SUSY enhancement from T-branes

TL;DR

This work provides a geometric framework for understanding supersymmetry enhancement along Maruyoshi–Song RG flows by encoding superpotential deformations as T‑brane backgrounds within F‑theory on elliptically fibered Calabi–Yau fourfolds. A simple algebraic criterion based on the factorization CY_4 → CY_IR_2 × C^2 selects enhancement flows and yields IR N=2 data without a_maximization, matching known field-theory results for rank‑1 theories. The authors concretely realize this for SU(2) with four flavors and three exceptional Argyres–Douglas cases, obtaining H_0, H_1, and H_2 IR fixed points, while demonstrating a no‑enhancement case in E_8. Overall, the paper shows how IR SCFT data and operator dimensions follow directly from the IR twofold geometry, tying spectral data of nilpotent orbits to geometric unfolded singularities with precise CY‑level constraints.

Abstract

We use the F-theoretic engineering of four-dimensional rank-one superconformal field theories to provide a geometric understanding of the phenomenon of supersymmetry enhancement along the RG flow, recently observed by Maruyoshi and Song. In this context, the superpotential deformations responsible for such flows are interpreted as T-brane backgrounds and encoded in the geometry of elliptically-fibered fourfolds. We formulate a simple algebraic criterion to select all supersymmetry-enhancing flows and, without any maximization process, derive the main features of the corresponding N=2 theories in the infrared.

Figures (1)

• Figure 1: In the IR, the D2 only probes a tiny neighborhood around $s=z=0$ of the curve $s-z^2=0$, where the D6 appears to be flat.