DOUBLED FIELD APPROACH TO YANG - MILLS REQUIRES NON-LOCALITY

Doubling a Yang-Mills field we apply the pattern which has been found to construct a "duality-symmetric" gravity with matter to the "duality-symmetric" Yang - Mills theory in five space-time dimen- sions. Constructing the action we conclude that dualizing a non-abelian theory requires non-locality. We analyze the symmetries of the theory and equations of motion. Extension to the supersymmetric theory is also demonstrated. Some of the fields of Superstring/M-theory spectrum are of special class which are called chiral p-forms, or chiral bosons. These fields play an im- portant role in establishing various dualities between different sectors of M-theory, but dealing with them beyond the mass-shell, i.e. at the level of the effective Lagrangians, is not a simple task. There are several methods (see (1) for a review and for the comprehensive list of Refs.) which were proposed to describe theories with self-dual or duality-symmetric fields. All of them could be split into the following major sets. The first one (2)-(6) contains the approaches that are duality invariant but are not manifestly Lorentz invariant. Introducing auxiliary fields is not required, but coupling to other fields, especially to gravity, may cause problems with establishing the consistency of such a coupling. The second set (7)-(12) is dealt with aux- iliary fields whose inclusion restores the Lorentz covariance. The number of these auxiliary fields may vary from one to infinity. Among the approaches with auxiliary fields the formalism proposed by Pasti, Sorokin and Tonin (12) takes a special place. It is manifestly Lorentz covariant and is minimal in a sense of having the only auxiliary field entering the action in a non-polynomial way. Successful applying the PST approach to the construction of different field theories of chiral p-forms, super-p-branes with worldvolume chiral fields, and of different sub-sectors of supergravities has demonstrated the advantages of this approach and its compatibility with supersymmetry (cf. (1) and Refs. therein). However, a gap for applying the PST formalism is a Yang-Mills theory. It is worth noting that the problem of dualising a non-abelian gauge the- ory has been intensively studied in literature. Getting rid of self-interactions it is straightforward to apply the machinery of dualization to the case. But the attempts to go beyond the free theory have faced the troubles. The latter