The notion of uniform and/or constant tensor fields of rank $>0$ is incompatible with general curved spacetimes. This work considers the consequences of certain tensor-valued coefficients for Lorentz violation in the Standard-Model extension varying with spacetime position. We focus on two of the coefficients, $a_{\mu }$ and $b_{\mu }$, that characterize Lorentz violation in massive fermions, particularly in those fermions that constitute ordinary matter. We calculate the nonrelativistic Hamiltonian describing these effects, and use it to extract the sensitivity of several precision experiments to coefficient variation.

We present a simple and consistent way to compute correlation functions in interacting theories with nontrivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional ${\mathbb{Z}}_2$-scalar theories. The idea is to perform the path integral by weighting the momentum modes that contribute to it according to their renormalization group (RG) relevance, i.e. we weight each mode according to the value of the running couplings at that scale. In this way, we are able to encode in a loop computation the information regarding the RG trajectory along which we are integrating. We show that depending on the initial condition, or initial point in the phase diagram, we obtain different behaviors of the four-point function at the endpoint of the flow.

A way to describe the hydrodynamics of the quark-gluon plasma using a Dirac-Born-Infeld (DBI) action is proposed, based on the model found by Heisenberg for high energy scattering of nucleons. The expanding plasma is described as a shockwave in a DBI model for a real scalar standing in for the pion, and I show that one obtains a fluid description in terms of a relativistic fluid that near the shock is approximately ideal ($\eta \simeq 0$) and conformal. One can introduce an extra term inside the square root of the DBI action that generates a shear viscosity term in the energy-momentum tensor near the shock, as well as a bulk viscosity, and regulates the behavior of the energy density at the shock, making it finite. The resulting fluid satisfies the relativistic Navier-Stokes equation with $u^{\mu },\rho ,P,\eta$ defined in terms of $\varphi$ and its derivatives. One finds a relation between the parameters of the theory and the quark-gluon plasma thermodynamics, $\alpha /{\beta }^2=\eta /(sT)$, and by fixing $\alpha$ and $\beta$ from usual (low multiplicity) particle scattering, one finds $T\propto m_{\pi }$.

We construct a class of Abelian and non-Abelian local gauge theories that consist only of matter fields of fermions. The Lagrangian is local and does not contain an auxiliary vector field nor a subsidiary condition on the matter fields. It does not involve an extra dimension nor supersymmetry. This Lagrangian can be extended to non-Abelian gauge symmetry only in the case of SU(2) doublet matter fields. We carry out an explicit diagrammatic computation in the leading $1/N$ order to show that massless spin-one bound states appear with the correct gauge coupling. Our diagram calculation exposes the dynamical features that cannot be seen in the formal auxiliary vector-field method. For instance, it shows that the $s$-wave fermion-antifermion interaction in the ${}^3{S}_1$ channel ($\overline{\psi }{\gamma }_{\mu }\psi$) alone cannot form the bound gauge bosons; the fermion-antifermion pairs must couple to the $d$-wave state too. One feature common to our class of Lagrangian is that the Noether current does not exist. Therefore it evades possible conflict with the no-go theorem of Weinberg and Witten on the formation of the non-Abelian gauge bosons.

We present a general formula for the topological part of the effective action for integer quantum Hall systems in higher dimensions, including fluctuations of the gauge field and metric around background fields of a specified topological class. The result is based on a procedure of integrating up from the Dolbeault index density which applies for the degeneracies of Landau levels, combined with some input from the standard descent procedure for anomalies. Features of the topological action in ($2+1$), ($4+1$), ($6+1$) dimensions, including the contribution due to gravitational anomalies, are discussed in some detail.

We extend the Einstein-aether theory to take into account the interaction between a pseudoscalar field, which describes the axionic dark matter, and a timelike dynamic unit vector field, which characterizes the velocity of the aether motion. The Lagrangian of the Einstein-aether-axion theory includes cross terms based on the axion field and its gradient four-vector, on the covariant derivative of the aether velocity four-vector, and on the Riemann tensor and its convolutions. We follow the principles of the effective field theory, and include in the Lagrangian of interactions all possible terms up to the second order in the covariant derivative. The interpretation of new couplings is given in terms of irreducible parts of the covariant derivative of the aether velocity—namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. A spatially isotropic and homogeneous cosmological model with a dynamic unit vector field and axionic dark matter is considered as an application of the established theory; new exact solutions are discussed, which describe models with big rip, pseudo-rip, and de Sitter–type asymptotic behavior.

It is known that the metric and Palatini formalisms of gravity theories have their own interesting features but also suffer from some different drawbacks. Recently, a novel gravity theory called hybrid metric-Palatini gravity was put forward to cure or improve their individual deficiencies. The action of this gravity theory is a hybrid combination of the usual Einstein-Hilbert action and a $f(\mathcal{R})$ term constructed by the Palatini formalism. Interestingly, it seems that the existence of a light and long-range scalar field in this gravity may modify the cosmological and galactic dynamics without conflicting with the laboratory and Solar System tests. In this paper, we focus on the tensor and scalar perturbations of the thick branes in this novel gravity theory. We consider two models as examples, namely, the thick branes constructed by a background scalar field and by pure gravity. The thick branes in both models have no inner structure. However, affected by the hybrid combination of the metric and Palatini formalisms, the graviton zero mode in the first model has inner structure when the parameter in this model is larger than its critical value, which is different from the cases of general relativity and Palatini $f(\mathcal{R})$ gravity. We find that the effective four-dimensional gravity can be reproduced on the brane for both models and the scalar zero mode in the model without a background scalar field cannot be localized on the brane, which avoids a fifth force. Moreover, the stability of both brane systems against the linear perturbations can also be ensured.

We use large-scale cosmological observations to place constraints on the dark-matter pressure, sound speed and viscosity and infer a limit on the mass of warm-dark-matter particles. Measurements of the cosmic microwave background anisotropies constrain the equation of state and sound speed of the dark matter (DM) at last scattering at the per mille level. Since the redshifting of collisionless particles universally implies that these quantities scale like $a^{-2}$ absent shell crossing, we infer that today $w_{(\mathrm{DM})}<10^{-10.0}$, $c_{\mathrm{s},(\mathrm{DM})}^2<10^{-10.7}$ and $c_{\text{vis},(\mathrm{DM})}^2<10^{-10.3}$ at the 99% confidence level. This very general bound can be translated to model-dependent constraints on dark-matter models: For warm dark matter these constraints imply $m>70\mathrm{eV}$, assuming it decoupled while relativistic around the same time as the neutrinos; for a cold relic, we show that $m>100\mathrm{eV}$. We separately constrain the properties of the DM fluid on linear scales at late times and find upper bounds $c_{\mathrm{s},(\mathrm{DM})}^2<10^{-5.9}$ and $c_{\text{vis},(\mathrm{DM})}^2<10^{-5.7}$, with no detection of nondust properties for the DM.

In the case of a structureless string the extrinsic curvature and torsion determine uniquely its shape in three-dimensional ambient space, by way of solution of the Frenet equation. In many physical scenarios there are in addition symmetries that constrain the functional form of the ensuing energy function. For example, the energy of a structureless string should be independent of the way the string is framed in the Frenet equation. Thus the energy should only involve the curvature and torsion as dynamical variables, in a manner that resembles the Hamiltonian of the Abelian Higgs model. Here we investigate the effect of symmetry principles in the construction of Hamiltonians for structureless strings. We deduce from the concept of frame independence that in addition to extrinsic curvature and torsion, the string can also engage a three-dimensional Abelian bulk gauge field as a dynamical variable. We find that the presence of a bulk gauge field gives rise to a long-range interaction between different strings. Moreover, when this gauge field is subject to Chern-Simons self-interaction, it becomes plausible that interacting strings are subject to fractional statistics in three space dimensions.

The dependence of the Landau gauge two-point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to ${128}^4$ and for two lattice spacings 0.10 fm and 0.06 fm corresponding to volumes of $\sim (13\mathrm{fm}{)}^4$ and $\sim (8\mathrm{fm}{)}^4$, respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators change with the lattice spacing $a$ in the infrared region, with the gluon propagator having a stronger dependence on $a$ compared to the ghost propagator. In what concerns the strong coupling constant ${\alpha }_s(p^2)$, as defined from gluon and ghost two-point functions, the simulations show a sizeable dependence on the lattice spacing for the infrared region and for momenta up to $\sim 1\mathrm{GeV}$.

We construct four kinds of $Z_3$-symmetric three-dimensional (3D) Potts models, each with a different number of states at each site on a 3D lattice, by extending the 3D 3-state Potts model. Comparing the ordinary Potts model with the four $Z_3$-symmetric Potts models, we investigate how $Z_3$ symmetry affects the sign problem and see how the deconfinement transition line changes in the $\mu \text{−}\kappa$ plane as the number of states increases, where $\mu$ ($\kappa$) plays a role of chemical potential (temperature) in the models. We find that the sign problem is almost cured by imposing $Z_3$ symmetry. This mechanism may happen in $Z_3$-symmetric QCD-like theory. We also show that the deconfinement transition line has stronger $\mu$ dependence with respect to increasing the number of states.

We discuss a possibility to explain the LHC diphoton excesses at 750 GeV by the new scalar $X$ that couples to the gauge bosons through the loop of new massive particles with standard model charges. We assume that the new particles decay into the standard model particles at the tree level. We systematically examine the models that preserve the vacuum stability and the perturbativity up to the Planck scale. When we take scalars for the new particles, we find that only a few diquark and dilepton models can explain the observed diphoton cross section without conflicting the experimental mass bounds. When we take vectorlike fermions for the new particles, we find rather different situations depending on whether their couplings to $X$ are scalar or pseudoscalar type. In the former case, a few models are allowed if we introduce only one species of fermions. The more fermions we introduce, the more models are allowed. In the latter case, most of the models are allowed because of the large coupling between $X$ and photon. It is interesting that the allowed mass regions of the scalar particles might be reached by the next lepton colliders.

The proton radius puzzle, i.e. the large discrepancy in the extraction of the proton charge radius between regular and muonic hydrogen, challenges our understanding of the structure of the proton. It can also be an indication of a new force that couples to muons, but not to electrons. An effective field theory analysis using nonrelativistic quantum electrodynamics (NRQED) indicates that the muonic hydrogen result can be interpreted as a large, compared to some model estimates, muon-proton spin-independent contact interaction. The muonic hydrogen result can be tested by a muon-proton scattering experiment, MUSE, that is planned at the Paul Scherrer Institute in Switzerland. The typical momenta of the muons in this experiment are of the order of the muon mass. In this energy regime the muons are relativistic but the protons are still nonrelativistic. The interaction between the muons and protons can be described by a hybrid QED-NRQED effective field theory. We present some elements of this effective field theory. In particular we consider $\mathcal{O}(Z\alpha )$ scattering up to power $m^2/M^2$, where $m$ ($M$) is the muon (proton) mass and $Z=1$ for a proton, and $\mathcal{O}(Z^2{\alpha }^2)$ scattering at leading power. We show how the former reproduces Rosenbluth scattering up to power $m^2/M^2$ and the latter the relativistic scattering off a static potential. Proton structure corrections at $\mathcal{O}(Z^2{\alpha }^2)$ will be considered in a subsequent paper.

We study the properties of a D6-brane probe in the Aharony-Bergman-Jafferis-Maldacena (ABJM) background with smeared massless dynamical quarks in the Veneziano limit. Working at zero temperature and nonvanishing charge density, we show that the system undergoes a quantum phase transition in which the topology of the brane embedding changes from a black hole to a Minkowski embedding. In the unflavored background the phase transition is of second order and takes place when the charge density vanishes. We determine the corresponding critical exponents and show that the scaling behavior near the quantum critical point has multiplicative logarithmic corrections. In the background with dynamical quarks the phase transition is of first order and occurs at nonzero charge density. In this case we compute the discontinuity of several physical quantities as functions of the number $N_f$ of unquenched quarks of the background.

We show how, by assuming at least eight real timelike supersymmetries in the maximally supersymmetric three-dimensional ungauged supergravity and a further simplifying ansatz, we are naturally led to a pair of Liouville field equations. These are solvable in terms of two meromorphic functions, and we present a novel and interesting large class of quarter-supersymmetric backgrounds. We also show that there are no solutions that preserve only six or seven real timelike supersymmetries. The solution relies on the classification of complex spinors of Spin(8) to which the problem quickly reduces.

We consider quantum entanglement of three accelerating qubits, each of which is locally coupled with a real scalar field, without causal influence among the qubits or among the fields. The initial states are assumed to be the GHZ and W states, which are the two representative three-partite entangled states. For each initial state, we study how various kinds of entanglement depend on the accelerations of the three qubits. All kinds of entanglement eventually suddenly die if at least two of three qubits have large enough accelerations. This result implies the eventual sudden death of all kinds of entanglement among three particles coupled with scalar fields when they are sufficiently close to the horizon of a black hole.

The explicit solution for a Kerr-Newman black hole immersed in an external magnetic field, sometimes called the Melvin-Kerr-Newman black hole, has been derived by Ernst and Wild in 1976. In this paper, we clarify the first law and Smarr formula for black holes in a magnetic field. We then define the unique mass which is integrable and reduces to the Kerr-Newman mass in the absence of magnetic field. This defines the thermodynamic potentials of the black hole. Quite strikingly, the mass coincides with the standard Christodoulou-Ruffini mass of a black hole as a function of the entropy, angular momentum and electric charge.

We calculate the mean free path in a hot and dense nuclear environment for a fermionic dark matter particle candidate in the $\sim \mathrm{GeV}$ mass range interacting with nucleons via scalar and vector effective couplings. We focus on the effects of density and temperature in the nuclear medium in order to evaluate the importance of the final state blocking in the scattering process. We discuss qualitatively possible implications for opacities in stellar nuclear scenarios, where dark matter may be gravitationally accreted.

We use the latest compilation of observational Hubble parameter measurements estimated with the differential evolution of cosmic chronometers, in combination with the local value of the Hubble constant recently measured with 2.4% precision, to constrain the cosmological scenario where dark energy interacts directly with the dark matter sector. To diminish the degeneracy between the parameters we additionally consider standard probes, such as supernovae type Ia from joint light-curve analysis samples, baryon acoustic oscillation distance measurements (BAO), and cosmic microwave background data from Planck 2015 estimations. Our analysis shows that the direct interaction between dark energy and dark matter is mildly favored, while the dark energy equation-of-state parameter is $w<-1$ at a $3\sigma$ confidence level.