Anticommutativity Equation in Topological Quantum Mechanics

We consider topological quantum mechanics as an example of topological field theory and show that its special properties lead to numerous interesting relations for topological corellators in this theory. We prove that the generating function $\mathcal{F}$ for thus corellators satisfies the anticommutativity equation $(\mathcal{D}- \mathcal{F})^2=0$. We show that the commutativity equation $[dB,dB]=0$ could be considered as a special case of the anticommutativity equation.Comment: 6 pages, no figures, Late

Drift of domain walls in a harmonic magnetic field

It is shown that a two-step form of the dynamic magnetization curve (and the hysteresis loop) established for a multiaxial ferrite-garnet wafer with a low quality factor (Q < 1) and considerable anisotropy in the plane (K p /K u = 14) in the frequency range of 25-1000 Hz is explained by the reconstruction of the dynamic domain structure, particularly by the established features of the drift of domain boundaries in the harmonic magnetic field. © 2013 Allerton Press, Inc

Fluid Super-Dynamics from Black Hole Superpartners

Recently the Navier-Stokes equations have been derived from the duality with the black branes in AdS_5. The zero modes of black branes are reinterpreted as dynamical degrees of freedom of a conformal fluid on the boundary of AdS_5. Here, we derive the corrections to the Navier-Stokes equations due to fermionic zero modes of the black branes. We study only the contributions due to bilinears in the fermionic zero modes in the first order of the parameter expansion. The need of a superextension of the fluid dynamics is a consequence of the full AdS/CFT correspondence and yet to be investigated.Comment: 15 pages, LaTex2

Casimir Energy of the Universe and the Dark Energy Problem

We regard the Casimir energy of the universe as the main contribution to the cosmological constant. Using 5 dimensional models of the universe, the flat model and the warped one, we calculate Casimir energy. Introducing the new regularization, called {\it sphere lattice regularization}, we solve the divergence problem. The regularization utilizes the closed-string configuration. We consider 4 different approaches: 1) restriction of the integral region (Randall-Schwartz), 2) method of 1) using the minimal area surfaces, 3) introducing the weight function, 4) {\it generalized path-integral}. We claim the 5 dimensional field theories are quantized properly and all divergences are renormalized. At present, it is explicitly demonstrated in the numerical way, not in the analytical way. The renormalization-group function (\be-function) is explicitly obtained. The renormalization-group flow of the cosmological constant is concretely obtained.Comment: 12 pages, 13 figures, Proceedings of DSU2011(2011.9.26-30,Beijin

On Pure Spinor Superfield Formalism

We show that a certain superfield formalism can be used to find an off-shell supersymmetric description for some supersymmetric field theories where conventional superfield formalism does not work. This "new" formalism contains even auxiliary variables in addition to conventional odd super-coordinates. The idea of this construction is similar to the pure spinor formalism developed by N.Berkovits. It is demonstrated that using this formalism it is possible to prove that the certain Chern-Simons-like (Witten's OSFT-like) theory can be considered as an off-shell version for some on-shell supersymmetric field theories. We use the simplest non-trivial model found in [2] to illustrate the power of this pure spinor superfield formalism. Then we redo all the calculations for the case of 10-dimensional Super-Yang-Mills theory. The construction of off-shell description for this theory is more subtle in comparison with the model of [2] and requires additional Z_2 projection. We discover experimentally (through a direct explicit calculation) a non-trivial Z_2 duality at the level of Feynman diagrams. The nature of this duality requires a better investigation

Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights

We study a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t = 0$ at the same positive value $x = a$, remain positive, and are conditioned to end at time $t = T$ at $x = 0$. In the limit $n \to \infty$, after appropriate rescaling, the paths fill out a region in the $tx$-plane that we describe explicitly. In particular, the paths initially stay away from the hard edge at $x = 0$, but at a certain critical time $t^*$ the smallest paths hit the hard edge and from then on are stuck to it. For $t \neq t^*$ we obtain the usual scaling limits from random matrix theory, namely the sine, Airy, and Bessel kernels. A key fact is that the positions of the paths at any time $t$ constitute a multiple orthogonal polynomial ensemble, corresponding to a system of two modified Bessel-type weights. As a consequence, there is a $3 \times 3$ matrix valued Riemann-Hilbert problem characterizing this model, that we analyze in the large $n$ limit using the Deift-Zhou steepest descent method. There are some novel ingredients in the Riemann-Hilbert analysis that are of independent interest.Comment: 59 pages, 11 figure

Safe and complete contig assembly via omnitigs

Contig assembly is the first stage that most assemblers solve when reconstructing a genome from a set of reads. Its output consists of contigs -- a set of strings that are promised to appear in any genome that could have generated the reads. From the introduction of contigs 20 years ago, assemblers have tried to obtain longer and longer contigs, but the following question was never solved: given a genome graph $G$ (e.g. a de Bruijn, or a string graph), what are all the strings that can be safely reported from $G$ as contigs? In this paper we finally answer this question, and also give a polynomial time algorithm to find them. Our experiments show that these strings, which we call omnitigs, are 66% to 82% longer on average than the popular unitigs, and 29% of dbSNP locations have more neighbors in omnitigs than in unitigs.Comment: Full version of the paper in the proceedings of RECOMB 201

Deconstructing holographic liquids

We argue that there exist simple effective field theories describing the long-distance dynamics of holographic liquids. The degrees of freedom responsible for the transport of charge and energy-momentum are Goldstone modes. These modes are coupled to a strongly coupled infrared sector through emergent gauge and gravitational fields. The IR degrees of freedom are described holographically by the near-horizon part of the metric, while the Goldstone bosons are described by a field-theoretical Lagrangian. In the cases where the holographic dual involves a black hole, this picture allows for a direct connection between the holographic prescription where currents live on the boundary, and the membrane paradigm where currents live on the horizon. The zero-temperature sound mode in the D3-D7 system is also re-analyzed and re-interpreted within this formalism.Comment: 21 pages, 2 figure