Multi giant graviton systems, SUSY breaking and CFT

In this article, we describe giant gravitons in AdS_5 x S^5 moving along generic trajectories in AdS_5. The giant graviton dynamics is solved by proving that the D3-brane effective action reduces to that of a massive point particle in AdS_5 and therefore the solutions are in one to one correspondence with timelike geodesics of AdS_5. All these configurations are related via isometries of the background, which induce target space symmetries in the world volume theory of the D-brane. Hence, all these configurations preserve the same amount of supersymmetry as the original giant graviton, i.e. half of the maximal supersymmetry. Multiparticle configurations of two or more giant gravitons are also considered. In particular, a binary system preserving one quarter of the supersymmetries is found, providing a non trivial time-dependent supersymmetric solution. A short study on the dual CFT description of all the above states is given, including a derivation of the exact induced isometry map in the CFT side of the correspondence.Comment: latex, 27+1 pages. v2: comment on mixing of states in section 4.3 added, reference added, typos corrected, final versio

A harmonic family of dielectric flow solutions with maximal supersymmetry

We construct a new harmonic family: dielectric flow solutions with maximal supersymmetry in eleven-dimensional supergravity. These solutions are asymptotically AdS_4 x S^7, while in the infra-red the M2 branes are dielectrically polarized into M5 branes. These solutions are holographically dual to vacua of the mass deformed theory on M2 branes. They also provide an interesting insight on the supergravity solutions sourced by giant gravitons, allowing one to see how supergravity solves the giant graviton puzzle.Comment: 21 pages, LaTeX. reference adde

Black Hole Statistics from Holography

We study the microstates of the ``small'' black hole in the \half-BPS sector of AdS$_5\times S^5$, the superstar of Myers and Tafjord, using the powerful holographic description provided by LLM. The system demonstrates the inherently statistical nature of black holes, with the geometry of Myer and Tafjord emerging only after averaging over an ensemble of geometries. The individual microstate geometries differ in the highly non-trivial topology of a quantum foam at their core, and the entropy can be understood as a partition of $N$ units of flux among 5-cycles, as required by flux quantization. While the system offers confirmation of the most controversial aspect of Mathur and Lunin's recent ``fuzzball'' proposal, we see signs of a discrepancy in interpreting its details.Comment: 21 pages, 4 figures; References adde

A KK-monopole giant graviton in AdS_5 x Y_5

We construct a new giant graviton solution in AdS_5 x Y_5, with Y_5 a quasi-regular Sasaki-Einstein manifold, consisting on a Kaluza-Klein monopole wrapped around the Y_5 and with its Taub-NUT direction in AdS_5. We find that this configuration has minimal energy when put in the centre of AdS_5, where it behaves as a massless particle. When we take Y_5 to be S^5, we provide a microscopical description in terms of multiple gravitational waves expanding into the fuzzy S^5 defined as an S^1 bundle over the fuzzy CP^2. Finally we provide a possible field theory dual interpretation of the construction.Comment: 11 pages, published versio

Rational foundation of GR in terms of statistical mechanic in the AdS/CFT framework

In this article, we work out the microscopic statistical foundation of the supergravity description of the simplest 1/2 BPS sector in the AdS(5)/CFT(4). Then, all the corresponding supergravity observables are related to thermodynamical observables, and General Relativity is understood as a mean-field theory. In particular, and as an example, the Superstar is studied and its thermodynamical properties clarified.Comment: 13 pages, 6 eps figures, latex, some improvements introduced, reference added, typos correcte

"Holey Sheets" - Pfaffians and Subdeterminants as D-brane Operators in Large N Gauge Theories

In the AdS/CFT correspondence, wrapped D3-branes (such as "giant gravitons") on the string theory side of the correspondence have been identified with Pfaffian, determinant and subdeterminant operators on the field theory side. We substantiate this identification by showing that the presence of pairs of such operators in a correlation function of a large N gauge theory naturally leads to a modified 't Hooft expansion including also worldsheets with boundaries. This happens independently of supersymmetry or conformal invariance.Comment: 39 pages, 10 figures, harvma

Half-BPS Giants, Free Fermions and Microstates of Superstars

We consider 1/2-BPS states in AdS/CFT. Using the matrix model description of chiral primaries explicit mappings among configurations of fermions, giant gravitons and the dual-giant gravitons are obtained. These maps lead to a `duality' between the giant and the dual-giant configurations which is the reflection of particle-hole duality of the fermion picture. These dualities give rise to some interesting consequences which we study. We then calculate the degeneracy of 1/2-BPS states both from the CFT and string theory and show that they match. The asymptotic degeneracy grows exponentially with the comformal dimension. We propose that the five-dimensional single charge `superstar' geometry should carry this density of states. An appropriate stretched horizon can be placed in this geometry and the entropy predicted by the CFT and the string theory microstate counting can be reproduced by the Bekenstein-Hawking formula up to a numerical coefficient. Similar M-theory examples are also considered.Comment: 21 pages, v2:typos corrected and references adde

Counting 1/8-BPS Dual-Giants

We count 1/8-BPS states in type IIB string theory on AdS_5 x S^5 background which carry three independent angular momenta on S^5. These states can be counted by considering configurations of multiple dual-giant gravitons up to N in number which share at least four supersymmetries. We map this counting problem to that of counting the energy eigen states of a system of N bosons in a 3-dimensional harmonic oscillator. We also count 1/8-BPS states with two independent non-zero spins in AdS_5 and one non-zero angular momentum on S^5 by considering configurations of arbitrary number of giant gravitons that share at least four supersymmetries.Comment: 19 page

Strings in flat space and pp waves from N=4{\cal N}=4 Super Yang Mills

We explain how the string spectrum in flat space and pp-waves arises from the large $N$ limit, at fixed $g^2_{YM}$, of U(N) ${\cal N} =4$ super Yang Mills. We reproduce the spectrum by summing a subset of the planar Feynman diagrams. We give a heuristic argument for why we can neglect other diagrams. We also discuss some other aspects of pp-waves and we present a matrix model associated to the DLCQ description of the maximally supersymmetric eleven dimensional pp-waves.Comment: 36 pages, 5 figures. v3: minor typos corrected, references adde

Squashed Giants: Bound States of Giant Gravitons

We consider giant gravitons in the maximally supersymmetric type IIB plane-wave, in the presence of a constant NSNS B-field background. We show that in response to the background B-field the giant graviton would take the shape of a deformed three-sphere, the size and shape of which depend on the B-field, and that the giant becomes classically unstable once the B-field is larger than a critical value B_{cr}. In particular, for the B-field which is (anti-)self-dual under the SO(4) isometry of the original giant S^3, the closed string metric is that of a round S^3, while the open string metric is a squashed three-sphere. The squashed giant can be interpreted as a bound state of a spherical three-brane and circular D-strings. We work out the spectrum of geometric fluctuations of the squashed giant and study its stability. We also comment on the gauge theory which lives on the brane (which is generically a noncommutative theory) and a possible dual gauge theory description of the deformed giant.Comment: Latex file, 32 pages, 6 .eps figures; v3: typos correcte