Excited States of Open Strings From N=4\mathcal{N}=4 SYM

We continue the analysis of building open strings stretched between giant gravitons from $\mathcal{N}=4$ SYM by going to second order in perturbation theory using the three-loop dilatation generator from the field theory. In the process we build a Fock-like space of states using Cuntz oscillators which can be used to access the excited open string states. We find a remarkable cancellation among the excited states that shows the ground state energy is consistent with a fully relativistic dispersion relation.Comment: 33 pages. Typos fixe

Giant gravitons and the emergence of geometric limits in β\beta-deformations of N=4{\cal N}=4 SYM

We study a one parameter family of supersymmetric marginal deformations of ${\cal N}=4$ SYM with $U(1)^3$ symmetry, known as $\beta$-deformations, to understand their dual $AdS\times X$ geometry, where $X$ is a large classical geometry in the $g_{YM}^2N\to \infty$ limit. We argue that we can determine whether or not $X$ is geometric by studying the spectrum of open strings between giant gravitons states, as represented by operators in the field theory, as we take $N\to\infty$ in certain double scaling limits. We study the conditions under which these open strings can give rise to a large number of states with energy far below the string scale. The number-theoretic properties of $\beta$ are very important. When $\exp(i\beta)$ is a root of unity, the space $X$ is an orbifold. When $\exp(i\beta)$ close to a root of unity in a double scaling limit sense, $X$ corresponds to a finite deformation of the orbifold. Finally, if $\beta$ is irrational, sporadic light states can be present.Comment: 1 Tabl

Massive quiver matrix models for massive charged particles in AdS

We present a new class of ${\cal N}=4$ supersymmetric quiver matrix models and argue that it describes the stringy low-energy dynamics of internally wrapped D-branes in four-dimensional anti-de Sitter (AdS) flux compactifications. The Lagrangians of these models differ from previously studied quiver matrix models by the presence of mass terms, associated with the AdS gravitational potential, as well as additional terms dictated by supersymmetry. These give rise to dynamical phenomena typically associated with the presence of fluxes, such as fuzzy membranes, internal cyclotron motion and the appearance of confining strings. We also show how these models can be obtained by dimensional reduction of four-dimensional supersymmetric quiver gauge theories on a three-sphere.Comment: 43 pages + appendices, 4 figure

Aspects of Emergent Geometry, Strings, and Branes in Gauge / Gravity Duality

We explore the emergence of locality and geometry in string theories from the perspective of gauge theories using gauge / gravity duality.First, we explicitly construct open strings stretched between giant gravitons in N=4 SYM. We find that these strings satisfy a relativistic dispersion relation up to three-loop order and conjecture that this should hold to all loop orders. We find the explicit dual solution to the string sigma model and find exact agreement with the geometric nature of the SYM operator and dispersion relation. Using these open strings as probes, we explore the local field theory on the worldvolume of the giant gravitons.Second, we use classical configurations in holographic matrix models to understand the emergence of geometry from matrix coordinates. We construct an effective Hamiltonian for a probe brane that observes the geometry in a background matrix configuration from which we can construct membranes embedded in three dimensional space. Adding angular momentum to these configurations we are able to observe continuous topology changes. We also study the classical evolution of holographic matrix models to generate a microcanonical ensemble of configurations and study their thermal and chaotic behavior. We argue that these thermal configurations are dual to black holes

Matrix embeddings on flat R3R^3 and the geometry of membranes

We show that given three hermitian matrices, what one could call a fuzzy representation of a membrane, there is a well defined procedure to define a set of oriented Riemann surfaces embedded in $R^3$ using an index function defined for points in $R^3$ that is constructed from the three matrices and the point. The set of surfaces is covariant under rotations, dilatations and translation operations on $R^3$, it is additive on direct sums and the orientation of the surfaces is reversed by complex conjugation of the matrices. The index we build is closely related to the Hanany-Witten effect. We also show that the surfaces carry information of a line bundle with connection on them. We discuss applications of these ideas to the study of holographic matrix models and black hole dynamics.Comment: 41 pages, 3 figures, uses revtex4-1. v2: references added, corrected an error in attribution of idea

Perturbative renormalization of lattice N=4 super Yang-Mills theory

We consider N=4 super Yang-Mills theory on a four-dimensional lattice. The lattice formulation under consideration retains one exact supersymmetry at non-zero lattice spacing. We show that this feature combined with gauge invariance and the large point group symmetry of the lattice theory ensures that the only counterterms that appear at any order in perturbation theory correspond to renormalizations of existing terms in the bare lattice action. In particular we find that no mass terms are generated at any finite order of perturbation theory. We calculate these renormalizations by examining the fermion and auxiliary boson self energies at one loop and find that they all exhibit a common logarithmic divergence which can be absorbed by a single wavefunction renormalization. This finding implies that at one loop only a fine tuning of the finite parts is required to regain full supersymmetry in the continuum limit.Comment: v2. Minor corrections, references adde