We apply to lattice QCD a bosonization method previously developed in which dynamical bosons are generated by time-dependent Bogoliubov transformations. The transformed action can be studied by an expansion in the inverse of the nilpotency index, which is the number of fermionic states in the structure function of composite bosons. When this number diverges the model is solved by the saddle-point method which has a variational interpretation. We give a stationary covariant solution for a background matter field whose fluctuations describe mesons. In the saddle-point approximation fermionic quasiparticles exist which have quark quantum numbers. They are confined in the sense that they propagate only in pointlike color singlets. Conditions for chiral symmetry breaking are determined, to be studied numerically, and a derivation of a mesons-nucleons action is outlined.

The shear ($\eta$) and bulk ($\zeta$) viscous coefficients have been evaluated for a gluonic fluid. The elastic, $gg\to gg$ and the inelastic, number nonconserving, $gg\to ggg$ processes have been considered as the dominant perturbative processes in evaluating the viscous coefficients to entropy density ($s$) ratios. Recently the processes: $gg\to ggg$ has been revisited and a correction to the widely used Gunion-Bertsch (GB) formula has been obtained. The $\eta$ and $\zeta$ have been evaluated for gluonic fluid with the formula recently derived. At large ${\alpha }_s$ the value of $\eta /s$ approaches its lower bound, $\sim 1/4\pi$.

The recently developed Nambu-Jona-Lasinio—jet model is used as an effective chiral quark theory to calculate the quark fragmentation functions to pions, kaons, nucleons, and antinucleons. The effects of the vector mesons $\rho$, $K^{*}$, and $\varphi$ on the production of secondary pions and kaons are included. The fragmentation processes to nucleons and antinucleons are described by using the quark-diquark picture, which has been shown to give a reasonable description of quark distribution functions. We incorporate effects of next-to-leading order in the $Q^2$ evolution, and compare our results with the empirical fragmentation functions.

The strong coupling constants, $g_{D_{s}D{K}_0^{*}}$, $g_{B_{s}B{K}_0^{*}}$, $g_{D_s^{*}DK}$, $g_{B_s^{*}BK}$, $g_{D_s^{*}D{K}_1}$ and $g_{B_s^{*}B{K}_1}$, where $K_0^{*}$, $K$ and $K_1$ are scalar, pseudoscalar, and axial-vector kaon mesons, respectively, are calculated in the framework of three-point QCD sum rules. In particular, the correlation functions of the considered vertices when both $B(D)$ and $K_0^{*}(K)(K_1)$ mesons are off shell are evaluated. In the case of $K_1$, which is either $K_1(1270)$ or $K_1(1400)$, the mixing between these two states are also taken into account. A comparison of the obtained result with the existing prediction on $g_{D_s^{*}DK}$ as the only coupling constant among the considered vertices, previously calculated in the literature, is also made.

The nonlocal Polyakov-loop-extended Nambu–Jona-Lasinio model is further improved by including momentum-dependent wave-function renormalization in the quark quasiparticle propagator. Both two- and three-flavor versions of this improved Polyakov-loop-extended Nambu–Jona-Lasinio model are discussed, the latter with inclusion of the (nonlocal) ’t Hooft-Kobayashi-Maskawa determinant interaction in order to account for the axial U(1) anomaly. Thermodynamics and phases are investigated and compared with recent lattice-QCD results.

We calculate and explore the moduli potential for $M$ theory compactified on $G_2$-manifolds in which the superpotential is dominated by a single membrane instanton term plus one from an asymptotically free hidden sector gauge interaction. We show that all moduli can be stabilized and that hidden sector gauge symmetries can be Higgsed at a high scale. We then compute the spectrum of superpartner masses at the grand unified theory scale and evolve it to the electroweak scale. We find a spectrum which is very similar to the $G_2$-minimal supersymmetric standard model with light gauginos—accessible at the LHC—and a neutral wino dark matter candidate.

A Lorentz-violating modification of massless QED is proposed, with higher-order space derivatives for the photon field. The fermion dynamical mass generation is studied with the Schwinger-Dyson approach. Perturbative properties of the model are calculated at one-loop and discussed at higher-order loops, showing the consistency of the model. We explain that there is no contradiction with the definition of the speed of light $c$, although fermions see an effective light cone, with a maximum speed smaller than $c$.

An exact calculation of electromagnetic scattering from a perfectly conducting parabolic cylinder is employed to compute Casimir forces in several configurations. These include interactions between a parabolic cylinder and a plane, two parabolic cylinders, and a parabolic cylinder and an ordinary cylinder. To elucidate the effect of boundaries, special attention is focused on the “knife-edge” limit in which the parabolic cylinder becomes a half-plane. Geometrical effects are illustrated by considering arbitrary rotations of a parabolic cylinder around its focal axis, and arbitrary translations perpendicular to this axis. A quite different geometrical arrangement is explored for the case of an ordinary cylinder placed in the interior of a parabolic cylinder. All of these results extend simply to nonzero temperatures.

Some recent studies of the AdS/CFT correspondence for condensed matter systems involve the Fermi liquid theory as a boundary field theory. Adding $B$-flux to the boundary D-branes leads in a certain limit to the noncommutative Fermi liquid, which calls for a field theory description of its critical behavior. As a preliminary step to more general consideration, the modification of the Landau’s Fermi liquid theory due to noncommutativity of spatial coordinates is studied in this paper. We carry out the renormalization of interactions at tree level and one loop in a weakly coupled fermion system in two spatial dimensions. Channels ZS, ZS’ and BCS are discussed in detail. It is shown that while the Gaussian fixed-point remains unchanged, the BCS instability is modified due to the space noncommutativity.

QCD amplitudes with many external fields have been studied for a long time. At tree-level, the amplitudes can be obtained effectively by the Britto-Cachazo-Feng-Witten (BCFW) recursion relations. In this article, we extend the BCFW relations to the QCD amplitude of which the external fields are all massive or include only one massless line. We find such amplitude can be split into two parts and each part of the amplitude is of some correlated spin configuration between the two shifted lines. After choosing proper momentum shift scheme, we can show that each part is constructible directly. Hence, we can obtain a general procedure for the amplitudes in QCD by the BCFW recursion relations. We apply the procedure to several amplitudes as examples. We find such methods are very efficient when there are many massive external fields in the amplitudes.

We study the properties of a non-Gaussian density matrix for an $O(N)$ scalar field in the context of the incomplete description picture. This is of relevance for studies of decoherence and entropy production in quantum field theory. In particular, we study how the inclusion of the simplest non-Gaussian correlator in the set of measured observables modifies the effective (Gaussian) description one can infer from the knowledge of the two-point functions only. We compute exactly the matrix elements of the non-Gaussian density matrix at leading order in a $1/N$ expansion. This allows us to study the quantum properties (purity, entropy, coherence) of the corresponding state for arbitrarily strong non-Gaussianity. We find that if the Gaussian and the non-Gaussian observers essentially agree concerning quantum purity or correlation entropy, their conclusion can significantly differ for other, more detailed aspects such as the degree of quantum coherence of the system.

We study the Bogomol’nyi-Prasad-Sommerfield wall solutions in massive Kähler nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ in three-dimensional spacetime. We show that $SO(2N)/U(N)$ and $Sp(N)/U(N)$ models have $2^{N-1}$ and $2^N$ discrete vacua, respectively. We explicitly construct the exact BPS multiwall solutions for $N\le 3$.

Gravity solutions dual to $d$-dimensional field theories at finite charge density have a near-horizon region, which is ${\mathrm{AdS}}_2\times {\mathbb{R}}^{d-1}$. The scale invariance of the ${\mathrm{AdS}}_2$ region implies that at low energies the dual field theory exhibits emergent quantum critical behavior controlled by a ($0+1$)-dimensional conformal field theories (CFT). This interpretation sheds light on recently-discovered holographic descriptions of Fermi surfaces, allowing an analytic understanding of their low-energy excitations. For example, the scaling behavior near the Fermi surfaces is determined by conformal dimensions in the emergent IR CFT. In particular, when the operator is marginal in the IR CFT, the corresponding spectral function is precisely of the “marginal Fermi liquid” form, postulated to describe the optimally doped cuprates.

We consider the planar MHV amplitude in $\mathcal{N}=4$ supersymmetric Yang-Mills theory for $2\to 4$ particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function found by Goncharov, Spradlin, Vergu and Volovich to the physical region, where the remainder function does not vanish in the Regge limit. After the continuation both the leading and the subleading in the logarithm of the energy terms are extracted and analyzed. Using this result we calculate the next-to-leading corrections to the impact factors required in the BFKL approach. The BFKL technique was used to find the leading imaginary and real parts of the remainder function at three loops.

We perform a numerical-relativity simulation for the merger of binary neutron stars with 6 nuclear-theory-based equations of states (EOSs) described by piecewise polytropes. Our purpose is to explore the dependence of the dynamical behavior of the binary neutron star merger and resulting gravitational waveforms on the EOS of the supernuclear-density matter. The numerical results show that the merger process and the first outcome are classified into three types: (i) a black hole is promptly formed, (ii) a short-lived hypermassive neutron star (HMNS) is formed, (iii) a long-lived HMNS is formed. The type of the merger depends strongly on the EOS and on the total mass of the binaries. For the EOS with which the maximum mass is larger than $2M_{\odot }$, the lifetime of the HMNS is longer than 10 ms for a total mass $m_0=2.7M_{\odot }$. A recent radio observation suggests that the maximum mass of spherical neutron stars is $M_{\max }\ge 1.97\pm 0.04M_{\odot }$ in one $\sigma$ level. This fact and our results support the possible existence of a HMNS soon after the onset of the merger for a typical binary neutron star with $m_0=2.7M_{\odot }$. We also show that the torus mass surrounding the remnant black hole is correlated with the type of the merger process; the torus mass could be large, $\ge 0.1M_{\odot }$, in the case that a long-lived HMNS is formed. We also show that gravitational waves carry information of the merger process, the remnant, and the torus mass surrounding a black hole.

Skyrme theory is among the viable effective theories which emerge from the low-energy limit of quantum chromodynamics. Many of its generalizations include also a dilaton. Here we find new self-gravitating solutions, both solitons and black holes, in a generalized Skyrme model in which a dilaton is present. The investigation of the properties of the solutions is done numerically. We find that the introduction of the dilaton in the theory does not change the picture qualitatively, only quantitatively. The model considered here has one free parameter more than the Einstein-Skyrme model which comes from the potential of the dilaton. We have applied also the turning point method to establish that one of the black-hole branches of solutions is unstable. The turning point method here is based on the first law of black-hole thermodynamics a detailed derivation of which is given in the Appendix of the paper.

We propose an action for a free particle in Hořava-Lifshitz gravity based on foliation preserving diffeomorphisms. The action reduces to the usual relativistic action in the low-energy limit and allows for subluminal and superluminal motions with upper and lower bounds on velocity, respectively. We find that deviation from general relativity is governed by a position-dependent coupling constant which also depends on the mass of the particle. As a result, lightlike geodesics are not affected whereas massive particles follow geodesics that become mass-dependent, hence the equivalence principle is violated. We make an exact study for geodesics in flat space and a qualitative analysis for those in a spherically symmetric curved background.

To have the correct picture of a black hole as a whole, it is of crucial importance to understand its interior. The singularities that lurk inside the horizon of the usual Kerr-Newman family of black hole solutions signal an endpoint to the physical laws and, as such, should be substituted in one way or another. A proposal that has been around for sometime is to replace the singular region of the spacetime by a region containing some form of matter or false vacuum configuration that can also cohabit with the black hole interior. Black holes without singularities are called regular black holes. In the present work, regular black hole solutions are found within general relativity coupled to Maxwell’s electromagnetism and charged matter. We show that there are objects which correspond to regular charged black holes, whose interior region is de Sitter, whose exterior region is Reissner-Nordström, and the boundary between both regions is made of an electrically charged spherically symmetric coat. There are several types of solutions: regular nonextremal black holes with a null matter boundary, regular nonextremal black holes with a timelike matter boundary, regular extremal black holes with a timelike matter boundary, and regular overcharged stars with a timelike matter boundary. The main physical and geometrical properties of such charged regular solutions are analyzed.

We study a flat brane solution in an effective $5D$ action for cascading gravity in six dimensions, and propose a mechanism to screen extrinsic curvature in the presence of a large tension on the brane. The screening mechanism leaves the bulk Riemann-flat, thus making it simpler to generalize large extra-dimension dark energy models to higher codimensions. By studying an action with cubic interactions for the brane-bending scalar mode, we find that the perturbed action suffers from ghostlike instabilities for positive tension. The solution can be made ghost-free for sufficiently small negative tension, though the connection to $6D$ cascading gravity is less clear in this case.

The use of a running coupling constant in renormalizable theories is well known, but the implementation of this idea for effective field theories with a dimensional coupling constant is, in general, less useful. Nevertheless, there are multiple attempts to define running couplings, including the effects of gravity, with varying conclusions. We sort through many of the issues involved, most particularly the idea of operator mixing and also the kinematics of crossing, using calculations in Yukawa and $\lambda {\varphi }^4$ theories as illustrative examples. We remain in the perturbative regime. In some theories with a high permutation symmetry, such as $\lambda {\varphi }^4$, a reasonable running coupling can be defined. However, in most cases, such as Yukawa and gauge theories, a running coupling fails to correctly account for the energy dependence of the interaction strength. As a by-product we also contrast on-shell and off-shell renormalization schemes and show that operators which are normally discarded, such as those that vanish by the equations of motion, are required for off-shell renormalization of effective field theories. Our results suggest that the inclusion of gravity in the running of couplings is not useful or universal in the description of physical processes.