Abstract
The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional mathcal{N} = 8, SO(8) gauged supergravity using Machine Learning software in [1] has led to a discovery of a new mathcal{N} = 1 vacuum with a triality-invariant SO(3) symmetry. Guided by the numerical data for that point, we obtain a consistent SO(3) × ℤ2-invariant truncation of the mathcal{N} = 8 theory to an mathcal{N} = 1 supergravity with three chiral multiplets. Critical points of the truncated scalar potential include both the mathcal{N} = 1 point as well as two new non-supersymmetric and perturbatively unstable points not found by previous searches. Studying the structure of the submanifold of SO(3) × ℤ2-invariant supergravity scalars, we find that it has a simple interpretation as a submanifold of the 14-dimensional {mathbb{Z}}_2^3 -invariant scalar manifold (SU(1, 1)/U(1))7, for which we find a rather remarkable superpotential whose structure matches the single bit error correcting (7, 4) Hamming code. This 14-dimensional scalar manifold contains approximately one quarter of the known critical points. We also show that there exists a smooth supersymmetric domain wall which interpolates between the new mathcal{N} = 1 AdS4 solution and the maximally supersymmetric AdS4 vacuum. Using holography, this result indicates the existence of an mathcal{N} = 1 RG flow from the ABJM SCFT to a new strongly interacting conformal fixed point in the IR.
Highlights
Particular, it has been a long standing problem to determine all of its critical points, which lead to AdS4 vacuum solutions of the theory
We show that there exists a smooth supersymmetric domain wall which interpolates between the new N = 1 AdS4 solution and the maximally supersymmetric AdS4 vacuum
This result indicates the existence of an N = 1 RG flow from the ABJM SCFT to a new strongly interacting conformal fixed point in the IR
Summary
Using the standard group theory summarized in appendix A, this completely determines the embedding of that SO(3) into both SO(8) and E7(7) at the level of Lie algebras: so(8) ⊃ so(3) × u(1) × u(1) and e7(7) ⊃ so(3) × g2(2) × su(1, 1) Those embeddings are confirmed by the U(1) × U(1) unbroken gauge symmetry and the presence of 8 + 2 = 10 scalar fluctuations that are SO(3) singlets in the N = 8 supergravity spectrum around that point. This degeneracy is expected given the corresponding invariance of the system of equations in (3.1) or, equivalently, (3.2) Those complex conjugate solutions are not related by an SO(8) rotation and represent two distinct critical points of the potential in the N = 8 supergravity.. This provides a nontrivial consistency test for the calculation of the spectra and of the unbroken supersymmetry
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