A Nonperturbative Test of M2-Brane Theory

Abstract

We discuss non-perturbative effects in the ABJM model due to monopole instantons. We begin by constructing the instanton solutions in the $U(2)\times U(2)$ model, explicitly, and computing the Euclidean action. The Wick-rotated Lagrangian is complex and its BPS monopole instantons are found to be a delicate version of the usual 't Hooft-Polyakov monopole solutions. They are generically 1/3 BPS but become 1/2 BPS at special locus in the moduli space of two M2-branes, yet each instanton carries eight fermionic zero modes, regardless of the vacuum choice. The low energy effective action induced by monopole instantons are quartic order in derivatives. The resulting vertices are nonperturbative in $1/k$, as expected, but are rational functions of the vacuum moduli. We also analyze the system of two M2-branes in the supergravity framework and compute the higher order interactions via 11-dimensional supergraviton exchange. The comparison of the two shows that the instanton vertices are precisely reproduced by this M2-brane picture, supporting the proposal that the ABJM model describes multiple M2-branes.

40 pages, 1 figure, references updated

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• N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations
• Three-dimensional N=6 SCFT's and their membrane dynamics
• The AdS4/CFT3 algebraic curve
• Classification of N=6 superconformal theories of ABJM type
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• Infrared Stability of N=2 Chern-Simons Matter Theories
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• Non-Abelian Vortices at Weak and Strong Coupling in Mass Deformed ABJM Theory
• SDiff Gauge Theory and the M2 Condensate
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• Topological Twisting of Multiple M2-brane Theory
• Two-loop test of the N=6 Chern-Simons theory S-matrix
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• Squashing Gravity Dual of N=6 Superconformal Chern-Simons Gauge Theory
• Abelian Vortex in Bagger-Lambert-Gustavsson Theory
• Membrane Dynamics in Three dimensional N=6 Supersymmetric Chern-Simons Theory
• Extracting the size of the cosmic electron-positron anomaly
• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
• Charges and homologies in AdS_4/CFT_3
• Aspects of ABJM orbifolds
• M5-branes in ABJM theory and Nahm equation
• Membrane scattering from Bagger-Lambert theory
• U(1) Instantons on AdS_4 and the Uplift to Exact Supergravity Solutions
• Monopole--Instantons in M2-brane Theories
• Eight Fermion Terms in the Effective Action of the ABJM Model
• BPS Vortices, $Q$-balls, and $Q$-vortices in $\mathcal{N}=6$} Chern-Simons Matter Theory
• Emergent geometry in N=6 Chern-Simons-matter theory