Holography, Singularities on Orbifolds and 4D N=2 SQCD

TL;DR

Pelc extends the holographic framework to orbifold hypersurface singularities and applies it to 4D $N=2$ SQCD, demonstrating a robust strong–weak duality between a decoupled $d$‑dimensional theory and a non‑critical string background $\mathbb{R}^{d-1,1}\times\mathbb{R}_\phi\times U(1)_Y\times LG_W/\Gamma$; using decoupling and double‑scaling limits, the IR fixed point data (dimensions, couplings, moduli) computed via the worldsheet description agree with Seiberg–Witten analyses for key cases such as $N_f=2N_c$, linking the singular geometry to IR SCFT structure and providing a concrete string‑based toolkit for studying 4D $N=2$ theories.

Abstract

Type II string theory compactified on a Calabi-Yau manifold, with a singularity modeled by a hypersurface in an orbifold, is considered. In the limit of vanishing string coupling, one expects a non gravitational theory concentrated at the singularity. It is proposed that this theory is holographicly dual to a family of ``non-critical'' superstring vacua, generalizing a previous proposal for hypersurfaces in flat space. It is argued that a class of such singularities is relevant for the study of non-trivial IR fixed points that appear in the moduli space of four-dimensional N=2 SQCD: SU(N_c) gauge theory with matter in the fundamental representation. This includes the origin in the moduli space of the SU(N_c) gauge theory with N_f=2N_c fundamentals. The 4D IR fixed points are studied using the anti-holographic description and the results agree with information available from gauge theory.