New Results on N = 4 SuperYang – Mills Theory
نویسنده
چکیده
The N = 4 SuperYang–Mills theory is covariantly determined by a U(1)×SU(2) ⊂ SL(2,R)× SU(2) internal symmetry and two scalar and one vector BRST topological symmetry operators. This determines an off-shell closed sector of N = 4 SuperYang–Mills, with 6 generators, which is big enough to fully determine the theory, in a Lorentz covariant way. This reduced algebra derives from horizontality conditions in four dimensions. The horizontality conditions only depend on the geometry of the Yang–Mills fields. They also descend from a genuine horizontality condition in eight dimensions. In fact, the SL(2,R) symmetry is induced by a dimensional reduction from eight to seven dimensions, which establishes a ghost-antighost symmetry, while the SU(2) symmetry occurs by dimensional reduction from seven to four dimensions. When the four dimensional manifold is hyperKähler, one can perform a twist operation that defines the N = 4 supersymmetry and its SL(2,H) ∼ SU(4) R-symmetry in flat space. (For defining a TQFT on a more general four manifold, one can use the internal SU(2)-symmetry and redefine a Lorentz SO(4) invariance). These results extend in a covariant way the light cone property that the N = 4 SuperYang–Mills theory is actually determined by only 8 independent generators, instead of the 16 generators that occur in the physical representation of the superPoincaré algebra. The topological construction disentangles the off-shell closed sector of the (twisted) maximally supersymmetric theory from the (irrelevant) sector that closes only modulo equations of motion. It allows one to escape the question of auxiliary fields in N = 4 SuperYang–Mills theory. email address: [email protected] email address: [email protected] ‡ 4 place Jussieu, F-75252 Paris Cedex 05, France. § Piscataway, NJ08855-0849, USA.
منابع مشابه
ar X iv : h ep - t h / 05 07 00 3 v 1 1 J ul 2 00 5 LPTHE - 05 New Results on N = 4 SuperYang – Mills Theory
The N = 4 SuperYang–Mills theory is covariantly determined by a U(1)×SU(2) ⊂ SL(2,R)× SU(2) internal symmetry and two scalar and one vector BRST topological symmetry operators. This determines an off-shell closed sector of N = 4 SuperYang–Mills, with 6 generators, which is big enough to fully determine the theory, in a Lorentz covariant way. This reduced algebra derives from horizontality condi...
متن کامل, v er si on 2 - 4 F eb 2 00 8 LPTHE - 05 New Results on N = 4 SuperYang – Mills Theory
The N = 4 SuperYang–Mills theory is covariantly determined by a U(1)×SU(2) ⊂ SL(2,R)× SU(2) internal symmetry and two scalar and one vector BRST topological symmetry operators. This determines an off-shell closed sector of N = 4 SuperYang–Mills, with 6 generators, which is big enough to fully determine the theory, in a Lorentz covariant way. This reduced algebra derives from horizontality condi...
متن کاملSuperYang-Mills,MatrixModels andGeometric Transitions SuperYang-Mills, modèles dematrices et transitions géométriques
I explain two applications of the relationship between four dimensional N = 1 supersymmetric gauge theories, zero dimensional gauged matrix models, and geometric transitions in string theory. The first is related to the spectrum of BPS domain walls or BPS branes. It is shown that one can smoothly interpolate between a D-brane state, whose weak coupling tension scales as N ∼ 1/gs, and a closed s...
متن کاملDrag force in AdS/CFT
The AdS/CFT correspondence and a classical test string approximation are used to calculate the drag force on an external quark moving in a thermal plasma of N = 4 superYang-Mills theory. This computation is motivated by the phenomenon of jet-quenching in relativistic heavy ion collisions.
متن کاملLow-energy features of SU(2) Yang-Mills theory with light gluinos
The numerical simulation we report on aims at a better understanding of the non-perturbative low-energy features of supersymmetric gauge theories. We concentrate on the simplest supersymmetric gauge theory, namely SU(2),N = 1 superYang-Mills. This model contains, in addition to the gauge field a massless Majorana fermion in the adjoint representation (called gluino). For the theoretical motivat...
متن کامل