Supersymmetry and the Yang-Mills Effective Action at Finite N

Abstract

We study the effective action of quantum mechanical SU(N) Yang-Mills theories with sixteen supersymmetries and N>2. We show that supersymmetry requires that the eight fermion terms in the supersymmetric completion of the $v^4$ terms be one-loop exact. We also show that the twelve fermion terms in the supersymmetric completion of the $v^6$ terms are two-loop exact for N=3. For N>3, this no longer seems to be true; we are able to find non-renormalization theorems for only certain twelve fermion structures. We call these structures `generalized F-terms.' We argue that as the rank of the gauge group is increased, there can be more generalized F-terms at higher orders in the derivative expansion.

18 pages, harvmac; a reference added

Cited by in corpus (22)

• M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
• Deformations of Superconformal Theories
• Ultraviolet properties of Maximal Supergravity
• Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (II): Nonrenormalization Theorems
• Two-loop N=4 Super Yang Mills effective action and interaction between D3-branes
• The Conformal Anomaly of M5-Branes
• Constraining Higher Derivative Supergravity with Scattering Amplitudes
• Absorption of dilaton partial waves by D3-branes
• Toward the End of Time
• Exact coefficients for higher dimensional operators with sixteen supersymmetries
• Three Graviton Scattering in M-Theory
• On Higher Derivative Couplings in Theories with Sixteen Supersymmetries
• Interpolating the Coulomb Phase of Little String Theory
• Warm p-soup and near extremal black holes
• Non-Renormalization Theorems for Operators with Arbitrary Numbers of Derivatives in $\mathcal{N}=4$ Yang Mills Theory
• On the Supersymmetry and Gauge Structure of Matrix Theory
• Conformal Symmetry and A New Gauge in the Matrix Model
• Structure in Supersymmetric Yang-Mills Theory
• Power of Supersymmetry in D-particle Dynamics
• Fully Off-shell Effective Action and its Supersymmetry in Matrix Theory
• A Theorem on the Power of Supersymmetry in Matrix Theory
• The SU(N) Matrix Model at Two Loops