Supergravity and The Large N Limit of Theories With Sixteen Supercharges

TL;DR

The work generalizes the gauge/gravity correspondence to theories with sixteen supercharges beyond conformal cases by analyzing decoupling limits of various Dp-brane systems. It shows how large-N gauge theories flow between perturbative YM regimes and diverse supergravity or M-theory descriptions (IIA/IIB, AdS_4×S^7, AdS_7×S^4) across energy scales, including finite-temperature and near-extremal setups. A key theme is the existence of intermediate regions where a reliable gravity dual emerges, while UV/IR limits may revert to perturbative YM or decoupled CFTs, and certain brane systems (notably D6) do not decouple from bulk gravity. The paper thereby extends the holographic intuition to non-conformal, sixteen-supercharge theories and highlights localization instabilities and the role of eleven-dimensional uplift in obtaining trustworthy descriptions.

Abstract

We consider field theories with sixteen supersymmetries, which includes U(N) Yang-Mills theories in various dimensions, and argue that their large N limit is related to certain supergravity solutions. We study this by considering a system of D-branes in string theory and then taking a limit where the brane worldvolume theory decouples from gravity. At the same time we study the corresponding D-brane supergravity solution and argue that we can trust it in certain regions where the curvature (and the effective string coupling, where appropriate) are small. The supergravity solutions typically have several weakly coupled regions and interpolate between different limits of string-M-theory.

Figures (6)

• Figure 1: The D2-brane map: The horizontal dashed line separates between the small $N$ region and the large $N$ region. The other dashed line separates the IR region from the rest. The UV description is via perturbative super-Yang-Mills (a). In the IR the theory flows to a super-conformal region (the marked region) with SO(8) R-symmetry sei. For large $N$ we have a region described by IIA supergravity (b), a region described by the periodic array of M2-branes solution in eleven dimensions (c) and finally in the IR we have M-theory on the $AdS_4\times S^7$ background (d).
• Figure 2: The D1-brane map: The horizontal dashed line separates between the small $N$ region and the large $N$ region. The other dashed line separates between the IR region and the rest. For any $N$ the UV region is described by perturbative SYM (a) and in the IR by a free orbifold CFT (d). When $N$ is large there is an intermediate region (b,c) which is described by a IIB supergravity solution interpolating between the D1 brane solution (b) and the F-string solution (c).
• Figure 3: The D0-brane map: The horizontal dashed line separates between the small $N$ region and the large $N$ region. For any $N$ the UV description is via perturbation theory in super quantum mechanics (a). For large $N$ we have a region (b) which is described by the IIA D0 brane solution, which for smaller energies becomes a gravitational wave background in eleven dimensions (c). Finally, at very low energies (d) we enter into the matrix black hole region.
• Figure 4: The D4-brane map: The horizontal dashed line separates between the small $N$ region and the large $N$ region. The UV region is described by a super-conformal theory on a circle (the marked region) (c,d), which is dual for large $N$ to M-theory on a background $AdS_4\times S^7$ (c) (with an identification). In the IR the theory is described by "perturbative" super-Yang-Mills (a). For large $N$ we have the intermediate region (b) described by the IIA D4 brane solution.
• Figure 5: The D5-brane map: The horizontal dashed line separates between the small $N$ region and the large $N$ region. In the IR the theory are described by "perturbative" SYM (a). For the UV description is via type IIB on NS background (c,d) which has supergravity description for large $N$ (c). For large $N$ there is an intermediate region described by the D5 brane background (b).