Supergravity and a Confining Gauge Theory: Duality Cascades and $χ$SB-Resolution of Naked Singularities

TL;DR

This work analyzes IIB supergravity with M fractional D3-branes on the conifold, showing that the decreasing 5-form flux is mirrored by a Seiberg duality cascade in the dual $SU(N+M)\times SU(N)$ gauge theory, with N stepping down by M. In the IR, strong dynamics generate a quantum deformation of the conifold, breaking the discrete R-symmetry to ${\bf Z}_2$ and producing confinement, domain walls, and a moduli space of deformed-conifold branches. The authors construct a nonsingular warped background based on the deformed conifold that encapsulates these IR phenomena, while preserving UV logarithmic running. They discuss the conjectured pure ${\cal N}=1$ Yang-Mills dual and the potential for a broader framework where a duality cascade underlies gauge theories including the Standard Model. The work connects precise supergravity solutions to rich IR gauge dynamics, offering a geometrical realization of confinement and chiral symmetry breaking within a holographic setting.

Abstract

We revisit the singular IIB supergravity solution describing M fractional 3-branes on the conifold [hep-th/0002159]. Its 5-form flux decreases, which we explain by showing that the relevant \NN=1 SUSY SU(N+M)xSU(N) gauge theory undergoes repeated Seiberg-duality transformations in which N -> N-M. Far in the IR the gauge theory confines; its chiral symmetry breaking removes the singularity of hep-th/0002159 by deforming the conifold. We propose a non-singular pure-supergravity background dual to the field theory on all scales, with small curvature everywhere if the `t Hooft coupling g_s M is large. In the UV it approaches that of hep-th/0002159, incorporating the logarithmic flow of couplings. In the IR the deformation of the conifold gives a geometrical realization of chiral symmetry breaking and confinement. We suggest that pure \NN=1 Yang-Mills may be dual to strings propagating at small g_s M on a warped deformed conifold. We note also that the standard model itself may lie at the base of a duality cascade.