A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance

We present a gauge-invariant and non-perturbative construction of the Glashow-Weinberg-Salam model on the lattice, based on the lattice Dirac operator satisfying the Ginsparg-Wilson relation. Our construction covers all SU(2) topological sectors with vanishing U(1) magnetic flux and would be usable for a description of the baryon number non-conservation. In infinite volume, it provides a gauge-invariant regularization of the electroweak theory to all orders of perturbation theory. First we formulate the reconstruction theorem which asserts that if there exists a set of local currents satisfying cetain properties, it is possible to reconstruct the fermion measure which depends smoothly on the gauge fields and fulfills the fundamental requirements such as locality, gauge-invariance and lattice symmetries. Then we give a closed formula of the local currents required for the reconstruction theorem.Comment: 32 pages, uses JHEP3.cls, the version to appear in JHE

Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible?

This is a review of the status and outstanding issues in attempts to construct chiral lattice gauge theories by decoupling the mirror fermions from a vectorlike theory. In the first half, we explain why studying nonperturbative chiral gauge dynamics may be of interest, enumerate the problems that a lattice formulation of chiral gauge theories must overcome, and briefly review our current knowledge. We then discuss the motivation and idea of mirror-fermion decoupling and illustrate the desired features of the decoupling dynamics by a simple solvable toy model. The role of exact chiral symmetries and matching of 't Hooft anomalies on the lattice is also explained. The second, more technical, half of the article is devoted to a discussion of the known and unknown features of mirror-decoupling dynamics formulated with Ginsparg-Wilson fermions. We end by pointing out possible directions for future studies.Comment: 53 pp; 6 figs; added table of contents, references, fixed typo

Towards an Asymptotic-Safety Scenario for Chiral Yukawa Systems

We search for asymptotic safety in a Yukawa system with a chiral $U(N_L)_L\otimes U(1)_R$ symmetry, serving as a toy model for the standard-model Higgs sector. Using the functional RG as a nonperturbative tool, the leading-order derivative expansion exhibits admissible non-Ga\ssian fixed-points for $1 \leq N_L \leq 57$ which arise from a conformal threshold behavior induced by self-balanced boson-fermion fluctuations. If present in the full theory, the fixed-point would solve the triviality problem. Moreover, as one fixed point has only one relevant direction even with a reduced hierarchy problem, the Higgs mass as well as the top mass are a prediction of the theory in terms of the Higgs vacuum expectation value. In our toy model, the fixed point is destabilized at higher order due to massless Goldstone and fermion fluctuations, which are particular to our model and have no analogue in the standard model.Comment: 16 pages, 8 figure

Parameterized Complexity of Asynchronous Border Minimization

Microarrays are research tools used in gene discovery as well as disease and cancer diagnostics. Two prominent but challenging problems related to microarrays are the Border Minimization Problem (BMP) and the Border Minimization Problem with given placement (P-BMP). In this paper we investigate the parameterized complexity of natural variants of BMP and P-BMP under several natural parameters. We show that BMP and P-BMP are in FPT under the following two combinations of parameters: 1) the size of the alphabet (c), the maximum length of a sequence (string) in the input (l) and the number of rows of the microarray (r); and, 2) the size of the alphabet and the size of the border length (o). Furthermore, P-BMP is in FPT when parameterized by c and l. We complement our tractability results with corresponding hardness results

Hole distribution for (Sr,Ca,Y,La)_14 Cu_24 O_41 ladder compounds studied by x-ray absorption spectroscopy

The unoccupied electronic structure for the Sr_14Cu_24O_41 family of two-leg ladder compounds was investigated for different partial substitutions of Sr^2+ by Ca^2+, leaving the nominal hole count constant, and by Y^3+ or La^3+, reducing the nominal hole count from its full value of 6 per formula unit. Using polarization-dependent x-ray absorption spectroscopy on single crystals, hole states on both the chain and ladder sites could be studied. While for intermediate hole counts all holes reside on O sites of the chains, a partial hole occupation on the ladder sites in orbitals oriented along the legs is observed for the fully doped compound Sr_14Cu_24O_41. On substitution of Ca for Sr orbitals within the ladder planes but perpendicular to the legs receive some hole occupation as well.Comment: 10 pages RevTeX style with 7 embedded figures + 1 table; accepted by Phys. Rev.

Non-commutative U(1) Super-Yang-Mills Theory: Perturbative Self-Energy Corrections

The quantization of the non-commutative N=1, U(1) super-Yang-Mills action is performed in the superfield formalism. We calculate the one-loop corrections to the self-energy of the vector superfield. Although the power-counting theorem predicts quadratic ultraviolet and infrared divergences, there are actually only logarithmic UV and IR divergences, which is a crucial feature of non-commutative supersymmetric field theories.Comment: 18 pages, latex, uses feynmf package; references added, Wess-Zumino gauge remove

Holographic chiral magnetic spiral

We study the ground state of baryonic/axial matter at zero temperature chiral-symmetry broken phase under a large magnetic field, in the framework of holographic QCD by Sakai-Sugimoto. Our study is motivated by a recent proposal of chiral magnetic spiral phase that has been argued to be favored against previously studied phase of homogeneous distribution of axial/baryonic currents in terms of meson super-currents dictated by triangle anomalies in QCD. Our results provide an existence proof of chiral magnetic spiral in strong coupling regime via holography, at least for large axial chemical potentials, whereas we don't find the phenomenon in the case of purely baryonic chemical potential.Comment: 24 pages, 15 figure

Generalized Ward identity and gauge invariance of the color-superconducting gap

We derive a generalized Ward identity for color-superconducting quark matter via the functional integral approach. The identity implies the gauge independence of the color-superconducting gap parameter on the quasi-particle mass shell to subleading order in covariant gauge.Comment: 5 pages, 1 Postscript figure, uses Revte

Asymptotic safety of simple Yukawa systems

We study the triviality and hierarchy problem of a Z_2-invariant Yukawa system with massless fermions and a real scalar field, serving as a toy model for the standard-model Higgs sector. Using the functional RG, we look for UV stable fixed points which could render the system asymptotically safe. Whether a balancing of fermionic and bosonic contributions in the RG flow induces such a fixed point depends on the algebraic structure and the degrees of freedom of the system. Within the region of parameter space which can be controlled by a nonperturbative next-to-leading order derivative expansion of the effective action, we find no non-Gaussian fixed point in the case of one or more fermion flavors. The fermion-boson balancing can still be demonstrated within a model system with a small fractional flavor number in the symmetry-broken regime. The UV behavior of this small-N_f system is controlled by a conformal Higgs expectation value. The system has only two physical parameters, implying that the Higgs mass can be predicted. It also naturally explains the heavy mass of the top quark, since there are no RG trajectories connecting the UV fixed point with light top masses.Comment: 14 pages, 3 figures, v2: references added, typos corrected, minor numerical correction

Abnormal number of Nambu-Goldstone bosons in the color-asymmetric 2SC phase of an NJL-type model

We consider an extended Nambu--Jona-Lasinio model including both (q \bar q)- and (qq)-interactions with two light-quark flavors in the presence of a single (quark density) chemical potential. In the color superconducting phase of the quark matter the color SU(3) symmetry is spontaneously broken down to SU(2). If the usual counting of Goldstone bosons would apply, five Nambu-Goldstone (NG) bosons corresponding to the five broken color generators should appear in the mass spectrum. Unlike that expectation, we find only three gapless diquark excitations of quark matter. One of them is an SU(2)-singlet, the remaining two form an SU(2)-(anti)doublet and have a quadratic dispersion law in the small momentum limit. These results are in agreement with the Nielsen-Chadha theorem, according to which NG-bosons in Lorentz-noninvariant systems, having a quadratic dispersion law, must be counted differently. The origin of the abnormal number of NG-bosons is shown to be related to a nonvanishing expectation value of the color charge operator Q_8 reflecting the lack of color neutrality of the ground state. Finally, by requiring color neutrality, two massive diquarks are argued to become massless, resulting in a normal number of five NG-bosons with usual linear dispersion laws.Comment: 13 pages, 4 figures, revtex