It has maximal supersymmetry and is superconformal. Very little is known about this intriguing theory. While the spectrum of fields occurring in its description has been given and their equations of motion in the absence of interactions have been written down, no action principle has been formulated, even in the free case. We extend here previous analyses by writing explicitly the action of the free (4, 0) theory from which the equations of motion derive. The variables of the variational principle are prepotentials adapted to the self-duality properties of the fields. The “exotic gravitini”, described by chiral fermionic two-forms, are given special attention. The supersymmetry transformations are written down and the invariance of the action is explicitly proven. Even though the action is not manifestly covariant, the symmetry transformations are shown to close according to the (4, 0)-extended Poincaré supersymmetry algebra. We also discuss exotic supergravity models with fewer supersymmetries. Remarks on dimensional reduction close the paper.

Erratum to: The action of the (free) (4, 0)-theory

A bstractAbelian vector fields non-minimally coupled to uncharged scalar fields arise in many contexts. We investigate here through algebraic methods their consistent deformations (“gaugings”), i.e., the deformations that preserve the number (but not necessarily the form or the algebra) of the gauge symmetries. Infinitesimal consistent deformations are given by the BRST cohomology classes at ghost number zero. We parametrize explicitly these classes in terms of various types of global symmetries and corresponding Noether currents through the characteristic cohomology related to antifields and equations of motion. The analysis applies to all ghost numbers and not just ghost number zero. We also provide a systematic discussion of the linear and quadratic constraints on these parameters that follow from higher-order consistency. Our work is relevant to the gaugings of extended supergravities.

E 7(7) invariant non-extremal entropy

The variety of consistent ‘gauging’ deformations of supergravity theories in four dimensions depends on the choice of Lagrangian formulation. One important goal is to get the most general deformations without making hidden assumptions. Ignoring supersymmetry we consider in this paper n v abelian vector potentials in four spacetime dimensions with non-minimal kinetic coupling to n s uncharged (possibly nonlinear) scalar fields. As in the case of extended supergravities, one model may possess different formulations related by . The symplectic group mixes its electric and magnetic potentials. The model admits a global duality symmetry subgroup G which acts also on the scalars. We recall first how the general second order Lagrangian, its local deformations and those of its abelian gauge group will depend on the choice of 2n v directions (choice of ‘Darboux frame’). We start from a general frame defined by the symplectic transformation relating it to a fixed ‘reference’ one. Combinations of symplectic matrix coefficients appear then as constant parameters in the second order Lagrangians. Another gauging method uses an ‘embedding tensor’ that characterizes the realization of the gauge group via the global duality group. It involves additional 2-form gauge fields. A suitable zero charge limit of this realization has abelian gauge group and the ‘gauging’ can be viewed as a consistent deformation of that limit. We show that the two methods applied to the corresponding ungauged models have equivalent local deformations—and more generally, have isomorphic local BRST cohomology at all ghost numbers. We finally consider manifestly duality invariant first order actions with abelian gauge group. We point out that obstructions to non-abelian deformations of the Yang–Mills type exhibited in a previous work remain present when couplings to scalar fields are included.

Prepotentials for linearized supergravity

A bstractWe investigate the conjectured infinite-dimensional hidden symmetries of six-dimensional chiral supergravity coupled to two vector multiplets and two tensor multiplets, which is known to possess the F4,4 symmetry upon dimensional reduction to three spacetime dimensions. Two things are done. (i) First, we analyze the geodesic equations on the coset space F4,4+ +/K(F4,4+ +) using the level decomposition associated with the subalgebra gl5⊕sl2