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.
Highlights
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
We find that such highly extended superconformal quantum mechanical models arise from the M2-branes wrapping a torus and that our reduced quantum mechanical actions agree with the predicted form for N > 4 superconformal quantum mechanics (SCQM) in [16, 17, 18]
We show that OSp(16|2) superconformal quantum mechanics appears from the reduced system after integrating out the auxiliary gauge field
Summary
The BLG-model is a three-dimensional N = 8 superconformal Chern-Simons-matter theory proposed as a low energy world-volume theory of multiple M2-branes [4, 5, 6, 7, 8] It is based on a 3-algebra A, which is an N dimensional vector space endowed with a trilinear skew-symmetric product [A, B, C] satisfying [A, B, [C, D, E]] = [[A, B, C], D, E] + [C, [A, B, D], E] + [C, D, [A, B, E]]. The Lagrangian of the BLG-model is specified by the structure constant f abcd and the bi-invariant metric hab. The bosonic scalar fields XI and the fermionic fields ΨAare 8v and 8c of an SO(8) R-symmetry respectively They are the fundamental representations of the 3-algebra. The limitation on the rank of the gauge algebra may only allow the BLG-model to describe two M2-branes in analogy with D-branes 2
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