On gravitational description of Wilson lines

We study solutions of Type IIB supergravity, which describe the geometries dual to supersymmetric Wilson lines in N=4 super-Yang-Mills. We show that the solutions are uniquely specified by one function which satisfies a Laplace equation in two dimensions. We show that if this function obeys a certain Dirichlet boundary condition, the corresponding geometry is regular, and we find a simple interpretation of this boundary condition in terms of D3 and D5 branes which are dissolved in the geometry. While all our metrics have AdS_5 x S^5 asymptotics, they generically have nontrivial topologies, which can be uniquely specified by a set of non-contractible three- and five-spheres.Comment: 46 page

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

BPS Electromagnetic Waves on Giant Gravitons

We find new 1/8-BPS giant graviton solutions in $AdS_5 \times S^5$, carrying three angular momenta along $S^5$, and investigate their properties. Especially, we show that nonzero worldvolume gauge fields are admitted preserving supersymmetry. These gauge field modes can be viewed as electromagnetic waves along the compact D3 brane, whose Poynting vector contributes to the BPS angular momenta. We also analyze the (nearly-)spherical giant gravitons with worldvolume gauge fields in detail. Expressing the $S^3$ in Hopf fibration ($S^1$ fibred over $S^2$), the wave propagates along the $S^1$ fiber.Comment: 25 pages, no figures, v2: references adde

BIons in topological string theory

When many fundamental strings are stacked together, they puff up into D-branes. BIons and giant gravitons are the examples of such D-brane configurations that arise from coincident strings. We propose and demonstrate analogous transitions in topological string theory. Such transitions can also be understood in terms of the Fourier transform of D-brane amplitudes.Comment: 21 pages; v.2 references added; v.3 reference added; v.4 minor corrections; v.5 substantial rewritin

Exact operator bosonization of finite number of fermions in one space dimension

We derive an exact operator bosonization of a finite number of fermions in one space dimension. The fermions can be interacting or noninteracting and can have an arbitrary hamiltonian, as long as there is a countable basis of states in the Hilbert space. In the bosonized theory the finiteness of the number of fermions appears as an ultraviolet cut-off. We discuss implications of this for the bosonized theory. We also discuss applications of our bosonization to one-dimensional fermion systems dual to (sectors of) string theory such as LLM geometries and c=1 matrix model.Comment: 47 pages, 1 figure; (v2) typos correcte

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

Gravity duals of half-BPS Wilson loops

We explicitly construct the fully back-reacted half-BPS solutions in Type IIB supergravity which are dual to Wilson loops with 16 supersymmetries in $\mathcal{N}=4$ super Yang-Mills. In a first part, we use the methods of a companion paper to derive the exact general solution of the half-BPS equations on the space $AdS_2 \times S^2 \times S^4 \times \Sigma$, with isometry group $SO(2,1)\times SO(3) \times SO(5)$ in terms of two locally harmonic functions on a Riemann surface $\Sigma$ with boundary. These solutions, generally, have varying dilaton and axion, and non-vanishing 3-form fluxes. In a second part, we impose regularity and topology conditions. These non-singular solutions may be parametrized by a genus $g \geq 0$ hyperelliptic surface $\Sigma$, all of whose branch points lie on the real line. Each genus $g$ solution has only a single asymptotic $AdS_5 \times S^5$ region, but exhibits $g$ homology 3-spheres, and an extra $g$ homology 5-spheres, carrying respectively RR 3-form and RR 5-form charges. For genus 0, we recover $AdS_5 \times S^5$ with 3 free parameters, while for genus $g \geq 1$, the solution has $2g+5$ free parameters. The genus 1 case is studied in detail. Numerical analysis is used to show that the solutions are regular throughout the $g=1$ parameter space. Collapse of a branch cut on $\Sigma$ subtending either a homology 3-sphere or a homology 5-sphere is non-singular and yields the genus $g-1$ solution. This behavior is precisely expected of a proper dual to a Wilson loop in gauge theory.Comment: 62 pages, LaTeX, 6 figures, v2: minor change

Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries

We study a relation between droplet configurations in the bubbling AdS geometries and a complex matrix model that describes the dynamics of a class of chiral primary operators in dual N=4 super Yang Mills (SYM). We show rigorously that a singlet holomorphic sector of the complex matrix model is equivalent to a holomorphic part of two-dimensional free fermions, and establish an exact correspondence between the singlet holomorphic sector of the complex matrix model and one-dimensional free fermions. Based on this correspondence, we find a relation of the singlet holomorphic operators of the complex matrix model to the Wigner phase space distribution. By using this relation and the AdS/CFT duality, we give a further evidence that the droplets in the bubbling AdS geometries are identified with those in the phase space of the one-dimensional fermions. We also show that the above correspondence actually maps the operators of N=4 SYM corresponding to the (dual) giant gravitons to the droplet configurations proposed in the literature.Comment: 27 pages, 6 figures, some clarification, typos corrected, published versio

From Gravitons to Giants

We discuss exact quantization of gravitational fluctuations in the half-BPS sector around AdS$_5 \times$S$^5$ background, using the dual super Yang-Mills theory. For this purpose we employ the recently developed techniques for exact bosonization of a finite number $N$ of fermions in terms of $N$ bosonic oscillators. An exact computation of the three-point correlation function of gravitons for finite $N$ shows that they become strongly coupled at sufficiently high energies, with an interaction that grows exponentially in $N$. We show that even at such high energies a description of the bulk physics in terms of weakly interacting particles can be constructed. The single particle states providing such a description are created by our bosonic oscillators or equivalently these are the multi-graviton states corresponding to the so-called Schur polynomials. Both represent single giant graviton states in the bulk. Multi-particle states corresponding to multi-giant gravitons are, however, different, since interactions among our bosons vanish identically, while the Schur polynomials are weakly interacting at high enough energies.Comment: v2-references added, minor changes and typos corrected; 24 pages, latex, 3 epsf figure

1/16-BPS Black Holes and Giant Gravitons in the AdS_5 X S^5 Space

We explore 1/16-BPS objects of type IIB string theory in AdS_5 * S^5. First, we consider supersymmetric AdS_5 black holes, which should be 1/16-BPS and have a characteristic that not all physical charges are independent. We point out that the Bekenstein-Hawking entropy of these black holes admits a remarkably simple expression in terms of (dependent) physical charges, which suggests its microscopic origin via certain Cardy or Hardy-Ramanujan formula. We also note that there is an upper bound for the angular momenta given by the electric charges. Second, we construct a class of 1/16-BPS giant graviton solutions in AdS_5 * S^5 and explore their properties. The solutions are given by the intersections of AdS_5 * S^5 and complex 3 dimensional holomorphic hyperspaces in C^{1+5}, the latter being the zero loci of three holomorphic functions which are homogeneous with suitable weights on coordinates. We investigate examples of giant gravitons, including their degenerations to tensionless strings.Comment: 25 pages, no figures, v2: references added, comments added in the conclusio