Localized intersections of M5-branes and four-dimensional superconformal field theories

TL;DR

This work constructs SUSY-preserving, localized intersections of M5-branes yielding 4D ${\cal N}=2$ SCFTs, including the case with $N_f=2N_c$ and a generalized SU($N$)^n quiver, by encoding the solution in a Kahler metric $g_{m\bar n}$ on a complex 2-space and a Kahler potential $K$ that fixes the metric via $g_{m\bar n}=\partial_m\partial_{\bar n}K$. The near-horizon limit produces $AdS_5\times M$ with the appropriate R-symmetry, and a T-duality along a compact direction relates the IIA Hanany–Witten setup to Type IIB with D3-branes at a ${\bf C^2}/{\bf Z}_n$ orbifold, providing a geometric gravity dual to the 4D SCFT. A simple one-brane example reproduces the known localized M5-brane solution and the general framework clarifies how localization requires nonzero cross-terms $g_{v\bar s}$; the paper also outlines a pathway to fully localized M5 intersections and broader matter content via further localization and orientifold constructions.

Abstract

We write supersymmetry preserving conditions for infinite M5-branes intersecting on a (3+1)-dimensional space. In contrast to previously known solutions, these intersections are completely localized. We solve the equations for a particular class of configurations which in the near-horizon decoupling limit are dual to N_f = 2N_c Seiberg-Witten superconformal field theories with gauge group SU(N) and generalisations to SU(N)^n. We also discuss the relationship to D3-branes in the presence of an A_k singularity.