Solitons in Seiberg-Witten Theory and D-branes in the Derived Category

We analyze the "geometric engineering" limit of a type II string on a suitable Calabi-Yau threefold to obtain an N=2 pure SU(2) gauge theory. The derived category picture together with Pi-stability of B-branes beautifully reproduces the known spectrum of BPS solitons in this case in a very explicit way. Much of the analysis is particularly easy since it can be reduced to questions about the derived category of CP1.Comment: 20 pages, LaTex2

Homological Type of Geometric Transitions

The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \emph{homological type} of a geometric transition. The obtained results agree with, and go further than, most results and estimates, given to date by several authors, both in mathematical and physical literature.Comment: 36 pages. Minor changes: A reference and a related comment in Remark 3.2 were added. This is the final version accepted for publication in the journal Geometriae Dedicat

Nonexistence of marginally trapped surfaces and geons in 2+1 gravity

We use existence results for Jang's equation and marginally outer trapped surfaces (MOTSs) in 2+1 gravity to obtain nonexistence of geons in 2+1 gravity. In particular, our results show that any 2+1 initial data set, which obeys the dominant energy condition with cosmological constant \Lambda \geq 0 and which satisfies a mild asymptotic condition, must have trivial topology. Moreover, any data set obeying these conditions cannot contain a MOTS. The asymptotic condition involves a cutoff at a finite boundary at which a null mean convexity condition is assumed to hold; this null mean convexity condition is satisfied by all the standard asymptotic boundary conditions. The results presented here strengthen various aspects of previous related results in the literature. These results not only have implications for classical 2+1 gravity but also apply to quantum 2+1 gravity when formulated using Witten's solution space quantization.Comment: v3: Elements from the original two proofs of the main result have been combined to give a single proof, thereby circumventing an issue with the second proof associated with potential blow-ups of solutions to Jang's equation. To appear in Commun. Math. Phy

Dynamic wormholes, anti-trapped surfaces, and energy conditions

Adapting and extending a suggestion due to Page, we define a wormhole throat to be a marginally anti-trapped surface, that is, a closed two-dimensional spatial hypersurface such that one of the two future-directed null geodesic congruences orthogonal to it is just beginning to diverge. Typically a dynamic wormhole will possess two such throats, corresponding to the two orthogonal null geodesic congruences, and these two throats will not coincide, (though they do coalesce into a single throat in the static limit). The divergence property of the null geodesics at the marginally anti-trapped surface generalizes the ``flare-out'' condition for an arbitrary wormhole. We derive theorems regarding violations of the null energy condition (NEC) at and near these throats and find that, even for wormholes with arbitrary time-dependence, the violation of the NEC is a generic property of wormhole throats. We also discuss wormhole throats in the presence of fully antisymmetric torsion and find that the energy condition violations cannot be dumped into the torsion degrees of freedom. Finally by means of a concrete example we demonstrate that even temporary suspension of energy-condition violations is incompatible with the flare-out property of dynamic throats.Comment: 32 pages in plain LaTex, no figures. Additional text and references adde

Black String Entropy and Fourier-Mukai Transform

We propose a microscopic description of black strings in F-theory based on string duality and Fourier-Mukai transform. These strings admit several different microscopic descriptions involving D-brane as well as M2 or M5-brane configurations on elliptically fibered Calabi-Yau threefolds. In particular our results can also be interpreted as an asymptotic microstate count for D6-D2-D0 configurations in the limit of large D2-charge on the elliptic fiber. The leading behavior of the microstate degeneracy in this limit is shown to agree with the macroscopic entropy formula derived from the black string supergravity solution.Comment: 22 pages, latex; v2: substantial revision of the macroscopic description of the system; results essentially unchange

The Particle Spectrum of Heterotic Compactifications

Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over elliptically fibered Calabi-Yau threefolds. These cohomology groups explicitly determine the spectrum of the low energy, four-dimensional theory. Generic points in vector bundle moduli space manifest an identical spectrum. However, it is shown that on subsets of moduli space of co-dimension one or higher, the spectrum can abruptly jump to many different values. Both analytic and numerical data illustrating this phenomenon are presented. This result opens the possibility of tunneling or phase transitions between different particle spectra in the same heterotic compactification. In the course of this discussion, a classification of SU(5) GUT theories within a specific context is presented.Comment: 77 pages, 3 figure

Stochastic association of neighboring replicons creates replication factories in budding yeast

Peer reviewedPublisher PD

The dynamics of genome replication using deep sequencing

Peer reviewedPublisher PD

Magnetization steps in a diluted Heisenberg antiferromagnetic chain: Theory and experiments on TMMC:Cd

A theory for the equilibrium low-temperature magnetization M of a diluted Heisenberg antiferromagnetic chain is presented. The magnetization curve, M versus B, is calculated using the exact contributions of finite chains with 1 to 5 spins, and the "rise and ramp approximation" for longer chains. Some non-equilibrium effects that occur in a rapidly changing B, are also considered. Specific non-equilibrium models based on earlier treatments of the phonon bottleneck, and of spin flips associated with cross relaxation and with level crossings, are discussed. Magnetization data on powders of TMMC diluted with cadmium [i.e., (CH_3)_4NMn_xCd_(1-x)Cl_3, with 0.16<=x<=0.50 were measured at 0.55 K in 18 T superconducting magnets. The field B_1 at the first MST from pairs is used to determine the NN exchange constant, J, which changes from -5.9 K to -6.5 K as x increases from 0.16 to 0.50. The magnetization curves obtained in the superconducting magnets are compared with simulations based on the equilibrium theory. Data for the differential susceptibility, dM/dB, were taken in pulsed magnetic fields (7.4 ms duration) up to 50 T, with the powder samples in a 1.5 K liquid-helium bath. Non-equilibrium effects, which became more severe as x decreased, were observed. The non-equilibrium effects are tentatively interpreted using the "Inadequate Heat Flow Scenario," or to cross-relaxation, and crossings of energy levels, including those of excited states.Comment: 16 pages, 14 figure

Quantum Black Holes from Quantum Collapse

The Schwarzschild black hole can be viewed as the special case of the marginally bound Lema\^\i tre-Tolman-Bondi models of dust collapse which corresponds to a constant mass function. We have presented a midi-superspace quantization of this model for an arbitrary mass-function in a separate publication. In this communication we show that our solution leads both to Bekenstein's area spectrum for black holes as well as to the black hole entropy, which, in this context, is naturally interpreted as the loss of information of the original matter distribution within the collapsing dust cloud.Comment: LaTeX file, 6 pages, 1 figure, Paper re-written into sections, some references added, some elaborations, conclusions unchanged, to appear in Physical Review