The non-zero energy of 2+1 Minkowski space

We compute the energy of 2+1 Minkowski space from a covariant action principle. Using Ashtekar and Varadarajan's characterization of 2+1 asymptotic flatness, we first show that the 2+1 Einstein-Hilbert action with Gibbons-Hawking boundary term is both finite on-shell (apart from past and future boundary terms) and stationary about solutions under arbitrary smooth asymptotically flat variations of the metric. Thus, this action provides a valid variational principle and no further boundary terms are required. We then obtain the gravitational Hamiltonian by direct computation from this action. The result agrees with the Hamiltonian of Ashtekar and Varadarajan up to an overall addititve constant. This constant is such that 2+1 Minkowski space is assigned the energy E = -1/4G, while the upper bound on the energy is set to zero. Any variational principle with a boundary term built only from the extrinsic and intrinsic curvatures of the boundary is shown to lead to the same result. Interestingly, our result is not the flat-space limit of the corresponding energy -1/8G of 2+1 anti-de Sitter space.Comment: 16 pages, minor change

Velocity Statistics in Holographic Fluids: Magnetized Quark-Gluon Plasma and Superfluid Flow

We study the velocity statistics distribution of an external heavy particle in holographic fluids. We argue that when the dual supergravity background has a finite temperature horizon the velocity statistics goes generically as $1/v$, compatible with the jet-quenching intuition from the quark-gluon plasma. A careful analysis of the behavior of the classical string whose apparent worldsheet horizon deviates from the background horizon reveals that other regimes are possible. We numerically discuss two cases: the magnetized quark-gluon plasma and a model of superfluid flow. We explore a range of parameters in these top-down supergravity solutions including, respectively, the magnetic field and the superfluid velocity. We determine that the velocity statistics goes largely as $1/v$, however, as we leave the non-relativistic regime we observe some deviations.Comment: 32 pages, 12 figures, references added and minor correction

Chaos, Diffusivity, and Spreading of Entanglement in Magnetic Branes, and the Strengthening of the Internal Interaction

We use holographic methods to study several chaotic properties of a super Yang-Mills theory at temperature $T$ in the presence of a background magnetic field of constant strength $\mathcal{B}$. The field theory we work on has a renormalization flow between a fixed point in the ultraviolet and another in the infrared, occurring in such a way that the energy at which the crossover takes place is a monotonically increasing function of the dimensionless ratio $\mathcal{B}/T^2$. By considering shock waves in the bulk of the dual gravitational theory, and varying $\mathcal{B}/T^2$, we study how several chaos-related properties of the system behave while the theory they live in follows the renormalization flow. In particular, we show that the entanglement and butterfly velocities generically increase in the infrared theory, violating the previously suggested upper bounds but never surpassing the speed of light. We also investigate the recent proposal relating the butterfly velocity with diffusion coefficients. We find that electric diffusion constants respect the lower bound proposed by Blake. All our results seam to consistently indicate that the global effect of the magnetic field is to strengthen the internal interaction of the system.Comment: 49 pages, 17 figure

Complexity of Magnetization and Magnetic Simplification

We use the Complexity=Volume (CV) prescription to study the effect of a magnetic field on the complexity of formation for states in the gauge theories dual to two different gravitational models. In one of these theories the complexity increases with the intensity of the magnetic field, while in the other a more interesting behavior is discovered, resulting in a phenomenon that we term magnetic simplification. The relevant difference between the two theories is that the content of the second includes a scalar operator with a non-vanishing vacuum expectation value. This leads us to conclude that the direct impact of the magnetic field is to increase the complexity of formation of a state, but it can indirectly lower it by diminishing the complexity associated to additional degrees of freedom when these do not vanish across the space. We additionally compare the results obtained working in the full ten dimensional backgrounds and in their effective five dimensional truncations, exhibiting that the question is still current about which surface, whether the uplift of the 5D extremal hypersurface or the extremal surface in 10D, should be used in the CV prescription.Comment: 17 pages, 15 figure