Monopoles, three-algebras and ABJM theories with $\mathbb{N}=5,6,8$ supersymmetry

Abstract

We extend the hermitian three-algebra formulation of ABJM theory to include $U(1)$ factors. With attention payed to extra $U(1)$ factors, we refine the classification of $\mathbb{N}=6$ ABJM theories. We argue that essentially the only allowed gauge groups are $SU(N)\times SU(N)$, $U(N)\times U(M)$ and $Sp(N)\times U(1)$ and that we have only one independent Chern-Simons level in all these cases. Our argument is based on integrality of the $U(1)$ Chern-Simons levels and supersymmetry. A relation between monopole operators and Wilson lines in Chern-Simons theory suggests certain gauge representations of the monopole operators. From this we classify cases where we can not expect enhanced $\mathbb{N}=8$ supersymmetry. We also show that there are two equivalent formulations of $\mathbb{N}=5$ ABJM theories, based on hermitian three-algebra and quaternionic three-algebra respectively. We suggest properties of monopoles in $\mathbb{N}=5$ theories and show how these monopoles may enhance supersymmetry from $\mathbb{N}=5$ to $\mathbb{N}=6$.

arXiv comment52 pages

References in corpus (24)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Fractional M2-branes
• Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory
• N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds
• The complete superconformal index for N=6 Chern-Simons theory
• Three-Algebras and N=6 Chern-Simons Gauge Theories
• Nonperturbative Tests of Three-Dimensional Dualities
• Scaled momentum distributions of charged particles in dijet photoproduction at HERA
• Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry
• Supersymmetry enhancement by monopole operators
• Classification of N=6 superconformal theories of ABJM type
• On the Lie-algebraic origin of metric 3-algebras
• Charges of Monopole Operators in Chern-Simons Yang-Mills Theory
• 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
• Supersymmetric vacua of mass-deformed M2-brane theory
• M2-Branes and Background Fields
• The Superconformal Gaugings in Three Dimensions
• N=6 Superspace Constraints, SUSY Enhancement and Monopole Operators
• Three-algebras, triple systems and 3-graded Lie superalgebras
• Three-Algebras in N = 5, 6 Superconformal Chern-Simons Theories: Representations and Relations
• Symplectic Three-Algebra Unifying N=5,6 Superconformal Chern-Simons-Matter Theories

Cited by in corpus (16)

• The tensor hierarchy algebra
• Non-Abelian Vortices in Supersymmetric Gauge Field Theory via Direct Methods
• M-Theory in the Gaugeon Formalism
• Higgsing M2 to D2 with gravity: N=6 chiral supergravity from topologically gauged ABJM theory
• Exceptional geometry and Borcherds superalgebras
• Super-Yang-Mills Theory in SIM(1) Superspace
• Aspects of ABJ Theory
• Chern-Simons Theory in SIM(1) Superspace
• Non-anticommutative ABJ Theory
• Duality between N=5 and N=6 Chern-Simons matter theory
• Unifying N=5 and N=6
• Deconstructing graviphoton from mass-deformed ABJM
• Superloop Space
• Five-dimensional super Yang-Mills theory from ABJM theory
• Monopoles in Superloop Space
• Supersymmetric Duality in Deformed Superloop Space