Non-Commutative Instantons and the Seiberg-Witten Map

We present several results concerning non-commutative instantons and the Seiberg-Witten map. Using a simple ansatz we find a large new class of instanton solutions in arbitrary even dimensional non-commutative Yang-Mills theory. These include the two dimensional ``shift operator'' solutions and the four dimensional Nekrasov-Schwarz instantons as special cases. We also study how the Seiberg-Witten map acts on these instanton solutions. The infinitesimal Seiberg-Witten map is shown to take a very simple form in operator language, and this result is used to give a commutative description of non-commutative instantons. The instanton is found to be singular in commutative variables.Comment: 26 pages, AMS-LaTeX. v2: the formula for the commutative description of the Nekrasov-Schwarz instanton corrected (sec. 4). v3: minor correction

GEKKO/HIPER-driven shock waves and equation-of-state measurements at ultrahigh pressures

Copyright 2004 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Plasmas, 11(4), 1600-1608, 2004 and may be found at http://dx.doi.org/10.1063/1.165084

On the Matter of the Dijkgraaf--Vafa Conjecture

With the aim of extending the gauge theory -- matrix model connection to more general matter representations, we prove that for various two-index tensors of the classical gauge groups, the perturbative contributions to the glueball superpotential reduce to matrix integrals. Contributing diagrams consist of certain combinations of spheres, disks, and projective planes, which we evaluate to four and five loop order. In the case of $Sp(N)$ with antisymmetric matter, independent results are obtained by computing the nonperturbative superpotential for $N=4,6$ and 8. Comparison with the Dijkgraaf-Vafa approach reveals agreement up to $N/2$ loops in matrix model perturbation theory, with disagreement setting in at $h=N/2+1$ loops, $h$ being the dual Coxeter number. At this order, the glueball superfield $S$ begins to obey nontrivial relations due to its underlying structure as a product of fermionic superfields. We therefore find a relatively simple example of an ${\cal N}=1$ gauge theory admitting a large $N$ expansion, whose dynamically generated superpotential differs from the one obtained in the matrix model approach.Comment: 20 pages, harvmac. v2: added comments and reference

A Note on D1-D5-J System and 5D Small Black Ring

The ``small'' black ring in 5D obtained by giving angular momentum to the D1-D5 system compactified on S^1 x K3 is a very interesting object in the sense that it does not have an event horizon in the supergravity limit whereas it microscopically has a finite entropy. The microscopic origin of this small black ring can be analyzed in detail since it is constructed by adding angular momentum to the well-studied D1-D5 system. On the other hand, its macroscopic, geometrical picture is difficult to study directly. In this note, by duality transformations and the 4D-5D connection, we relate this 5D small black ring to a 4D small non-rotating black hole, where the latter is known to develop a non-vanishing horizon due to stringy R^2 corrections to the supergravity action. This gives an indirect evidence that a non-vanishing horizon is formed for the 5D small black ring. We also show that the entropy of the 4D small black hole agrees with the microscopic entropy of the 5D small black ring, which supports that the 4D-5D connection is indeed valid even for small black objects.Comment: 12 pages, LaTeX. v2: minor correction

Brownian motion in AdS/CFT

We study Brownian motion and the associated Langevin equation in AdS/CFT. The Brownian particle is realized in the bulk spacetime as a probe fundamental string in an asymptotically AdS black hole background, stretching between the AdS boundary and the horizon. The modes on the string are excited by the thermal black hole environment and consequently the string endpoint at the boundary undergoes an erratic motion, which is identified with an external quark in the boundary CFT exhibiting Brownian motion. Semiclassically, the modes on the string are thermally excited due to Hawking radiation, which translates into the random force appearing in the boundary Langevin equation, while the friction in the Langevin equation corresponds to the excitation on the string being absorbed by the black hole. We give a bulk proof of the fluctuation-dissipation theorem relating the random force and friction. This work can be regarded as a step toward understanding the quantum microphysics underlying the fluid-gravity correspondence. We also initiate a study of the properties of the effective membrane or stretched horizon picture of black holes using our bulk description of Brownian motion.Comment: 54 pages (38 pages + 5 appendices), 5 figures. v2: references added, clarifications in 6.2. v3: clarifications, version submitted to JHE

Hugoniot measurement of diamond under laser shock compression up to 2 Tpa

Copyright 2006 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Plasmas, 13(5), 052705, 2006 and may be found at http://dx.doi.org/10.1063/1.220519

Massless black holes and black rings as effective geometries of the D1-D5 system

We compute correlation functions in the AdS/CFT correspondence to study the emergence of effective spacetime geometries describing complex underlying microstates. The basic argument is that almost all microstates of fixed charges lie close to certain "typical" configurations. These give a universal response to generic probes, which is captured by an emergent geometry. The details of the microstates can only be observed by atypical probes. We compute two point functions in typical ground states of the Ramond sector of the D1-D5 CFT, and compare with bulk two-point functions computed in asymptotically AdS_3 geometries. For large central charge (which leads to a good semiclassical limit), and sufficiently small time separation, a typical Ramond ground state of vanishing R-charge has the M=0 BTZ black hole as its effective description. At large time separation this effective description breaks down. The CFT correlators we compute take over, and give a response whose details depend on the microstate. We also discuss typical states with nonzero R-charge, and argue that the effective geometry should be a singular black ring. Our results support the argument that a black hole geometry should be understood as an effective coarse-grained description that accurately describes the results of certain typical measurements, but breaks down in general.Comment: 47 pages, 4 figures. v2: references added. v3: minor corrections to Appendix A, references adde

A New Diketopiperazine, Cyclo-(4-S-hydroxy-R-proline-R-isoleucine), from an Australian Specimen of the Sponge Stelletta sp. †

While investigating the cytotoxic activity of the methanol extract of an Australian marine sponge Stelletta sp. (Demospongiae), a new diketopiperazine, cyclo-(4-S-hydroxy-R-proline-R-isoleucine) (1), was isolated together with the known bengamides; A (2), F (3), N (4), Y (5), and bengazoles; Z (6), C4 (7) and C6 (8). The isolation and structure elucidation of the diketopiperazine (1), together with the activity of 1–8 against a panel of human and mammalian cell lines are discussed