Supersymmetric Yang-Mills theory and Riemannian Geometry

Abstract

We introduce new local gauge invariant variables for N = 1 supersymmetric Yang-Mills theory, explicitly parameterizing the physical Hilbert space of the theory. We show that these gauge invariant variables have a geometrical interpretation, and can be constructed such that the emergent geometry is that of N = 1 supergravity: a Riemannian geometry with vector-spinor generated torsion. Full geometrization of supersymmetric Yang-Mills theory is carried out, and geometry independent divergences associated to the inversion of a differential operator with zero modes -that were encountered in the non-supersymmetric case -do not arise in this situation.

An algebraic method for solving the SU(3) Gauss law

“…I have presented here a method by which the Gauss law (8) can be solved in the case of the SU(3) algebra using the ansatz (9). The fact that the l.h.s.…”

Unifying Geometrical Representations of Gauge Theory

“…Towards the end of the nineties Schiappa adapted these local gauge-invariant variables for supersymmetric gauge theory [41]. An independent variation of this school was pursued by Slizovskiy and Niemi [38].…”

“…The second school uses a Grassmannian manifold to represent gauge fields using a type of gauge-theory embedding [35,36,3,13,15,17,9,11,10,49,5,6,47,48,51,44,45,22,16,21,14,4,39,12] [ 34,27,30]. The third school introduces alternative variables for gauge theory that uncover a hidden spatial metric which reproduces the gauge fields [23,19,20,33,28,29,41,38,53]. Each of the schools start with a different geometrical representation which then faithfully maps onto the traditional gauge fields A µ .…”

Entropy bounds and Cardy–Verlinde formula in Yang–Mills theory

“…If we define J ai by (18), any solution of (27) satisfies the equations of motion (5) by the identification (22). Moreover, if the energy momentum tensor (25) satisfies the conservation law ∇ i T ij = 0, the solution of the equation ( 27) also satisfies the Bianchi identity (6).…”