Membrane Quantum Mechanics

TL;DR

This paper derives superconformal quantum mechanics models from wrapped M2-branes on Riemann surfaces, revealing new supersymmetric structures and potential descriptions of brane dynamics in Calabi-Yau spaces.

Contribution

It introduces novel superconformal quantum mechanics models from M2-branes wrapped on Riemann surfaces, including a model for branes in K3 surfaces, with explicit supersymmetry and twisting prescriptions.

Findings

Derived N=16 and N=12 superconformal gauged quantum mechanics from BLG and ABJM models.

Identified gauge groups OSp(16|2) and SU(1,1|6) in the reduced models.

Proposed a superconformal quantum mechanics for M2-branes in K3 surfaces.

Abstract

We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N = 16 and N = 12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2) and SU(1,1|6) quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi-Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N = 8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.