Evaporating Firewalls

In this note, we begin by reviewing an argument (independent from 1304.6483) that the large AdS black holes dual to typical high-energy pure states of a single holographic CFT must have some structure at the horizon (i.e. a firewall/fuzzball). By weakly coupling the CFT to an auxiliary system, such a black hole can be made to evaporate. In a case where the auxiliary system is a second identical CFT, it is possible (for specific initial states) that the system evolves to precisely the thermofield double state as the original black hole evaporates. In this case, the dual geometry should include the "late-time" part of the eternal AdS black hole spacetime which includes smooth spacetime behind the horizon of the original black hole. Thus, we can say that the firewall evaporates. This provides a specific realization of the recent ideas of Maldacena and Susskind that the existence of smooth spacetime behind the horizon of an evaporating black hole can be enabled by maximal entanglement with a Hawking radiation system (in our case the second CFT) rather than prevented by it. For initial states which are not finely-tuned to produce the thermofield double state, the question of whether a late-time infalling observer experiences a firewall translates to a question about the gravity dual of a typical high-energy state of a two-CFT system.Comment: 18 pages, LaTe

Canonical Energy is Quantum Fisher Information

In quantum information theory, Fisher Information is a natural metric on the space of perturbations to a density matrix, defined by calculating the relative entropy with the unperturbed state at quadratic order in perturbations. In gravitational physics, Canonical Energy defines a natural metric on the space of perturbations to spacetimes with a Killing horizon. In this paper, we show that the Fisher information metric for perturbations to the vacuum density matrix of a ball-shaped region B in a holographic CFT is dual to the canonical energy metric for perturbations to a corresponding Rindler wedge R_B of Anti-de-Sitter space. Positivity of relative entropy at second order implies that the Fisher information metric is positive definite. Thus, for physical perturbations to anti-de-Sitter spacetime, the canonical energy associated to any Rindler wedge must be positive. This second-order constraint on the metric extends the first order result from relative entropy positivity that physical perturbations must satisfy the linearized Einstein's equations.Comment: 26 pages, 1 figur

Supergravity currents and linearized interactions for Matrix Theory configurations with fermionic backgrounds

The leading terms in the long-range interaction potential between an arbitrary pair of matrix theory objects are calculated at one-loop order. This result generalizes previous calculations by including arbitrary fermionic background field configurations. The interaction potential at orders 1/r^7 and 1/r^8 is shown to correspond precisely with the leading terms expected from linearized supergravity interactions between arbitrary objects in M-theory. General expressions for the stress tensor, membrane current and 5-brane current of an arbitrary matrix configuration are derived, including fermionic contributions. Supergravity effects which are correctly reproduced include membrane/5-brane interactions, 0-brane/6-brane interactions, supercurrent/supercurrent interactions and the spin contributions to moments of the supergravity currents. The matrix theory description of the supergravity stress tensor, membrane current and 5-brane current are used to propose an explicit formulation of matrix theory in an arbitrary background metric and 3-form field.Comment: 71 pages, LaTeX; v2: added references, fixed minor typos v3: minor errors fixed, comments adde

A note on dilaton absorption and near-infrared D3 brane holography

We consider the first subleading terms in the low-energy cross section for the absorption of dilaton partial waves by D3-branes. We demonstrate that these corrections, computed previously via supergravity, can be reproduced exactly in a worldvolume calculation using a deformation of N=4 SYM theory by a dimension eight chiral operator. The calculation does not depend on how the theory is regularized. This result provides another hint that holographic duality between the D3-brane worldvolume theory and the corresponding supergravity solution may be valid beyond the near horizon limit.Comment: 13 pages, LaTe

Multiple D0-branes in Weakly Curved Backgrounds

We investigate further our recent proposal for the form of the matrix theory action in weak background fields. Using Seiberg's scaling argument we relate the matrix theory action to a low-energy system of many D0-branes in an arbitrary but weak NS-NS and R-R background. The resulting multiple D0-brane action agrees with the known Born-Infeld action in the case of a single brane and gives an explicit formulation of many additional terms which appear in the multiple brane action. The linear coupling to an arbitrary background metric satisfies the nontrivial consistency condition suggested by Douglas that the masses of off-diagonal fields are given by the geodesic distance between the corresponding pair of D0-branes. This agreement arises from combinatorial factors which depend upon the symmetrized trace ordering prescription found earlier for higher moments of the matrix theory stress-energy tensor. We study the effect of a weak background metric on two graviton interactions and find that our formalism agrees with the results expected from supergravity. The results presented here can be T-dualized to give explicit formulae for the operators in any D-brane world-volume theory which couple linearly to bulk gravitational fields and their derivatives.Comment: 34 pages, LaTeX; v2: comments and reference added, minor correction

Dynamic Dependency Pairs for Algebraic Functional Systems

We extend the higher-order termination method of dynamic dependency pairs to Algebraic Functional Systems (AFSs). In this setting, simply typed lambda-terms with algebraic reduction and separate {\beta}-steps are considered. For left-linear AFSs, the method is shown to be complete. For so-called local AFSs we define a variation of usable rules and an extension of argument filterings. All these techniques have been implemented in the higher-order termination tool WANDA