Vortex counting from field theory

The vortex partition function in 2d N = (2,2) U(N) gauge theory is derived from the field theoretical point of view by using the moduli matrix approach. The character for the tangent space at each moduli space fixed point is written in terms of the moduli matrix, and then the vortex partition function is obtained by applying the localization formula. We find that dealing with the fermionic zero modes is crucial to obtain the vortex partition function with the anti-fundamental and adjoint matters in addition to the fundamental chiral multiplets. The orbifold vortex partition function is also investigated from the field theoretical point of view.Comment: 21 pages, no figure

Supersymmetry Breaking on Gauged Non-Abelian Vortices

There are a large number of systems characterized by a completely broken gauge symmetry, but with an unbroken global color-flavor diagonal symmetry, i.e., systems in the so-called color-flavor locked phase. If the gauge symmetry breaking supports vortices, the latter develop non-Abelian orientational zero-modes and become non-Abelian vortices, a subject of intense study in the last several years. In this paper we consider the effects of weakly gauging the full exact global flavor symmetry in such systems, deriving an effective description of the light excitations in the presence of a vortex. Surprising consequences are shown to follow. The fluctuations of the vortex orientational modes get diffused to bulk modes through tunneling processes. When our model is embedded in a supersymmetric theory, the vortex is still 1/2 BPS saturated, but the vortex effective action breaks supersymmetry spontaneously.Comment: Latex, 24 pages, 1 figur

Structurally Parameterized d-Scattered Set

In $d$-Scattered Set we are given an (edge-weighted) graph and are asked to select at least $k$ vertices, so that the distance between any pair is at least $d$, thus generalizing Independent Set. We provide upper and lower bounds on the complexity of this problem with respect to various standard graph parameters. In particular, we show the following: - For any $d\ge2$, an $O^*(d^{\textrm{tw}})$-time algorithm, where $\textrm{tw}$ is the treewidth of the input graph. - A tight SETH-based lower bound matching this algorithm's performance. These generalize known results for Independent Set. - $d$-Scattered Set is W[1]-hard parameterized by vertex cover (for edge-weighted graphs), or feedback vertex set (for unweighted graphs), even if $k$ is an additional parameter. - A single-exponential algorithm parameterized by vertex cover for unweighted graphs, complementing the above-mentioned hardness. - A $2^{O(\textrm{td}^2)}$-time algorithm parameterized by tree-depth ($\textrm{td}$), as well as a matching ETH-based lower bound, both for unweighted graphs. We complement these mostly negative results by providing an FPT approximation scheme parameterized by treewidth. In particular, we give an algorithm which, for any error parameter $\epsilon > 0$, runs in time $O^*((\textrm{tw}/\epsilon)^{O(\textrm{tw})})$ and returns a $d/(1+\epsilon)$-scattered set of size $k$, if a $d$-scattered set of the same size exists

Unfair competition governs the interaction of pCPI-17 with myosin phosphatase (PP1-MYPT1).

The small phosphoprotein pCPI-17 inhibits myosin light-chain phosphatase (MLCP). Current models postulate that during muscle relaxation, phosphatases other than MLCP dephosphorylate and inactivate pCPI-17 to restore MLCP activity. We show here that such hypotheses are insufficient to account for the observed rapidity of pCPI-17 inactivation in mammalian smooth muscles. Instead, MLCP itself is the critical enzyme for pCPI-17 dephosphorylation. We call the mutual sequestration mechanism through which pCPI-17 and MLCP interact inhibition by unfair competition: MLCP protects pCPI-17 from other phosphatases, while pCPI-17 blocks other substrates from MLCP\u27s active site. MLCP dephosphorylates pCPI-17 at a slow rate that is, nonetheless, both sufficient and necessary to explain the speed of pCPI-17 dephosphorylation and the consequent MLCP activation during muscle relaxation

Multi-parameter scaling of the Kondo effect in quantum dots with an even number of electrons

We address a recent theoretical discrepancy concerning the Kondo effect in quantum dots with an even number of electrons where spin-singlet and -triplet states are nearly degenerate. We show that the discrepancy arises from the fact that the Kondo scaling involves many parameters, which makes the results depend on concrete microscopic models. We illustrate this by the scaling calculations of the Kondo temperature, $T_K$, as a function of the energy difference between the singlet and triplet states $\Delta$. $T_K(\Delta)$ decreases with increasing $\Delta$, showing a crossover from a power law with a universal exponent to that with a nonuniversal exponent. The crossover depends on the initial parameters of the model.Comment: 8 pages, 3 figure

Color Magnetic Flux Tubes in Dense QCD

QCD is expected to be in the color-flavor locking phase in high baryon density, which exhibits color superconductivity. The most fundamental topological objects in the color superconductor are non-Abelian vortices which are topologically stable color magnetic flux tubes. We present numerical solutions of the color magnetic flux tube for diverse choices of the coupling constants. We also analytically study its asymptotic profiles and find that they are different from the case of usual superconductors. We propose the width of color magnetic fluxes and find that it is larger than naive expectation of the Compton wave length of the massive gluon when the gluon mass is larger than the scalar mass.Comment: 24 pages, 5 figures; v2: typos corrected, references added, minor changes; v3: published versio

Quantum SUSY Algebra of QQ-lumps in the Massive Grassmannian Sigma Model

We compute the $\mathcal{N}=2$ SUSY algebra of the massive Grassmannian sigma model in 2+1 dimensions. We first rederive the action of the model by using the Scherk-Schwarz dimensional reduction from $\mathcal{N}=1$ theory in 3+1 dimensions. Then, we perform the canonical quantization by using the Dirac method. We find that a particular choice of the operator ordering yields the quantum SUSY algebra of the $Q$-lumps with cental extension.Comment: 7 pages, references adde

Are "EIT Waves" Fast-Mode MHD Waves?

We examine the nature of large-scale, coronal, propagating wave fronts (``EIT waves'') and find they are incongruous with solutions using fast-mode MHD plane-wave theory. Specifically, we consider the following properties: non-dispersive single pulse manifestions, observed velocities below the local Alfven speed, and different pulses which travel at any number of constant velocities, rather than at the ``predicted'' fast-mode speed. We discuss the possibility of a soliton-like explanation for these phenomena, and show how it is consistent with the above-mentioned aspects.Comment: to be published in the Astrophysical Journa

Kondo Effect in Multiple-Dot Systems

We study the Kondo effect in multiple-dot systems for which the inter- as well as intra-dot Coulomb repulsions are strong, and the inter-dot tunneling is small. The application of the Ward-Takahashi identity to the inter-dot dynamical susceptibility enables us to analytically calculate the conductance for a double-dot system by using the Bethe-ansatz exact solution of the SU(4) impurity Anderson model. It is clarified how the inter-dot Kondo effect enhances or suppresses the conductance under the control of the gate voltage and the magnetic field. We then extend our analysis to multiple-dot systems including more than two dots, and discuss their characteristic transport properties by taking a triple-dot system as an example.Comment: 8 pages, 9 figure

Vortices and Monopoles in Mass-deformed SO and USp Gauge Theories

Effects of mass deformations on 1/2 Bogomol'nyi-Prasad-Sommerfield (BPS) non-Abelian vortices are studied in 4d N=2 supersymmetric U(1) \times SO(2n) and U(1) \times USp(2n) gauge theories, with Nf=2n quark multiplets. The 2d N=(2,2) effective worldsheet sigma models on the Hermitian symmetric spaces SO(2n)/U(n) and USp(2n)/U(n) found recently which describe the low-energy excitations of the orientational moduli of the vortices, are generalized to the respective massive sigma models. The continuous vortex moduli spaces are replaced by a finite number (2^{n-1} or 2^{n}) of vortex solutions. The 1/2 BPS kinks connecting different vortex vacua are magnetic monopoles in the 4d theory, trapped inside the vortex core, with total configurations being 1/4 BPS composite states. These configurations are systematically studied within the semi-classical regime.Comment: 55 pages, 7 figure