A manifestly Lorentz and diffeomorphism invariant form for the abelian gauge field action with local duality symmetry of Schwarz and Sen is given. Some of the underlying symmetries of the covariant action are further considered. The Noether conserved charge under continuous local duality rotations is found.The covariant couplings with gravity and the axidilaton field are discussed.
Using the parent Lagrangian approach we construct a dual formulation, in the sense originally proposed by Curtright and Freund, of a massive spin two Fierz-Pauli theory in arbitrary dimensions D. This is achieved in terms of a mixed symmetry tensor, without the need of auxiliary fields. The relation of this method with an alternative formulation based on a gauge symmetry principle proposed by Zinoviev is elucidated. We show that the latter formulation in four dimensions, with a given gauge fixing together with a definite sequence of auxiliary fields elimination via their equations of motion, leads to the parent Lagrangian already considered by West completed by a FierzPauli mass term, which in turns yields the Curtright-Freund action. This motivates our generalization to arbitrary dimensions leading to the corresponding extension of the four dimensional result. We identify the transverse true degrees of freedom of the dual theory and verify that their number is in accordance with those of the massive Fierz-Pauli field.
Using the parent Lagrangian method together with a dimensional reduction from D to (D − 1) dimensions we construct dual theories for massive spin two fields in arbitrary dimensions in terms of a mixed symmetry tensor T A[A 1 A 2 ...A D−2 ] . Our starting point is the well studied massless parent action in dimension D. The resulting massive Stueckelberg-like parent actions in (D − 1) dimensions inherits all the gauge symmetries of the original massless action and can be gauge fixed in two alternative ways, yielding the possibility of having either a parent action with a symmetric or a non-symmetric Fierz-Pauli field eAB. Even though the dual sector in terms of the standard spin two field includes only the symmetrical part e {AB} in both cases, these two possibilities yield different results in terms of the alternative dual field. In particular, the non-symmetric case reproduces the Freund-Curtright action as the dual to the massive spin two field action in four dimensions.
The SL(2,R) duality symmetric action for the Born-Infeld theory in terms of two potentials, coupled with nontrivial background fields in four dimensions, is established. This construction is carried out in detail by analyzing the Hamiltonian structure of the Born-Infeld theory. The equivalence with the usual Born-Infeld theory is shown. ͓S0556-2821͑98͒01114-X͔ PACS number͑s͒: 11.10. Lm, 11.25.Mj Nowadays the concept of duality is widely recognized by its unifying role in physics. The five known different superstring theories are now unified by duality in the framework of M theory ͑see, for example, ͓1͔͒. The simplest case where duality appears is Maxwell's equations without sources, interchanging the equations of motions and the Bianchi identities. Schwarz and Sen ͓2͔ have developed a method to raise duality symmetry at the level of the action but at the price of losing the explicit Lorentz invariance. The classical and quantum equivalence with electromagnetism has been well established ͓3-5͔. Earlier, Deser and Teitelboim ͓6͔ noticed that the Maxwell theory in its Hamiltonian formulation is invariant under nonlocal duality transformations. Moreover, several attempts have been made at conciliating duality symmetry with Lorentz invariance ͓7͔. On the other hand, the Born-Infeld theory ͓8͔, initially conceived as an alternative for electromagnetism, has recently received considerable attention because the world volume action of a D-brane is described by a kind of nonlinear Born-Infeld action ͓9͔. Several aspects of the duality symmetry in the Born-Infeld theory have been developed recently ͓10,11͔. In particular, Perry and Schwarz ͓12͔ proposed a nonmanifestly Lorentz invariant Born-Infeld action for a self-interacting self-dual antisymmetric tensor field in Dϭ6. Afterward, Pasti, Sorokin, and Tonin presented a manifestly covariant formulation of this action ͓13͔, from which Berman ͓14͔, after dimensional reduction to four dimensions and breaking the Lorentz symmetry, obtained an action for the Born-Infeld theory coupled with the axion and dilaton fields with a Z(2) symmetry.In this article, we will study the Born-Infeld theory both pure and coupled with the axion and dilaton fields from the point of view of their Hamiltonian structures in four dimensions, setting up the formulation in the manner of Schwarz and Sen of the SL(2,R) duality invariant Born-Infeld action. Our results extend those obtained by Berman when the axion field is involved, making evident the SL(2,R) duality invariance. We will show that our results lead to the Born-Infeld theory after the elimination of one of two potentials.We will start with the Born-Infeld theory without nontrivial background fields. Despite its highly nonlinear character, the Abelian gauge Born-Infeld theory whose action is given by Iϭ ͵ d 4 x͓1ϪͱϪdet͑ mn ϩF mn ͔͒,
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