Rigid Holography and Six-Dimensional N=(2,0) Theories on AdS_5 times S^1

TL;DR

The paper develops a framework of rigid holography to study non-gravitational field theories on AdS spaces by isolating decoupled sectors that survive in the large-N limit of string-theoretic holography. Focusing on the 6d ${\rm N}=(2,0)$ ${A}_{K-1}$ theory on $AdS_5\times S^1$, embedded in Type IIB backgrounds, it identifies a universal 4d ${\cal N}=2$ subsector—described by a boundary $SU(K)\times P(K)$ theory—that captures boundary-source correlators of the 6d theory. The work analyzes two complementary descriptions: (i) a bulk 5d $SU(K)$ gauge theory on $AdS_5$ coupled to a 4d boundary theory, and (ii) a bulk description featuring massless higher-spin fields at the singular point, arguing that these are dual facets of the same underlying physics. It further extends the framework to decoupling limits yielding little string theories on $AdS_5\times S^1$, demonstrates universality across various string constructions, and outlines extensive future directions, including a systematic boundary-condition classification and precise mappings via localization techniques.

Abstract

Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories (CFTs), this relates some of the observables of these field theories on AdS to a subsector of the dual CFTs. We exemplify this `rigid holography' by studying in detail the 6d N=(2,0) A_{K-1} superconformal field theory (SCFT) on AdS_5xS^1, with equal radii for AdS_5 and for S^1. We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS_5xS^5/Z_K. On R^{4,1}xS^1, this 6d theory has a 5(K-1)-dimensional moduli space, with unbroken 5d SU(K) gauge symmetry at (and only at) the origin. On AdS_5xS^1, the theory has a 2(K-1)-dimensional `moduli space' of supersymmetric configurations. We argue that in this case the SU(K) gauge symmetry is unbroken everywhere in the `moduli space' and that this 5d gauge theory is coupled to a 4d theory on the boundary of AdS_5 whose coupling constants depend on the `moduli'. This involves non-standard boundary conditions for the gauge fields on AdS_5. Near the origin of the `moduli space', the theory on the boundary contains a weakly coupled 4d N=2 supersymmetric SU(K) gauge theory. We show that this implies large corrections to the metric on the `moduli space'. The embedding in string theory implies that the 6d N=(2,0) theory on AdS_5xS^1 with sources on the boundary is a subsector of the large N limit of various 4d N=2 quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different 4d N=2 SCFTs. We also discuss a decoupling limit that leads to N=(2,0) `little string theories' on AdS_5xS^1.

Figures (9)

• Figure 1: The quiver diagram of $\widehat{A}_{K-1}$. In the dual four-dimensional ${\cal N}=2$ SCFT, each node (grey blob) describes a ${\cal N}=2$ vector multiplet in the adjoint representation of $SU(N)$, while each link (double line) describes a ${\cal N}=2$ hypermultiplet in the bifundamental representation of two adjacent $SU(N) \otimes SU(N)$ groups. The global symmetry includes the R-symmetry and a $[U(1)]^K$ coming from the hypermultiplets on each link.
• Figure 2: The Type IIA brane configuration of the four-dimensional quiver theory, at the perturbative orbifold point (a) and at the singular orbifold point (b) that we will discuss below. The red lines are NS5-branes, and the blue lines are D4-branes.
• Figure 3: The UV curve of the four-dimensional ${\cal N}=2$ SCFT with $\widehat{A}_{K-1}$ quiver gauge group.
• Figure 4: The strong coupling singular limit of the UV curve for the four-dimensional, ${\cal N}=2$ SCFT with ${\widehat{A}}_{K-1}$ quiver gauge group.
• Figure 5: The UV curve of the four-dimensional ${\cal N}=2$ superconformal quiver gauge theory in the singular limit, exhibiting the separation into three decoupled sectors.