We present a new class of N = 4 $$ \mathcal{N}=4 $$ 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.

United States

Curtis Asplund

Frederik Denef

Eric Dzienkowski

Massive quiver matrix models for massive charged particles in AdS

We continue the analysis of building open strings stretched between giant gravitons from N = 4 $$ \mathcal{N}=4 $$ 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.

Excited states of open strings from N = 4 $$ \mathcal{N}=4 $$ SYM

We construct various exact analytical solutions of the SO(3) BMN matrix model that correspond to rotating fuzzy spheres and rotating fuzzy tori. These are also solutions of Yang Mills theory compactified on a sphere times time and they are also translationally invariant solutions of the  <math><mi>N</mi><mo>=</mo><msup><mn>1</mn><mo>*</mo></msup></math> $$ \mathcal{N}={1}^{*} $$ field theory with a non-trivial chargedensity. The solutions we construct have a ℤ  N  symmetry, where N is the rank of the matrices. After an appropriate ansatz, we reduce the problem to solving a set of polynomial equations in 2N real variables. These equations have a discrete set of solutions for each value of the angular momentum. We study the phase structure of the solutions for various values of N . Also the continuum limit where N → ∞, where the problem reduces to finding periodic solutions of a set of coupled differential equations. We also study the topology change transition from the sphere to the torus.

United Kingdom

David Berenstein

Robin Lashof-Regas

Spinning the fuzzy sphere

We study a one parameter family of supersymmetric marginal deformations of N = 4 $$ \mathcal{N}=4 $$ SYM with U(1) 3 symmetry, known as β -deformations, to understand their dual AdS × X geometry, where X is a large classical geometry in the g YM 2 N  → ∞ 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 → ∞ 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 β are very important. When exp( iβ ) is a root of unity, the space X is an orbifold. When exp( iβ ) close to a root of unity in a double scaling limit sense, X corresponds to a finite deformation of the orbifold. Finally, if β is irrational, sporadic light states can be present.