Strings on conifolds from strong coupling dynamics: quantitative results

Three quantitative features of string theory on AdS_5 x X_5, for any (quasi)regular Sasaki-Einstein X_5, are recovered exactly from an expansion of field theory at strong coupling around configurations in the moduli space of vacua. These configurations can be thought of as a generalized matrix model of (local) commuting matrices. First, we reproduce the spectrum of scalar Kaluza-Klein modes on X_5. Secondly, we recover the precise spectrum of BMN string states, including a nontrivial dependence on the volume of X_5. Finally, we show how the radial direction in global AdS_5 emerges universally in these theories by exhibiting states dual to AdS giant gravitons.Comment: 1+28 pages. 1 figur

A study of open strings ending on giant gravitons, spin chains and integrability

We systematically study the spectrum of open strings attached to half BPS giant gravitons in the N=4 SYM AdS/CFT setup. We find that some null trajectories along the giant graviton are actually null geodesics of AdS_5x S^5, so that we can study the problem in a plane wave limit setup. We also find the description of these states at weak 't Hooft coupling in the dual CFT. We show how the dual description is given by an open spin chain with variable number of sites. We analyze this system in detail and find numerical evidence for integrability. We also discover an interesting instability of long open strings in Ramond-Ramond backgrounds that is characterized by having a continuum spectrum of the string, which is separated from the ground state by a gap. This instability arises from accelerating the D-brane on which the strings end via the Ramond-Ramond field. From the integrable spin chain point of view, this instability prevents us from formulating the integrable structure in terms of a Bethe Ansatz construction.Comment: 38 pages+appendices, 9 figures. Uses JHEP3. v2: added reference

A Monte-Carlo study of the AdS/CFT correspondence: an exploration of quantum gravity effects

In this paper we study the AdS/CFT correspondence for N=4 SYM with gauge group U(N), compactified on S^3 in four dimensions using Monte-Carlo techniques. The simulation is based on a particular reduction of degrees of freedom to commuting matrices of constant fields, and in particular, we can write the wave functions of these degrees of freedom exactly. The square of the wave function is equivalent to a probability density for a Boltzman gas of interacting particles in six dimensions. From the simulation we can extract the density particle distribution for each wave function, and this distribution can be interpreted as a special geometric locus in the gravitational dual. Studying the wave functions associated to half-BPS giant gravitons, we are able to show that the matrix model can measure the Planck scale directly. We also show that the output of our simulation seems to match various theoretical expectations in the large N limit and that it captures 1/N effects as statistical fluctuations of the Boltzman gas with the expected scaling. Our results suggest that this is a very promising approach to explore quantum corrections and effects in gravitational physics on AdS spaces.Comment: 40 pages, 7 figures, uses JHEP. v2: references adde

On the shape of a D-brane bound state and its topology change

As is well known, coordinates of D-branes are described by NxN matrices. From generic non-commuting matrices, it is difficult to extract physics, for example, the shape of the distribution of positions of D-branes. To overcome this problem, we generalize and elaborate on a simple prescription, first introduced by Hotta, Nishimura and Tsuchiya, which determines the most appropriate gauge to make the separation between diagonal components (D-brane positions) and off-diagonal components. This prescription makes it possible to extract the distribution of D-branes directly from matrices. We verify the power of it by applying it to Monte-Carlo simulations for various lower dimensional Yang-Mills matrix models. In particular, we detect the topology change of the D-brane bound state for a phase transition of a matrix model; the existence of this phase transition is expected from the gauge/gravity duality, and the pattern of the topology change is strikingly similar to the counterpart in the gravity side, the black hole/black string transition. We also propose a criterion, based on the behavior of the off-diagonal components, which determines when our prescription gives a sensible definition of D-brane positions. We provide numerical evidence that our criterion is satisfied for the typical distance between D-branes. For a supersymmetric model, positions of D-branes can be defined even at a shorter distance scale. The behavior of off-diagonal elements found in this analysis gives some support for previous studies of D-brane bound states.Comment: 29 pages, 16 figure

BPS Condensates, Matrix Models and Emergent String Theory

A prescription is given for computing anomalous dimensions of single trace operators in SYM at strong coupling and large $N$ using a reduced model of matrix quantum mechanics. The method involves treating some parts of the operators as "BPS condensates" which, in certain limit, have a dual description as null geodesics on the $S^5$. In the gauge theory, the condensate is similar to a representative of the chiral ring and it is described by a background of commuting matrices. Excitations around these condensates correspond to excitations around this background and take the form of "string bits" which are dual to the "giant magnons" of Hofman and Maldacena. In fact, the matrix model approach gives a {\it quantum} description of these string configurations and explains why the infinite momentum limit suppresses the quantum effects. This method allows, not only to derive part of the classical sigma model Hamiltonian of the dual string (in the infinite momentum limit), but also its quantum canonical structure. Therefore, it provides an alternative method of testing the AdS/CFT correspondence without the need of integrability.Comment: 36 pages, 1 figure, 2 appendices, v2: references adde

Aspects of ABJM orbifolds with discrete torsion

We analyze orbifolds with discrete torsion of the ABJM theory by a finite subgroup $\Gamma$ of $SU(2)\times SU(2)$ . Discrete torsion is implemented by twisting the crossed product algebra resulting after orbifolding. It is shown that, in general, the order $m$ of the cocycle we chose to twist the algebra by enters in a non trivial way in the moduli space. To be precise, the M-theory fiber is multiplied by a factor of $m$ in addition to the other effects that were found before in the literature. Therefore we got a $\mathbb{Z}_{\frac{k|\Gamma|}{m}}$ action on the fiber. We present a general analysis on how this quotient arises along with a detailed analysis of the cases where $\Gamma$ is abelian

NC Calabi-Yau Manifolds in Toric Varieties with NC Torus fibration

Using the algebraic geometry method of Berenstein and Leigh (BL), hep-th/0009209 and hep-th/0105229), and considering singular toric varieties ${\cal V}_{d+1}$ with NC irrational torus fibration, we construct NC extensions ${\cal M}_{d}^{(nc)}$ of complex d dimension Calabi-Yau (CY) manifolds embedded in ${\cal V}_{d+1}^{(nc)}$. We give realizations of the NC $\mathbf{C}^{\ast r}$ toric group, derive the constraint eqs for NC Calabi-Yau (NCCY) manifolds ${\cal M}^{nc}_d$ embedded in ${\cal V}_{d+1}^{nc}$ and work out solutions for their generators. We study fractional $D$ branes at singularities and show that, due to the complete reducibility property of $\mathbf{C}^{\ast r}$ group representations, there is an infinite number of non compact fractional branes at fixed points of the NC toric group.Comment: 12 pages, LaTex, no figur

A renormalization procedure for tensor models and scalar-tensor theories of gravity

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian configurations are parameterized by a scalar and a symmetric two-tensor, it is argued that, in general situations, the infrared dynamics of the tensor models should be described by scalar-tensor theories of gravity.Comment: 20 pages, 3 figures, references added, minor correction

Aspects of emergent geometry in the AdS/CFT context

We study aspects of emergent geometry for the case of orbifold superconformal field theories in four dimensions, where the orbifolds are abelian within the AdS/CFT proposal. In particular, we show that the realization of emergent geometry starting from the N=4 SYM theory in terms of a gas of particles in the moduli space of vacua of a single D3 brane in flat space gets generalized to a gas of particles on the moduli space of the corresponding orbifold conformal field theory (a gas of D3 branes on the orbifold space). Our main purpose is to show that this can be analyzed using the same techniques as in the N=4 SYM case by using the method of images, including the measure effects associated to the volume of the gauge orbit of the configurations. This measure effect gives an effective repulsion between the particles that makes them condense into a non-trivial vacuum configuration, and it is exactly these configurations that lead to the geometry of X in the AdS x X dual field theoryComment: 24 page