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

Instantons, supersymmetric vacua, and emergent geometries

We study instanton solutions and superpotentials for the large number of vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills theory on $R\times S^2$ with sixteen supercharges. We get the superpotential in the weak coupling limit from the gauge theory description. We study the gravity description of these instantons. Perturbatively with respect to a background, they are Euclidean branes wrapping cycles in the dual gravity background. Moreover, the superpotential can be given by the energy of the electric charge system characterizing each vacuum. These charges are interpreted as the eigenvalues of matrices from a reduction for the 1/8 BPS sector of the gauge theories. We also discuss qualitatively the emergence of the extra spatial dimensions appeared on the gravity side.Comment: 29 pages, 3 figures, latex. v2: references added, comments added. v3: accepted version in PR

Dynamical tachyons on fuzzy spheres

We study the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the BMN plane wave matrix model. The displacement is along the plane of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles classical tachyons develop and that the spectrum of these modes can be computed analytically. These tachyons can be related to the familiar Nielsen-Olesen instabilities in Yang-Mills theory on a constant magnetic background. Many features of the problem become more apparent when we compare with maximally supersymmetric Yang-Mills on a sphere, of which this system is a truncation. We also set up a simple oscillatory trajectory on the displacement between the fuzzy spheres and study the dynamics of the modes as they become tachyonic for part of the oscillations. We speculate on their role regarding the possible thermalization of the system.Comment: 34 pages, 4 figures; v2: 35 pages, expanded sec. 4.3, added reference

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

Dynamical Decompactification and Three Large Dimensions

We study string gas dynamics in the early universe and seek to realize the Brandenberger - Vafa mechanism - a goal that has eluded earlier works - that singles out three or fewer spatial dimensions as the number which grow large cosmologically. Considering wound string interactions in an impact parameter picture, we show that a strong exponential suppression in the interaction rates for d > 3 spatial dimensions reflects the classical argument that string worldsheets generically intersect in at most four spacetime dimensions. This description is appropriate in the early universe if wound strings are heavy - wrapping long cycles - and diluted. We consider the dynamics of a string gas coupled to dilaton-gravity and find that a) for any number of dimensions the universe generically stays trapped in the Hagedorn regime and b) if the universe fluctuates to a radiation regime any residual winding modes are diluted enough so that they freeze-out in d > 3 large dimensions while they generically annihilate for d = 3. In this sense the Brandenberger-Vafa mechanism is operative.Comment: 20 pages, 2 figures, minor changes, updated figures, as will appear in Phys.Rev.

Holographic representation of local bulk operators

The Lorentzian AdS/CFT correspondence implies a map between local operators in supergravity and non-local operators in the CFT. By explicit computation we construct CFT operators which are dual to local bulk fields in the semiclassical limit. The computation is done for general dimension in global, Poincare and Rindler coordinates. We find that the CFT operators can be taken to have compact support in a region of the complexified boundary whose size is set by the bulk radial position. We show that at finite N the number of independent commuting operators localized within a bulk volume saturates the holographic bound.Comment: 36 pages, LaTeX, 4 eps figure