Membrane Quantum Mechanics

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.

54 pages, v2: errors corrected and notations improved

References in corpus (34)

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• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Supergravity description of field theories on curved manifolds and a no go theorem
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Fivebranes, Membranes and Non-Perturbative String Theory
• Comments on Multiple M2-branes
• D-Branes and Topological Field Theories
• Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence
• Black Holes and Superconformal Mechanics
• Superconformal Chern-Simons Theories
• The M2-M5 Brane System and a Generalized Nahm's Equation
• Black Holes and Calogero Models
• Topological Reduction of 4D SYM to 2D $\sigma$--Models
• Selfdual strings and loop space Nahm equations
• Constraining Maximally Supersymmetric Membrane Actions
• BPS States, String Duality, and Nodal Curves on K3
• M2-branes, 3-Lie Algebras and Plucker relations
• Supersymmetry and generalized calibrations
• Conformal quantum mechanics as the CFT${}_1$ dual to AdS${}_2$
• Holomorphic reduction of N=2 gauge theories, Wilson-'t Hooft operators, and S-duality
• Supersymmetric Calogero models by gauging
• Membranes Wrapped on Holomorphic Curves
• Superconformal mechanics
• Notes on Supersymmetry Enhancement of ABJM Theory
• (Super)conformal many-body quantum mechanics with extended supersymmetry
• ABC of N=8, d=1 supermultiplets
• Enhanced N=8 Supersymmetry of ABJM Theory on R(8) and R(8)/Z(2)
• Relating U(N)xU(N) to SU(N)xSU(N) Chern-Simons Membrane theories
• New and old N=8 superconformal field theories in three dimensions
• New insight into WDVV equation
• Conformal Blocks for the 4-Point Function in Conformal Quantum Mechanics
• Conformal Symmetry on World Volumes of Branes

Cited by in corpus (12)

• Baryon Spectrum from Superconformal Quantum Mechanics and its Light-Front Holographic Embedding
• A slow review of the AGT correspondence
• N=4 superconformal mechanics from the su(2) perspective
• Topological M-Strings and Supergroup WZW Models
• New realizations of the supergroup D(2,1;α) in N=4 superconformal mechanics
• Superconformal Quantum Mechanics from M2-branes
• Qubits from Black Holes in M-theory on K3 Surface
• Two-dimensional superconformal field theories from Riemann surfaces with boundary
• $\mathcal{N}=2$ supersymmetry and anisotropic scale invariance
• Mock Modular Index of M2-M5 Brane System
• $SU(1,1|N)$ superconformal mechanics with fermionic gauge symmetry
• On $OSp(N|2)$ superconformal mechanics