Generalized Dynamical Spin Chain and 4-Loop Integrability in N=6 Superconformal Chern-Simons Theory

Abstract

We revisit unitary representation of centrally extended (2 | 2) excitation superalgebra. We find most generally that `pseudo-momentum', not lattice momentum, diagonalizes spin chain Hamiltonian and leads to generalized dynamic spin chain. All known results point to lattice momentum diagonalization for N=4 super Yang-Mills theory. Having different interacting structure, we ask if N=6 superconformal Chern-Simons theory provides an example of pseudo-momentum diagonalization. For SO(6) sector, we study maximal shuffling and next-to-maximal shuffling terms in the dilatation operator and compare them with results expected from psu(2|2) superalgebbra and integrability. At two loops, we rederive maximal shuffling term (3-site) and find perfect agreement with known results. At four loops, we first find absence of next-to-maximal shuffling term (4-site), in agreement with prediction based on integrability. We next extract maximal shuffling term (5-site), the most relevant term for checking the possibility of pseudo-momentum diagonalization. Curiously, we find that result agrees with integraility prediction based on lattice momentum, as in N=4 super Yang-Mills theory. Consistency of our results is fully ensured by checks of renormalizability up to six loops.

30 pages, 13 figures, v2. references added and conclusion changed; v3. references updated, v4. final published version

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• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Giant Magnons
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Cited by in corpus (25)

• Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
• Dual Superconformal Symmetry of N=6 Chern-Simons Theory
• Enhanced N=8 Supersymmetry of ABJM Theory on R(8) and R(8)/Z(2)
• Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories
• Magnon dispersion to four loops in the ABJM and ABJ models
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Marginal Deformations and 3-Algebra Structures
• One-Loop Corrections to Type IIA String Theory in AdS4 x CP3
• Full Lagrangian and Hamiltonian for quantum strings on AdS_4 x CP^3 in a near plane wave limit
• The worldsheet low-energy limit of the AdS_4 x CP^3 superstring
• Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond
• Observables and Correlators in Nonrelativistic ABJM Theory
• On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring
• Two-Loop Spectroscopy of Short ABJM Operators
• Scattering of Giant Magnons in CP^3
• Thermal Aspects of ABJM theory: Currents and Condensations
• The Leading Order Dressing Phase in ABJM Theory
• Integrable Open Spin Chains from Flavored ABJM Theory
• On the absence of reflection in AdS4/CFT3
• On thermodynamics of N=6 superconformal Chern-Simons theory
• Symmetry Breaking Phase Transitions in ABJM Theory with a Finite U(1) Chemical Potential
• Static Length Scales of N=6 Chern-Simons Plasma
• Fermionic reductions of the AdS4 x CP3 superstring
• Exact 4-point Scattering Amplitude of the Superconformal Schrodinger Chern-Simons Theory