Supersymmetric Yang–Mills theory in eleven dimensions

Physics Letters B, 1998

We present a lagrangian formulation for recently-proposed supersymmetric Yang-Mills theory in twelve dimensions. The field content of our multiplet has an additional auxiliary vector field in the adjoint representation. The usual Yang-Mills field strength is modified by a Chern-Simons form containing this auxiliary vector field. This formulation needs no constraint imposed on the component field from outside, and a constraint on the Yang-Mills field is generated as the field equation of the auxiliary vector field. The invariance check of the action is also performed without any reference to constraints by hand. Even though the total lagrangian takes a simple form, it has several highly non-trivial extra symmetries. We couple this twelve-dimensional supersymmetric Yang-Mills background to Green-Schwarz superstring, and confirm fermionic κ-invariance. As another improvement of this theory, we present a set of fully Lorentz-covariant and supercovariant field equations with no use of null-vectors. This system has an additional scalar field, whose gradient plays a role of the null-vector. This system exhibits spontaneous breaking of the original Lorentz symmetry SO(10, 2) for twelve-dimensions down to SO(9, 1) for ten-dimensions.

Physics Letters B, 1996

We present a model for supersymmetric Yang-Mills theory in 10+2 dimensions. Our construction uses a constant null vector, and leads to a consistent set of field equations and constraints. The model is invariant under generalized translations and an extra gauge transformation. Ordinary dimensional reduction to ten dimensions yields the usual supersymmetric Yang-Mills equations, while dimensional reduction to 2+2 yields supersymmetric Yang-Mills equations in which the Poincaré supersymmetry is reduced by a null vector. We also give the corresponding formulation in superspace.

Communications in Mathematical Physics, 1986

We give a complete proof of the equivalence between constraint equations and field equations for the d = 10, N = 1 supersymmetric Yang-Milts theory, a result proposed and partially proved recently by Witten [1]. Our approach explicitly reconstructs the superconnection satisfying the constraints from the on shell component fields. A key ingredient of the method is the choice of a suitable family of gauges, effectively eliminating all gauge dependence on anti-commuting coordinates. As a corollary, obtained by dimensional reduction, we also deduce the equivalence of constraints and field equations for the d = 4, N = 4 theory, as well as for d = 6, N = 2.

Nucl.Phys. B224 (1983) 159, 1983

We show that the usual formulation of the N = 4 supersymmetric Yang-Mills theory in terms of N = 1 superfields can be generalized to describe the full ten-dimensional theory.

Spacetime superalgebras with 64 or less number of real supercharges, containing the type IIB Poincaré superalgebra in (9, 1) dimensions and the N = 1 Poincaré superalgebra in (10, 1) are considered. The restriction D ≤ 14, and two distinct possibilities arise: The N = (1, 0) superalgebra in (11, 3) dimensions, and the N = (2, 0) superalgebra in (10, 2) dimensions. Emphasizing the former, we describe superparticle and super Yang-Mills systems in (11, 3) dimensions. We also propose an N = (2, 1) superstring theory in (n, n) dimensions as a possible origin of super Yang-Mills in (8 + n, n) dimensions.

Nuclear Physics B, 1998

We present supersymmetric Yang-Mills theories in arbitrary even dimensions with the signature (9 + m, 1 + m) where m = 0, 1, 2, • • • beyond ten-dimensions up to infinity. This formulation utilizes null-vectors and is a generalization of our previous work in 10+2 dimensions to arbitrary even dimensions with the above signature. We have overcome the previously-observed obstruction beyond 11+3 dimensions, by the aid of projection operators. Both component and superspace formulations are presented. This also suggests the possibility of consistent supergravity theories in any even dimensions beyond 10+1 dimensions.

Nuclear Physics B, 1989

We construct a gauge-invariant superspace action in terms of unconstrained off-shell superfields for the D = 10 supersymmetric Yang-Mills (SYM) theory. We use to this effect: (i) the point particle limit of the BRST charge of the covariantly quantized harmonic Green-Schwarz superstring, (ii) a general covariant action principle for overdetermined systems of nonlinear field equations of motion. One obtains gauge and super-Poincard invariant equations of motion equivalent to the Nilsson's constraints for D = 10 SYM. In the previous approaches (light-cone-gauge, component-fields) one would have to sacrifice either explicit Lorentz invariance or explicit supersymmetry while in the present approach they are both manifest. Unfortunately the action we find is nonlocal in space-time. To restore locality one may have to introduce additional degrees of freedom.

Nuclear Physics B, 1988

A new type of D = 10 harmonic superspace with two generations of harmonics allows us to reduce the D = 10, N = 1 Brink-Schwarz (BS) superparticle to a system whose constraints are all first class, functionally independent and Lorentz-covariant. Given these properties, the covariant BFV-BRST quantization of the system is straightforward. By second quantizing this system, we circumvent the no-go theorem which forbids the existence of a covariant off-shell unconstrained superfield action for the linearized D = 10 super-Yang-Mills theory. * The recently proposed formalism of ref. [14] for BFV quantization of the heterotic string with finite level of reduciblity breaks the Lorentz-invariance explicitly by introducing two constant light-like oectors which are not dynamical degrees of freedom.

Nuclear Physics B, 2006

We classify the supersymmetric mass deformations of all the super Yang-Mills quantum mechanics, which are obtained by dimensional reductions of minimal super Yang-Mills in spacetime dimensions: ten, six, four, three and two. The resulting actions can be viewed as the matrix descriptions of supermembranes in nontrivial backgrounds of one higher dimensional supergravity theories. We also discuss the utmost generalization of the light-cone formulation of the Nambu-Goto action for a p-brane, including time dependent backgrounds.

Nuclear Physics B, 1999

It is shown that there exists an on-shell light cone gauge where half of the fermionic components of the super vector potential vanish, so that part of the superspace flatness conditions becomes linear. After reduction to (1+ 1) space-time dimensions, the general solution of this subset of equations is derived. The remaining non-linear equations are written in a form which is analogous to Yang equations, albeit with superderivatives involving sixteen fermionic coordinates. It is shown that this non-linear part may, nevertheless, be solved by methods similar to powerful technics previously developed for the (purely bosonic) self-dual Yang Mills equations in four dimensions.