A covariantisation of M5-brane action in dual formulation

Abstract

We construct a manifestly diffeomorphic M5-brane action in dual formulation coupled to an eleven-dimensional supergravity target space. The covariantisation is carried out by using (generalised) PST technique with 5 auxiliary scalar fields, which are obtained by using a geometrical consideration as a reduction of an auxiliary 4−form of MaznytsiaPreitschopf-Sorokin. As is typical in PST-covariantised theory, our construction possesses as usual the two local PST symmetries. By using one of the local PST symmetries, the action can be reduced to the non-manifestly covariant M5-brane action in dual formulation constructed earlier by the authors. The discussion on double dimensional reduction to D4-brane, and on the comparison of on-shell action then easily follows.

Dual formulation of covariant nonlinear duality-symmetric action of kappa-symmetric D3-brane

“…The theory was extended to a non-manifestly covariant M5-brane theory in dual formulation [18]. It was then covariantised, by using five auxiliary scalar fields, in the recent work [19]. The use of five auxiliary scalar fields instead of an auxiliary four-form field makes it clear that the theory has all the desirable symmetries.…”

“…We make use of the set up and notations given in the previous section. In order to construct a covariant theory in dual formulation, we make use of the idea from [19]. This suggests the use of three auxiliary scalars 1 a I , I = 0, 1, 2.…”

“…with 6) and similarly for P ⊥ P. For more details, see [19]. The induced linear transformations form the following identities…”

“…In [3], the auxiliary 2−form B 2 arises from the dualisation of the auxiliary field of the PST-covariantised duality-symmetric action in standard JHEP02 (2018)116 formulation [4]. Our choice of three (4 − 1 = 3) auxiliary scalar fields a I , however, is motivated by the successful covariantisation of M5-brane action in dual formulation [19] using five (6 − 1 = 5) auxiliary scalar fields, which in turn is a specific restriction, motivated by a basic geometrical argument, of the auxiliary 4−form.…”

Covariant M5-brane action with self-dual 3-form

“…Actions for chiral 2-form of this type are given in [7][8][9][10]. Complete M5-brane actions of this type are constructed in [11][12][13][14]. Actions for theories within either of these types contain terms which describe dynamics of the chiral 2-form field.…”