Massive super Yang-Mills quantum mechanics: classification and the relation to supermembrane

Abstract

We classify the supersymmetric mass deformations of all the super Yang-Mills quantum mechanics, which are obtained by dimensional reductions of minimal super Yang-Mills in spacetime dimensions: ten, six, four, three and two. The resulting actions can be viewed as the matrix descriptions of supermembranes in nontrivial backgrounds of one higher dimensional supergravity theories. We also discuss the utmost generalization of the light-cone formulation of the Nambu-Goto action for a p-brane, including time dependent backgrounds.

1+42 pages; References added, to appear in NPB

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• Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges
• Supersymmetric gauged Double Field Theory: Systematic derivation by virtue of \textit{Twist}
• Lectures on Matrix Field Theory I
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• Four-dimensional N=1 super Yang-Mills from matrix model
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• Superconformal Yang-Mills quantum mechanics and Calogero model with OSp(N|2,R) symmetry
• Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models II
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• The Confining Transition in the Bosonic BMN Matrix Model
• Mass Deformations of Super Yang-Mills Theories in D= 2+1, and Super-Membranes: A Note
• A Supersymmetry Preserving Mass-Deformation of N=1 Super Yang-Mills in D=2+1
• The nonperturbative phase diagram of the bosonic BMN matrix model
• An anisotropic hybrid non-perturbative formulation for 4D N = 2 supersymmetric Yang-Mills theories
• Exploring new variational quantum circuit ansatzes for solving $SU(2)$ matrix models
• M-theory on pp-waves with a holomorphic superpotential and its membrane and matrix descriptions
• Remarks on the eigenvalues distributions of D\leq 4 Yang-Mills matrix models
• High-Precision Bootstrap of Multimatrix Quantum Mechanics
• Matrix at slow roll: Nonrelativistic and Perturbative
• Matrix equations and trilinear commutation relations