We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[$$ \mathcal{T} $$ T rank 0], to a (2+1)D interacting $$ \mathcal{N} $$ N = 4 superconformal field theory (SCFT) $$ \mathcal{T} $$ T rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = maxα (− log|$$ {S}_{0\alpha}^{\left(+\right)} $$ S 0 α + |) = maxα (− log|$$ {S}_{0\alpha}^{\left(-\right)} $$ S 0 α − |), where F is the round three-sphere free energy of $$ \mathcal{T} $$ T rank 0 and $$ {S}_{0\alpha}^{\left(\pm \right)} $$ S 0 α ± is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ 5 − 5 10 ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal $$ \mathcal{N} $$ N = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

We explore the spectrum of lower-dimensional anti-de Sitter (AdS) solutions in F (4) gauged supergravity in six dimensions. The ansatz employed corresponds to D4-branes partially wrapped on various supersymmetric cycles in special holonomy manifolds. Re-visiting and extending previous results, we study the cases of two, three, and four-dimensional supersymmetric cycles within Calabi-Yau threefold, fourfold, G 2 , and Spin (7) holonomy manifolds. We also report on non-supersymmetric AdS vacua, and check their stability in the consistently truncated lowerdimensional effective action, using the Breitenlohner-Freedman bound. We also analyze the IR behavior and discuss the admissibility of singular flows.

The recent proposal [1, 2] of implementing electric-magnetic duality rotation at the level of perturbative scattering amplitudes and its generalisation to gravitational context where usual gravitational mass is rotated to the NUT parameter of the Taub-NUT spacetime opens up an interesting avenue for studying NUT-charged objects as dynamical entities, in contrast to the usual approach where NUT-charged objects are considered as a static background. We extend the tree-order analysis to one-loop order, and find a disagreement between geodesic motion on Taub-NUT background and impulse computation of scattering amplitudes. As a by-product of our analysis, we find a relation between tidal response parameters and resonance excitation parameters in the language of quantum field theory scattering amplitudes.

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