Ten-dimensional Supersymmetric Yang-Mills Research Articles

Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions

We study discrete flavor symmetries of the models based on a ten-dimensional supersymmetric Yang-Mills (10D SYM) theory compactified on magnetized tori. We assume non-vanishing non-factorizable fluxes as well as the orbifold projections. These setups allow model-building with more various flavor structures. Indeed, we show that there exist various classes of non-Abelian discrete flavor symmetries. In particular, we find that S 3 flavor symmetries can be realized in the framework of the magnetized 10D SYM theory for the first time.

Eleven dimensional supergravity in light cone gauge

Light-cone gauge manifestly supersymmetric formulation of eleven dimensional supergravity is developed. The formulation is given entirely in terms of light cone scalar superfield, allowing us to treat all component fields on an equal footing. All higher derivative on mass shell manifestly supersymmetric 4-point functions invariant with respect to linear supersymmetry transformations and corresponding (in gravitational bosonic sector) to terms constructed from four Riemann tensors and derivatives are found. Superspace representation for 4-point scattering amplitudes is also obtained. Superfield representation of linearized interaction vertex of superparticle and supergravity fields is presented. All 4-point higher derivative interaction vertices of ten-dimensional supersymmetric Yang-Mills theory are also determined.

The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections

We solve the superspace Bianchi identities for ten-dimensional supersymmetric Yang-Mills theory without imposing any kind of constraints apart from the standard conventional one. In this way we obtain a set of algebraic conditions on certain fields which in the on-shell theory are constructed as composite ones out of the physical fields. These conditions must hence be satisfied by any kind of theory in ten dimensions invariant under supersymmetry and some, abelian or non-abelian, gauge symmetry. Deformations of the ordinary SYM theory (as well as the fields) are identified as elements of a certain spinorial cohomology, giving control over field redefinitions and the distinction between physically relevant higher-order corrections and those removable by field redefinitions. The conditions derived severely constrain theories involving F^2-level terms plus higher-order corrections, as for instance those derived from open strings as effective gauge theories on D-branes.

Twelve-dimensional supersymmetric gauge theory as the large N limit

Starting with the ordinary ten-dimensional supersymmetric Yang-Mills theory for the gauge group U( N), we obtain a twelve-dimensional supersymmetric gauge theory as the large N limit. The two symplectic canonical coordinates parametrizing the unitary N× N matrices for U( N) are identified with the extra coordinates in twelve dimensions in the N→∞ limit. Applying further a strong/weak duality, we get the `decompactified' twelve-dimensional theory. The resulting twelve-dimensional theory has peculiar gauge symmetry which is compatible also with supersymmetry. We also establish a corresponding new superspace formulation with the extra coordinates. By performing a dimensional reduction from twelve dimensions directly into three dimensions, we see that the Poisson bracket terms which are needed for identification with supermembrane action arises naturally. This result indicates an universal duality mechanism that the 't Hooft limit of an arbitrary supersymmetric theory promotes the original supersymmetric theory in ( D−1,1) dimensions into a theory in ( D,2) dimensions with an additional pair of space-time coordinates. This also indicates interesting dualities between supermembrane theory, type IIA superstring with D0-branes, and the recently-discovered twelve-dimensional supersymmetric theories.

Supersymmetric Yang-Mills, octonionic instantons and triholomorphic curves

In four-dimensional gauge theory there exists a well-known correspondence between instantons and holomorphic curves, and a similar correspondence exists between certain octonionic instantons and triholomorphic curves. We prove that this latter correspondence stems from the dynamics of various dimensional reductions of ten-dimensional supersymmetric Yang-Mills theory. More precisely we show that the dimensional reduction of the (5+1)-dimensional supersymmetric sigma model with hyper-Kähler (but otherwise arbitrary) target X to a four-dimensional hyper-Kähler manifold M is a topological sigma model localising on the space of triholomorphic maps M -+ X (or hyperinstantons). When X is the moduli space M k of instantons on a four-dimensional hyper-Kdhler manifold K, this theory has an interpretation in terms of supersymmetric gauge theory. In this case, the topological sigma model can be understood as an adiabatic limit of the dimensional reduction of ten-dimensional supersymmetric Yang-Mills on the eight-dimensional manifold M × K of holonomy Sp(1) × Sp(1) ⊂ Spin(7), which is a cohomological theory localising on the moduli space of octonionic instantons.

Particles, superparticles and super Yang-Mills

This paper is concerned with theories describing spinning particles that are formulated in terms of actions possessing either local world-line supersymmetry of local fermionic kappa invariance. These classical actions are obtained by adding a finite number of spinor or vector coordinates to the usual space-time coordinates. Generalising to superspace leads to corresponding types of “spinning superparticle” theories in which the wave-functions are superfields in some (generally reducible) representation of the Lorentz group. A class of these spinning superparticle actions possesses the same spectrum as ten-dimensional supersymmetric Yang-Mills theory, which it is shown can be formulated in terms of either vector or spinor superfields satisfying supercovariant constraints. The models under consideration include some that were known previously and some new ones.

Pure spinor lines in superspace and ten-dimensional supersymmetric theories

Demanding analyticity along supersymmetric lines in superspace defined by pure spinors yields the essential on-shell constraints of ten-dimensional supersymmetric Yang-Mills. A similar procedure in loop superspace yields the constraints of on-shell ten-dimensional supergravity.

Higher conservation laws for ten-dimensional supersymmetric Yang-Mills theories

It is shown that ten-dimensional supersymmetric Yang-Mills theories are integrable systems, in the (weak) sense of admitting a (superspace) Lax representation for their equations of motion. This is achieved by means of an explicit proof that the equations of motion are not only a consequence of but in fact fully equivalent to the superspace constraint F αβ = 0. Moreover, a procedure for deriving infinite series of non-local conservation laws is outlined.

Twistor-like transform in ten dimensions

A twistor-like transform of ten-dimensional supersymmetric Yang-Mills theory is described. It generalizes previous work on N = 4 supersymmetric Yang-Mills theory in four dimensions. Partial results are obtained concerning a twistorial transform of N = 1 supergravity in ten dimensions. The motivation for this work is the possibility that the twistor transform of ten-dimensional supersymmetric field theory is the proper starting point for understanding the geometrical meaning of superstring theory. Developing the twistor transform requires developing the needed tools for coupling a superstring to a background supergravity field; this coupling is described in the last section.

Ten-dimensional supersymmetric Yang-Mills theory with SO(8)-covariant light-cone superfields

The ten-dimensional supersymmetric Yang-Mills theory is formulated in terms of light-cone superfields that transform as vectors under the group of transverse Lorentz transformations (SO(8)). These superfields are constrained by a projection condition, which is solved explicitly. The superfield action is obtained by comparing its component expansion with the usual light-cone gauge component action.

Ten-dimensional supersymmetric Yang-Mills theory in terms of four-dimensional superfields

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.

Ten-dimensional supersymmetric Yang-Mills theory is not ultraviolet finite on-shell

We find that the one-loop on-shell transition amplitude with four external fermions is not ultraviolet finite in the ten-dimensional supersymmetric Yang-Mills model.