Interacting Giant Gravitons from Spin Matrix Theory

Using the non-abelian DBI action we find an effective matrix model that describes the dynamics of weakly interacting giant gravitons wrapped on three-spheres in the AdS part of AdS_5 x S^5 at high energies with two angular momenta on the S^5. In parallel we consider the limit of \CN=4 super Yang-Mills theory near a certain unitarity bound where it reduces to the quantum mechanical theory called SU(2) Spin Matrix Theory. We show that the exact same matrix model that describes the giant gravitons on the string theory side also provides the effective description in the strong coupling and large energy limit of the Spin Matrix Theory. Thus, we are able to match non-supersymmetric dynamics of D-branes on AdS_5 x S^5 to a finite-N regime in \CN=4 super Yang-Mills theory near a unitarity bound.Comment: 7 page

Supergravity and Space-Time Non-Commutative Open String Theory

We study the non-critical space-time non-commutative open string (NCOS) theory using a dual supergravity description in terms of a certain near-horizon limit of the F1-Dp bound state. We find the thermodynamics of NCOS theory from supergravity. The thermodynamics is equivalent to Yang-Mills theory on a commutative space-time. We argue that this fact does not have to be in contradiction with the expected Hagedorn behaviour of NCOS theory. To support this we consider string corrections to the thermodynamics. We also discuss the relation to Little String Theory in 6 dimensions.Comment: 19 pages, latex, v2,v3: comments and details added, refs. added, minor corrections, page format changed, v4: refs. adde

The Hagedorn temperature of AdS5/CFT4 via integrability

We establish a framework for calculating the Hagedorn temperature of AdS5/CFT4 via integrability. Concretely, we derive the thermodynamic Bethe ansatz equations that yield the Hagedorn temperature of planar N=4 super Yang-Mills theory at any value of the 't Hooft coupling. We solve these equations perturbatively at weak coupling via the associated Y-system, confirming the known results at tree-level and one-loop order as well as deriving the previously unknown two-loop Hagedorn temperature. Finally, we comment on solving the equations at finite coupling.Comment: 6 pages; v3: references and further clarification added, matches journal versio

Nonrelativistic Corners of N=4{\cal N} = 4 Supersymmetric Yang--Mills Theory

We show that ${\cal N} = 4$ supersymmetric-Yang-Mills (SYM) theory on $\mathbb{R} \times S^3$ with gauge group $\text{SU}(N)$ is described in a near-BPS limit by a simple lower-dimensional nonrelativistic field theory with $\text{SU}(1,1) \times \text{U}(1)$ invariant interactions. In this limit, a single complex adjoint scalar field survives, and part of its interaction is obtained by exactly integrating out the gauge boson of the SYM theory. Taking into account normal ordering, the interactions match the one-loop dilatation operator of the $\text{SU}(1,1)$ sector, establishing the consistency of the limit at the quantum level. We discover a tantalizing field-theoretic structure, corresponding to a $(1+1)$-dimensional complex chiral boson on a circle coupled to a nondynamical gauge field, both in the adjoint representation of $\text{SU}(N)$. The successful construction of a lower-dimensional nonrelativistic field theory in the $\text{SU}(1,1)$ near-BPS limit provides a proof of concept for other BPS bounds. These are expected to lead to richer field theories in nonrelativistic corners of ${\cal N} = 4$ SYM that include fermions, gauge fields and supersymmetry and can provide a novel path towards understanding strongly coupled finite-$N$ dynamics of gauge theories.Comment: 6 pages, 1 figure; v2: minor clarifications added, matches journal versio

The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve

Building on the recently established connection between the Hagedorn temperature and integrability [Phys.Rev.Lett. 120 (2018) no.7, 071605], we show how the Quantum Spectral Curve formalism can be used to calculate the Hagedorn temperature of AdS5/CFT4 for any value of the 't Hooft coupling. We solve this finite system of finite-difference equations perturbatively at weak coupling and numerically at finite coupling. We confirm previous results at weak coupling and obtain the previously unknown three-loop Hagedorn temperature. Our finite-coupling results interpolate between weak and strong coupling and allow us to extract the first perturbative order at strong coupling. Our results indicate that the Hagedorn temperature for large 't Hooft coupling approaches that of type IIB string theory in ten-dimensional Minkowski space.Comment: 7 page

Constraints on the effective fluid theory of stationary branes

We develop further the effective fluid theory of stationary branes. This formalism applies to stationary blackfolds as well as to other equilibrium brane systems at finite temperature. The effective theory is described by a Lagrangian containing the information about the elastic dynamics of the brane embedding as well as the hydrodynamics of the effective fluid living on the brane. The Lagrangian is corrected order-by-order in a derivative expansion, where we take into account the dipole moment of the brane which encompasses finite-thickness corrections, including transverse spin. We describe how to extract the thermodynamics from the Lagrangian and we obtain constraints on the higher-derivative terms with one and two derivatives. These constraints follow by comparing the brane thermodynamics with the conserved currents associated with background Killing vector fields. In particular, we fix uniquely the one- and two-derivative terms describing the coupling of the transverse spin to the background space-time. Finally, we apply our formalism to two blackfold examples, the black tori and charged black rings and compare the latter to a numerically generated solution.Comment: v2: 26pp, 3 figures, minor clarifications, presentation improved, to be published in JHE

Supersymmetric Godel Universes in String Theory

Supersymmetric backgrounds in string and M-theory of the Godel Universe type are studied. We find several new Godel Universes that preserve up to 20 supersymmetries. In particular, we obtain an interesting Godel Universe in M-theory with 18 supersymmetries which does not seem to be dual to a pp-wave. We show that not only T-duality but also the type-IIA/M-theory S-duality can give supersymmetric Godel Universes from pp-waves. We find solutions that can interpolate between Godel Universes and pp-waves. We also compute the string spectrum on two type IIA Godel Universes. Furthermore, we obtain the spectrum of D-branes on a Godel Universe and find the supergravity solution for a D4-brane on a Godel Universe.Comment: latex, 36 pages, 1 figure; v2: typos corrected, refs. added, v3: typos correcte

Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence

We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U(N). We show that SMT describes N=4 super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of N=4 SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the infinite g limit of SMT can be mapped to the supersymmetric sector of string theory on AdS_5 x S^5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite-N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g=0 it is a theory of N^2+1 harmonic oscillators while for large g it becomes 2N harmonic oscillators.Comment: 36 pages, 3 figures. v2: Refs. adde

Black Holes and Biophysical (Mem)-branes

We argue that the effective theory describing the long-wavelength dynamics of black branes is the same effective theory that describes the dynamics of biophysical membranes. We improve the phase structure of higher-dimensional black rings by considering finite thickness corrections in this effective theory, showing a striking agreement between our analytical results and recent numerical constructions while simultaneously drawing a parallel between gravity and the effective theory of biophysical membranes.Comment: v2: 5pp, 3 figures, improved introduction, to be published in PR