No go for a flow

TL;DR

The paper investigates the existence of UV lagrangians that flow to AD theories via the Maruyoshi–Song mechanism. It combines IIB geometrical engineering to compute CB spectra and central charges with an anomaly-driven algorithm to search for UV Lagrangian completions, applying it to a large $(G,G')$ landscape. The main finding is that, out of a wide scan of 20100 theories, only known MS UV lagrangians survive and no new examples appear for $(G,G')$ AD theories, supporting a conjecture of non-existence in general. The work also provides efficient tools to compute CB data and central charges for high-rank $(G,G')$ theories and makes the accompanying code publicly available, facilitating further exploration of UV completions in this class of theories.

Abstract

We prove that a very large class of $15502$ general Argyres-Douglas theories cannot admit a UV lagrangian which flows to them via the Maruyoshi-Song supersymmetry enhancement mechanism. We do so by developing a computer program which brute-force lists, for any given 4d $\mathcal{N}=2$ superconformal theory $\mathcal{T}_{\text{IR}}$, all possible UV candidate superconformal lagrangians $\mathcal{T}_{\text{UV}}$ satisfying some necessary criteria for the supersymmetry enhancement to happen. We argue that this is enough evidence to conjecture that it is impossible, in general, to find new examples of Maruyoshi-Song lagrangians for generalized Argyres-Douglas theories. All lagrangians already known are, on the other hand, recovered and confirmed in our scan. Finally, we also develop another program to compute efficiently Coulomb branch spectrum, masses, couplings and central charges for $(G,G')$ Argyres-Douglas theories of arbitrarily high rank.

Figures (2)

• Figure 1: We plot how the central charges scale with the rank for $(A_m,E_6)$ with $m$ in $[1,1500]$.
• Figure 2: Quiver for the theory UV completion of $(A_3,A_7)$.