Igor A. Bandos

Covariant Action for the Super-Five-Brane of M Theory

We propose a complete, d=6 covariant and kappa-symmetric, action for the M theory five-brane propagating in D=11 supergravity background. This opens a direct way of relating a wide class of super-p -brane solutions of string theory with the five-brane of M theory, which should be useful for studying corresponding dualities and nonperturbative aspects of these theories. {copyright} {ital 1997} {ital The American Physical Society}

Superstrings and supermembranes in the doubly supersymmetric geometrical approach

Abstract We perform a generalization of the geometrical approach to describing extended objects for studying the doubly supersymmetric twistor-like formulation of super p -branes. Some basic features of the embedding world supersurface into target superspace specified by a geometrodynamical condition are considered. It is shown that the main attributes of the geometrical approach, such as the second fundamental form and extrinsic torsion of the embedded surface, and the Codazzi, Gauss and Ricci equations, have their doubly supersymmetric counterparts. At the same time the embedding of the supersurface into target superspace has its particular features. For instance, the embedding may cause more rigid restrictions on the geometrical properties of the supersurface. This is demonstrated with the examples of an N = 1 twistor-like supermembrane in D = 11 and type II superstrings in D = 10, where the geometrodynamical condition causes the embedded supersurface to be minimal and puts the theories on the mass shell.

On the Equivalence of Different Formulations of the M Theory Five-Brane

Abstract We show that the field equations for the supercoordinates and the self-dual antisymmetric tensor field derived from the recently constructed κ-invariant action for the M theory five-brane are equivalent to the equations of motion obtained in the doubly supersymmetric geometrical approach at the worldvolume component level.

Duality-symmetric eleven-dimensional supergravity and its coupling to M-branes

The standard eleven-dimensional supergravity action depends on a three-form gauge field and does not allow direct coupling to five-branes. Using previously developed methods, we construct a covariant eleven-dimensional supergravity action depending on a three-form and six-form gauge field in a duality-symmetric manner. This action is coupled to both the M-theory two-brane and five-brane, and corresponding equations of motion are obtained. Consistent coupling relates D = 11 duality properties with self-duality properties of the M5-brane. From this duality-symmetric formulation, one derives an action describing coupling of the M-branes to standard D = 11 supergravity.

Generalized action principle and superfield equations of motion for D = 10 Dp-branes

Abstract The action for the D = 10 type II Dirichlet super p-branes, which has been obtained recently, is reconstructed in a more geometrical form involving Lorentz harmonic variables. This new (Lorentz harmonic) formulation possesses κ-symmetry in an irreducible form and is used as a basis for applying a generalized action principle that provides the superfield equations of motion and clarifies the geometrical nature of the κ-symmetry of these models. The case of a Dirichlet super 3-brane is considered in detail.

Green-Schwarz superstrings in spinor moving frame formalism

Abstract Green-Schwarz superstring theory in D = 4 and D = 10 is formulated in an extended space including additional spinor coordinates of the Cartan moving frame. These spinor coordinates, realized in the form of the Lorentz harmonics, are used for constructing covariant irreducible generators of fermionic k -symmetry. Generalizations of the suggested superstring formulations for the cases of super- p -brane theories in the D -dimensional space time including the D = 11 supermembrane are discussed.

N=1 super- p-branes in twistor-like Lorentz harmonic formulation

A unique twistor-like Lorentz harmonic formulation for all N=1 supersymmetric extended objects (super-p-branes) moving in spacetime of arbitrary dimension D (admissible for given p) is suggested. The equations of motion are derived, the explicit form of the -symmetry transformations is presented and the classical equivalence to the standard formulation is proved. The cases with minimal worldsheet dimensions p=1,2, namely the D=10 heterotic string and the D=11 supermembrane, are considered in detail. In particular, the explicit form of irreducible -symmetry transformations for the D=11 supermembrane is derived.

The type IIA NS5-brane

Abstract The kappa-invariant worldvolume action for the NS5-brane in a D=10 type IIA supergravity background is obtained by carrying out the dimensional reduction of the M5-brane action.

NB BLG model in N=8 superfields

Abstract We develop the N = 8 superfield description of the Bagger–Lambert–Gustavsson (BLG) model in its Nambu bracket (NB) realization. The basic ingredient is the octet of scalar d = 3 , N = 8 superfields ϕ I depending also on the coordinates of a compact three-dimensional space M 3 . It is restricted by the superembedding-like equation, D A ˙ ϕ I = 2 i ψ B γ B A ˙ I , which can be treated as covariantization of the linearized superembedding equation for supermembrane (M2-brane) with respect to volume preserving diffeomorphisms of M 3 . The curvatures of SDiff3 connection are expressed through ϕ I by the N = 8 superfield generalization of the BLG Chern–Simons equation (super-CS equation). We show how the dynamical BLG equations appear when studying consistency of these basic equations.

Duality-symmetric actions for non-Abelian tensor fields

We construct the duality-symmetric actions for a large class of six-dimensional models describing hierarchies of non-Abelian scalar, vector and tensor fields related to each other by first-order (self-)duality equations that follow from these actions. In particular, this construction provides a Lorentz invariant action for non-Abelian self-dual tensor fields. The class of models includes the bosonic sectors of the 6d (1,0) superconformal models of interacting non-Abelian self-dual tensor, vector, and hypermultiplets.