Linearized supergravity from Matrix theory

We show that the linearized supergravity potential between two objects arising from the exchange of quanta with zero longitudinal momentum is reproduced to all orders in 1/r by terms in the one-loop Matrix theory potential. The essential ingredient in the proof is the identification of the Matrix theory quantities corresponding to moments of the stress tensor and membrane current. We also point out that finite-N Matrix theory violates the equivalence principle.Comment: 13 pages, LaTex, v2: additional comments mostly in section

Probing black holes in non-perturbative gauge theory

We use a 0-brane to probe a ten-dimensional near-extremal black hole with N units of 0-brane charge. We work directly in the dual strongly-coupled quantum mechanics, using mean-field methods to describe the black hole background non-perturbatively. We obtain the distribution of W boson masses, and find a clear separation between light and heavy degrees of freedom. To localize the probe we introduce a resolving time and integrate out the heavy modes. After a non-trivial change of coordinates, the effective potential for the probe agrees with supergravity expectations. We compute the entropy of the probe, and find that the stretched horizon of the black hole arises dynamically in the quantum mechanics, as thermal restoration of unbroken U(N+1) gauge symmetry. Our analysis of the quantum mechanics predicts a correct relation between the horizon radius and entropy of a black hole.Comment: 30 pages, LaTeX, 8 eps figures. v2: references added. v3: more reference

Emergence of the fuzzy horizon through gravitational collapse

For a large enough Schwarzschild black hole, the horizon is a region of space where gravitational forces are weak; yet it is also a region leading to numerous puzzles connected to stringy physics. In this work, we analyze the process of gravitational collapse and black hole formation in the context of light-cone M theory. We find that, as a shell of matter contracts and is about to reveal a black hole horizon, it undergoes a thermodynamic phase transition. This involves the binding of D0 branes into D2's, and the new phase leads to large membranes of the size of the horizon. These in turn can sustain their large size through back-reaction and the dielectric Myers effect - realizing the fuzzball proposal of Mathur and the Matrix black hole of M(atrix) theory. The physics responsible for this phenomenon lies in strongly coupled 2+1 dimensional non-commutative dynamics. The phenomenon has a universal character and appears generic.Comment: 24 pages, 4 figures; v2: minor clarifications, citations adde

Holographic Construction of Excited CFT States

We present a systematic construction of bulk solutions that are dual to CFT excited states. The bulk solution is constructed perturbatively in bulk fields. The linearised solution is universal and depends only on the conformal dimension of the primary operator that is associated with the state via the operator-state correspondence, while higher order terms depend on detailed properties of the operator, such as its OPE with itself and generally involve many bulk fields. We illustrate the discussion with the holographic construction of the universal part of the solution for states of two dimensional CFTs, either on $R \times S^1$ or on $R^{1,1}$. We compute the 1-point function both in the CFT and in the bulk, finding exact agreement. We comment on the relation with other reconstruction approaches.Comment: 26 pages, 4 figures, v2: comments adde

Effects of precipitation uncertainty on discharge calculations for main river basins

This study quantifies the uncertainty in discharge calculations caused by uncertainty in precipitation input for 294 river basins worldwide. Seven global gridded precipitation datasets are compared at river basin scale in terms of mean annual and seasonal precipitation. The representation of seasonality is similar in all datasets, but the uncertainty in mean annual precipitation is large, especially in mountainous, arctic, and small basins. The average precipitation uncertainty in a basin is 30%, but there are strong differences between basins. The effect of this precipitation uncertainty on mean annual and seasonal discharge was assessed using the uncalibrated dynamic global vegetation and hydrology model Lund-Potsdam-Jena managed land (LPJmL), yielding even larger uncertainties in discharge (average 90%). For 95 basins (out of 213 basins for which measurements were available) calibration of model parameters is problematic because the observed discharge falls within the uncertainty of the simulated discharge. A method is presented to account for precipitation uncertainty in discharge simulations

Interaction of D-string with F-string: A Path-Integral Formalism

A path integral formalism is developed to study the interaction of an arbitrary curved Dirichlet (D-) string with elementary excitations of the fundumental (F-) string in bosonic string theory. Up to the next to leading order in the derivative expansion, we construct the properly renormalized vertex operator, which generalizes the one previously obtained for a D-particle moving along a curved trajectory. Using this vertex, an attempt is further made to quantize the D-string coordinates and to compute the quantum amplitude for scattering between elementary excitations of the D- and F-strings. By studying the dependence on the Liouville mode for the D-string, it is found that the vertex in our approximation consists of an infinite tower of local vertex operators which are conformally invariant on their respective mass-shell. This analysis indicates that, unlike the D-particle case, an off-shell extension of the interaction vertex would be necessary to compute the full amplitude and that the realization of symmetry can be quite non-trivial when the dual extended objects are simultaneously present. Possible future directions are suggested.Comment: 23 pages, latex, no figure

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

Anisotropy beta functions

The flow of couplings under anisotropic scaling of momenta is computed in $\phi^3$ theory in 6 dimensions. It is shown that the coupling decreases as momenta of two of the particles become large, keeping the third momentum fixed, but at a slower rate than the decrease of the coupling if all three momenta become large simultaneously. This effect serves as a simple test of effective theories of high energy scattering, since such theories should reproduce these deviations from the usual logarithmic scale dependence.Comment: uuencoded ps file, 6 page