Large branes in AdS and their field theory dual

TL;DR

Explores how gravitons with large angular momentum along $S^5$ in $AdS_5 \times S^5$ can blow up into spherical D3-branes, both in $S^5$ and in $AdS_5$, preserving 16 of 32 supersymmetries (BPS). Through a DBI/CS analysis in both backgrounds, it demonstrates stable brane configurations carrying the same quantum numbers $(E,L)$ and identifies the corresponding energies, $E = P = L/R$ for the compact $S^5$ case and $E = L$ for the AdS$_5$ case. It then constructs a classical BPS solution of ${\cal N}=4$ SYM on $S^3 \times \mathbb{R}$ with nonzero Higgs vevs that is dual to the large AdS-brane, thus refining the bulk-boundary dictionary. Overall, the work broadens the set of known bulk brane states and clarifies how angular-momentum-driven brane polarizations map to boundary operators and their dynamics, with implications for the stringy exclusion principle and holography.

Abstract

Recently it was suggested that a graviton in $AdS_5 \times S^5$ with a large momentum along the sphere can blow up into a spherical D-brane in $S^5$. In this paper we show that the same graviton can also blow up into a spherical D-brane in $AdS_5$ with exactly the same quantum numbers (angular momentum and energy). These branes are BPS, preserving 16 of the 32 supersymmetries. We show that there is a BPS {\it classical} solution for SYM on $S^3\times R$ with exactly the same quantum numbers. The solution has non-vanishing Higgs expectation values and hence is dual to the large brane in AdS.

Figures (2)

• Figure 1: Energy of spherical brane as a function of its radius. The local minima of this curve corresponds to classically stable brane configurations.
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