Constraints From Extended Supersymmetry in Quantum Mechanics

TL;DR

This paper investigates quantum mechanical theories with extended supersymmetry, showing the uniqueness of free theories with higher derivatives and deriving constraints on effective Lagrangians, including a non-renormalization theorem for D0-brane interactions.

Contribution

It introduces a method to derive constraints on effective Lagrangians in supersymmetric quantum mechanics and proves a non-renormalization theorem for D0-brane interactions.

Findings

The free theory with up to four derivatives is essentially unique under supersymmetry.

Small supersymmetry-preserving deformations can be gauged away.

A non-renormalization theorem for the $v^4$ interaction in D0-brane dynamics.

Abstract

We consider quantum mechanical gauge theories with sixteen supersymmetries. The Hamiltonians or Lagrangians characterizing these theories can contain higher derivative terms. In the operator approach, we show that the free theory is essentially the unique abelian theory with up to four derivatives in the following sense: any small deformation of the free theory, which preserves the supersymmetries, can be gauged away by a unitary conjugation. We also present a method for deriving constraints on terms appearing in an effective Lagrangian. We apply this method to the effective Lagrangian describing the dynamics of two well-separated clusters of D0-branes. As a result, we prove a non-renormalization theorem for the $v^4$ interaction.