Two-loop spectroscopy of short ABJM operators. (English) Zbl 1270.81186
Summary: We study the spectrum of anomalous dimensions of short operators in planar ABJM theory at two loops. Specifically we develop a method for solving the OSp\((6\mid 4)\) Bethe ansatz equations for a certain class of unpaired length-4 states with arbitrarily high number of excitations, and apply it to identify three new sequences of rational eigenvalues. Results for low-lying paired states in the OSp\((4\mid 2)\) sector are obtained by direct diagonalization of the spin chain Hamiltonian. We also study the SL\((2\mid 1)\) sector and identify the set of states that corresponds to the SL(2)-like Bethe ansatz of Gromov and Vieira. Finally we extend part of our analysis to length-6 operators.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 58J28 | Eta-invariants, Chern-Simons invariants |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
| 81Q40 | Bethe-Salpeter and other integral equations arising in quantum theory |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 53D45 | Gromov-Witten invariants, quantum cohomology, Frobenius manifolds |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
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