29 research outputs found

### The Action for Twisted Self-Duality

One may write the Maxwell equations in terms of two gauge potentials, one
electric and one magnetic, by demanding that their field strengths should be
dual to each other. This requirement is the condition of twisted self-duality.
It can be extended to p-forms in spacetime of D dimensions, and it survives the
introduction of a variety of couplings among forms of different rank, and also
to spinor and scalar fields, which emerge naturally from supergravity. In this
paper we provide a systematic derivation of the action principle, whose
equations of motion are the condition of twisted self-duality. The derivation
starts from the standard Maxwell action, extended to include the aforementioned
couplings, and proceeds via the Hamiltonian formalism through the resolution of
Gauss' law. In the pure Maxwell case we recover in this way an action that had
been postulated by other authors, through an ansatz based on an action given
earlier by us for untwisted self-duality. Those authors also extended their
ansatz to include Chern-Simons couplings. In that case, we find a different
result. The derivation from the standard extended Maxwell action implies of
course that the theory is Lorentz-invariant and can be locally coupled to
gravity. Nevertherless we include a direct compact Hamiltonian proof of these
properties, which is based on the surface-deformation algebra. The symmetry in
the dependence of the action on the electric and magnetic variables is
manifest, since they appear as canonical conjugates. Spacetime covariance,
although present, is not manifest.Comment: Version to appear in Phys. Rev.

### Supersymmetric electric-magnetic duality as a manifest symmetry of the action for super-Maxwell theory and linearized supergravity

For the free massless spin-one and spin-two field theories one may write the
action in a form which is manifestly invariant under electric-magnetic duality.
This is achieved by introducing new potentials through solving the constraints
of the Hamiltonian formulation. The price for making electric-magnetic duality
invariance manifest through this direct procedure is losing manifest Lorentz
invariance. Both theories admit supersymmetric extensions, which make the
bosonic fields and their corresponding fermionic partners to be parts of the
same geometrical object, a supermultiplet. We present in this paper the
supersymmetric extension of the manifestly electric-magnetic duality invariant
actions for the photon and the photino; and for the graviton and the gravitino.
In each case the spinor fields transform under electric-magnetic duality in a
chiral manner. For the spin-tree-half field, which possesses a gauge
invariance, it is necessary to bring in a spinor "prepotential". As in previous
cases the introduction of additional potentials to solve the constraints
increases the number of gauge invariances of the action, thus keeping the
number of degrees of freedom unaltered. The similarity in the formulations for
the photon-photino and graviton-gravitino systems is remarkable.Comment: Typos corrected, one reference adde

### Can (Electric-Magnetic) Duality Be Gauged?

There exists a formulation of the Maxwell theory in terms of two vector
potentials, one electric and one magnetic. The action is then manifestly
invariant under electric-magnetic duality transformations, which are rotations
in the two-dimensional internal space of the two potentials, and local. We ask
the question: can duality be gauged? The only known and battled-tested method
of accomplishing the gauging is the Noether procedure. In its decanted form, it
amounts to turn on the coupling by deforming the abelian gauge group of the
free theory, out of whose curvatures the action is built, into a non-abelian
group which becomes the gauge group of the resulting theory. In this article,
we show that the method cannot be successfully implemented for
electric-magnetic duality. We thus conclude that, unless a radically new idea
is introduced, electric-magnetic duality cannot be gauged. The implication of
this result for supergravity is briefly discussed.Comment: Some minor typos correcte

### Supersymmetric electric-magnetic duality of hypergravity

Hypergravity is the theory in which the graviton, of spin-2, has a
supersymmetric partner of spin-5/2. There are "no-go" theorems that prevent
interactions in these higher spin theories. However, it appears that one can
circumvent them by bringing in an infinite tower of higher spin fields. With
this possibility in mind, we study herein the electric-magnetic duality
invariance of hypergravity. The analysis is carried out in detail for the free
theory of the spin-(2,5/2) multiplet, and it is indicated how it may be
extended to the infinite tower of higher spins. Interactions are not
considered. The procedure is the same that was employed recently for the
spin-(3/2,2) multiplet of supergravity. One introduces new potentials
("prepotentials") by solving the constraints of the Hamiltonian formulation. In
terms of the prepotentials, the action is written in a form in which its
electric-magnetic duality invariance is manifest. The prepotential action is
local, but the spacetime invariance is not manifest. Just as for the spin-2 and
spin-(3/2,2) cases, the gauge symmetries of the prepotential action take a form
similar to those of the free conformal theory of the same multiplet. The
automatic emergence of gauge conformal invariance out of demand of manifest
duality invariance, is yet another evidence of the subtle interplay between
duality invariance and spacetime symmetry. We also compare and contrast the
formulation with that of the analogous spin-(1,3/2) multiplet