Supersymmetric Extension of GCA in 2d

We derive the infinite dimensional Supersymmetric Galilean Conformal Algebra (SGCA) in the case of two spacetime dimensions by performing group contraction on 2d superconformal algebra. We also obtain the representations of the generators in terms of superspace coordinates. Here we find realisations of the SGCA by considering scaling limits of certain 2d SCFTs which are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We focus on the Neveu-Schwarz sector of the parent SCFTs and develop, in parallel to the GCA studies recently in (arXiv:0912.1090), the representation theory based on SGCA primaries, Ward identities for their correlation functions and their descendants which are null states.Comment: La TeX file, 32 pages; v2: typos corrected, journal versio

Asymptotic W-symmetries in three-dimensional higher-spin gauge theories

We discuss how to systematically compute the asymptotic symmetry algebras of generic three-dimensional bosonic higher-spin gauge theories in backgrounds that are asymptotically AdS. We apply these techniques to a one-parameter family of higher-spin gauge theories that can be considered as large N limits of SL(N) x SL(N) Chern-Simons theories, and we provide a closed formula for the structure constants of the resulting infinite-dimensional non-linear W-algebras. Along the way we provide a closed formula for the structure constants of all classical W_N algebras. In both examples the higher-spin generators of the W-algebras are Virasoro primaries. We eventually discuss how to relate our basis to a non-primary quadratic basis that was previously discussed in literature.Comment: 61 page

Universality of Phases in QCD and QCD-like Theories

We argue that the whole or the part of the phase diagrams of QCD and QCD-like theories should be universal in the large-N_c limit through the orbifold equivalence. The whole phase diagrams, including the chiral phase transitions and the BEC-BCS crossover regions, are identical between SU(N_c) QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon chemical potential. Outside the BEC-BCS crossover region in these theories, the phase diagrams are also identical to that of SU(N_c) QCD at finite baryon chemical potential. We give examples of the universality in some solvable cases: (i) QCD and QCD-like theories at asymptotically high density where the controlled weak-coupling calculations are possible, (ii) chiral random matrix theories of different universality classes, which are solvable large-N (large volume) matrix models of QCD. Our results strongly suggest that the chiral phase transition and the QCD critical point at finite baryon chemical potential can be studied using sign-free theories, such as QCD at finite isospin chemical potential, in lattice simulations.Comment: v1: 35 pages, 6 figures; v2: 37 pages, 6 figures, minor improvements, conclusion unchanged; v3: version published in JHE

Fermionic Coset, Critical Level W^(2)_4-Algebra and Higher Spins

The fermionic coset is a limit of the pure spinor formulation of the AdS5xS5 sigma model as well as a limit of a nonlinear topological A-model, introduced by Berkovits. We study the latter, especially its symmetries, and map them to higher spin algebras. We show the following. The linear A-model possesses affine \AKMSA{pgl}{4}{4}_0 symmetry at critical level and its \AKMSA{psl}{4}{4}_0 current-current perturbation is the nonlinear model. We find that the perturbation preserves $\mathcal{W}^{(2)}_4$-algebra symmetry at critical level. There is a topological algebra associated to \AKMSA{pgl}{4}{4}_0 with the properties that the perturbation is BRST-exact. Further, the BRST-cohomology contains world-sheet supersymmetric symplectic fermions and the non-trivial generators of the $\mathcal{W}^{(2)}_4$-algebra. The Zhu functor maps the linear model to a higher spin theory. We analyze its \SLSA{psl}{4}{4} action and find finite dimensional short multiplets.Comment: 25 page

Static Charges in the Low-Energy Theory of the S-Duality Twist

We continue the study of the low-energy limit of N=4 super Yang-Mills theory compactified on a circle with S-duality and R-symmetry twists that preserve N=6 supersymmetry in 2+1D. We introduce external static supersymmetric quark and anti-quark sources into the theory and calculate the Witten Index of the resulting Hilbert space of ground states on a torus. Using these results we compute the action of simple Wilson loops on the Hilbert space of ground states without sources. In some cases we find disagreement between our results for the Wilson loop eigenvalues and previous conjectures about a connection with Chern-Simons theory.Comment: 73 pages, two paragraphs added, one to the introduction and one to the discussio

Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results

We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual space-time geometries are constructed from fundamental simplicial building blocks, and the path integral over geometries is approximated by summing over a class of piece-wise linear geometries. This method of ``dynamical triangulations'' is very powerful in 2d, where the regularized theory can be solved explicitly, and gives us more insights into the quantum nature of 2d space-time than continuum methods are presently able to provide. It also allows us to establish an explicit relation between the Lorentzian- and Euclidean-signature quantum theories. Analogous regularized gravitational models can be set up in higher dimensions. Some analytic tools exist to study their state sums, but, unlike in 2d, no complete analytic solutions have yet been constructed. However, a great advantage of our approach is the fact that it is well-suited for numerical simulations. In the second part of this review we describe the relevant Monte Carlo techniques, as well as some of the physical results that have been obtained from the simulations of Euclidean gravity. We also explain why the Lorentzian version of dynamical triangulations is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde

Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant

We show that the ABJM theory, which is an N=6 superconformal U(N)*U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS_4/CFT_3 duality at the quantum level. Here we calculate the free energy, and confirm the N^{3/2} scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models.Comment: 35 pages, 20 figures; reference added. The simulation code is available upon request to [email protected]

Super-W(infinity) Asymptotic Symmetry of Higher-Spin AdS(3) Supergravity

We consider (2+1)-dimensional (N, M)-extended higher-spin anti-de Sitter supergravity and study its asymptotic symmetries. The theory is described by the Chern-Simons action based on a real, infinite-dimensional higher-spin superalgebra. We specify consistent boundary conditions on the higher-spin super-gauge connection corresponding to asymptotically anti-de Sitter spacetimes. We then determine the residual gauge transformations that preserve these asymptotic conditions and compute their Poisson bracket algebra. We find that the asymptotic symmetry is enhanced from the higher-spin superalgebra to some (N,M)-extended super-W(infinity) nonlinear superalgebra. The latter has the same classical central charge as pure Einstein gravity. Special attention is paid to the (1,1)-case. Truncation to the bosonic sector yields the previously found W(infinity) algebra, while truncation to the underlying finite-dimensional superalgebra reproduces the N-extended superconformal algebra (in its nonlinear version for N>2). We discuss string theory realization of these higher-spin anti-de Sitter supergravity theories as well as relations to previous treatments of super-W(infinity) in the literature.Comment: References added. (N>2)-Extended supersymmetric models argued to be rigid with respect to lambda-deformation. Comments on G(3)-case adde

Microtubules Remodel Actomyosin Networks in Xenopus Egg Extracts via Two Mechanisms of F-Actin Transport

Interactions between microtubules and filamentous actin (F-actin) are crucial for many cellular processes, including cell locomotion and cytokinesis, but are poorly understood. To define the basic principles governing microtubule/F-actin interactions, we used dual-wavelength digital fluorescence and fluorescent speckle microscopy to analyze microtubules and F-actin labeled with spectrally distinct fluorophores in interphase Xenopus egg extracts. In the absence of microtubules, networks of F-actin bundles zippered together or exhibited serpentine gliding along the coverslip. When microtubules were nucleated from Xenopus sperm centrosomes, they were released and translocated away from the aster center. In the presence of microtubules, F-actin exhibited two distinct, microtubule-dependent motilities: rapid (∼250–300 nm/s) jerking and slow (∼50 nm/s), straight gliding. Microtubules remodeled the F-actin network, as F-actin jerking caused centrifugal clearing of F-actin from around aster centers. F-actin jerking occurred when F-actin bound to motile microtubules powered by cytoplasmic dynein. F-actin straight gliding occurred when F-actin bundles translocated along the microtubule lattice. These interactions required Xenopus cytosolic factors. Localization of myosin-II to F-actin suggested it may power F-actin zippering, while localization of myosin-V on microtubules suggested it could mediate interactions between microtubules and F-actin. We examine current models for cytokinesis and cell motility in light of these findings

Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity

We investigate the asymptotic symmetry algebra of (2+1)-dimensional higher spin, anti-de Sitter gravity. We use the formulation of the theory as a Chern-Simons gauge theory based on the higher spin algebra hs(1,1). Expanding the gauge connection around asymptotically anti-de Sitter spacetime, we specify consistent boundary conditions on the higher spin gauge fields. We then study residual gauge transformation, the corresponding surface terms and their Poisson bracket algebra. We find that the asymptotic symmetry algebra is a nonlinearly deformed W(infinity) algebra with classical central charges. We discuss implications of our results to quantum gravity and to various situations in string theory.Comment: 25 pages, no figure; v2. minor corrections, references added, v3. JHEP published versio