We investigate some peculiar aspects of the so-called Lee-Wick electrodynamics focusing on physical effects produced by the presence of sources for the vector field. The interactions between stationary charge distributions along parallel branes with arbitrary dimensions is investigated and the energy of a point charge is discussed. Some physical phenomena produced in the vicinity of a Dirac string are also investigated. We consider the Lee-Wick theory for the scalar field, where some interesting effects can emerge with no counterpart for the vector gauge field theory.

We address issues with extant formulations of dissipative effects in the effective field theory (EFT) which describe the post-Newtonian (PN) inspiral of two gravitating bodies by (re)formulating several parts of the theory. Novel ingredients include gauge-invariant spherical fields in the radiation zone; a system zone that preserves time reversal such that its violation arises not from local odd propagation but rather from interaction with the radiation sector in a way that resembles the balayage method; two-way multipoles to perform zone matching within the EFT action; and a double-field radiation-reaction action that is the nonquantum version of the closed time path formalism and generalizes to any theory with directed propagators including theories that are defined by equations of motion rather than an action. This formulation unifies the treatment of outgoing radiation and its reaction force. We demonstrate the method in the scalar, electromagnetic, and gravitational cases by economizing the following: the expression for the radiation source multipoles; the derivation of the leading outgoing radiation and associated reaction force such that it is maximally reduced to mere multiplication; and the derivation of the gravitational next-to-leading PN order. In fact we present a novel expression for the $+1\mathrm{PN}$ correction to all mass multipoles. We introduce useful definitions for multi-index summation, for the normalization of Bessel functions, and for the normalization of the gravitomagnetic vector potential.

We study the low-temperature expansion of the first law of thermodynamics for near-extremal black holes. We show that for extremal black holes with nonvanishing entropy, the leading-order contribution yields an expression for their extremal entropy that is in agreement with the entropy-function result. When their entropy vanishes due to the vanishing of a one-cycle on the horizon, such a leading contribution is always compatible with the first law satisfied by a Bañados-Teitelboim-Zanelli black hole. The universality of these results follows from universal facts about extremal black holes. Our results are consistent with both the presence of local ${\mathrm{AdS}}_2$ and ${\mathrm{AdS}}_3$ near-horizon throats for extremal black holes and with the suggested quantum microscopic descriptions (${\mathrm{AdS}}_2/{\mathrm{CFT}}_1$, Kerr/CFT, and extremal vanishing horizon/CFT).

We study the quantum thermodynamics of a model of quark-gluon plasma of $2+1$ flavors in terms of quasiparticles propagating in a condensate of Polyakov loops. The Polyakov loop is coupled to quasiparticles by means of a gaslike effective potential. This study is useful to identify the effective degrees of freedom propagating in the medium above the critical temperature. Our finding is that a dominant part of the phase transition dynamics is accounted for by the Polyakov loop, hence the thermodynamics can be described without the need for rapidly increasing quasiparticle masses as $T\to T_c$, at variance with respect to standard quasiparticle models.

Very recently the existence of a charged state near the $D_s{\overline{D}}^{*}/D_s^{*}\overline{D}$ threshold was predicted. This state, that we call $Z_{\mathrm{cs}}^{+}$, would be the strange partner of the recently observed $Z_c^{\pm }(3900)$. Using standard techniques of QCD sum rules, we evaluate the three-point function for the vertices $Z_{\mathrm{cs}}^{+}J/\psi K^{+}$, $Z_{\mathrm{cs}}^{+}{\eta }_c{K}^{*+}$ and $Z_{\mathrm{cs}}^{+}{D}_s^{+}{\overline{D}}^{*0}$, and we make predictions for the corresponding decay widths in these channels.

We consider QED on a two-dimensional Euclidean torus with $f$ flavors of massless fermions and flavor-dependent chemical potentials. The dependence of the partition function on the chemical potentials is reduced to a ($2f-2$)-dimensional theta function. At zero temperature, the system can exist in an infinite number of phases characterized by certain values of traceless particle numbers and separated by first-order phase transitions. Furthermore, there exist many points in the ($f-1$)-dimensional space of traceless chemical potentials where two or three phases can coexist for $f=3$ and two, three, four, or six phases can coexist for $f=4$. We conjecture that the maximal number of coexisting phases grows exponentially with increasing $f$.

We study novel types of contributions to the entropy of the Maxwell system defined on a compact manifold such as a torus. These new terms are not related to the physical propagating photons. Rather, these novel contributions emerge as a result of tunneling events when transitions occur between topologically different but physically identical vacuum winding states. We compute two new (topologically protected) types of contributions to the entropy in this system resulting from this dynamics. The first contribution has a negative sign, expressed in terms of the magnetic susceptibility, and it is similar in spirit to topological entanglement entropy discussed in condensed matter systems. The second contribution with a positive sign results from the emergent degeneracy which occurs when the system is placed into a background of external magnetic field. This degeneracy resembles a similar effect that occurs at $\theta =\pi$ in topological insulators. Based on these computations we claim that the Maxwell system defined on the four torus behaves in many respects as a topologically ordered system.

We discuss a holographic model consisting of a $U(1)$ gauge field and a scalar field coupled to a charged AdS black hole under a spatially homogeneous chemical potential. By turning on a higher-derivative interaction term between the $U(1)$ gauge field and the scalar field, a spatially dependent profile of the scalar field is generated spontaneously. We calculate the critical temperature at which the transition to the inhomogeneous phase occurs for various values of the parameters of the system. We solve the equations of motion below the critical temperature, and show that the dual gauge theory on the boundary spontaneously develops a spatially inhomogeneous charge density.

We introduce a general parametrization for non-Abelian gauge fields on the four-dimensional space ${\mathbb{C}\mathbb{P}}^2$. The volume element for the gauge-orbit space or the space of physical configurations is then investigated. The leading divergence in this volume element is obtained in terms of a higher dimensional Wess-Zumino-Witten action, which has previously been studied in the context of Kähler-Chern-Simons theories. This term, it is argued, implies that one needs to introduce a dimensional parameter to specify the integration measure, a step which is a nonperturbative version of the well-known dimensional transmutation in four-dimensional gauge theories.

We revisit the problem of constructing instantons on ADE orbifolds ${\mathbb{R}}^4/\Gamma$ and point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on ${\mathbb{R}}^4/\Gamma$ which are BPS equations for the Yang-Mills equations with an external current. The relation between level sets of the moment maps in the hyper-Kähler quotient construction of the instanton moduli space and sources in the Yang-Mills equations is discussed. We describe two types of spherically symmetric $\Gamma$-equivariant connections on complex V bundles over ${\mathbb{R}}^4/\Gamma$ which are tailored to the way in which the orbifold group acts on the fibers. Some explicit Abelian and non-Abelian SU(2)-invariant solutions to the instanton equations on the orbifold are worked out.

It is observed and illustrated in a greatly simplified example that the idea of AdS/QFT duality can be considered a special case of the Ehrenfest’s correspondence principle between classical and quantum mechanics in the context of relativistic dynamics of fields and renormalization group procedure for effective particles.

We study how to extract information on the neutron star equation of state from the gravitational wave signal emitted during the coalescence of a binary system composed of two neutron stars or a neutron star and a black hole. We use post-Newtonian templates which include the tidal deformability parameter and, when tidal disruption occurs before merger, a frequency cutoff. Assuming that this signal is detected by Advanced LIGO/Virgo or the Einstein Telescope, we evaluate the uncertainties on these parameters using different data-analysis strategies based on the Fisher matrix approach and on recently obtained analytical fits of the relevant quantities. We find that the tidal deformability is more effective than the stellar compactness to discriminate among different possible equations of state.

The quantization of gauge theories usually proceeds through the introduction of ghost fields and Becchi-Rouet-Stora-Tyutin (BRST) symmetry. In the case of quantum gravity in the presence of boundaries, the BRST-invariant boundary value problem for the gauge field operators is nonelliptic, and consequently the definition of the effective action using heat-kernel techniques becomes problematic. This paper examines general classes of BRST-invariant boundary conditions and presents new boundary conditions for quantum gravity that fix the extrinsic curvature on the boundary and lead to a well-defined effective action. This prompts a discussion of the wider issue of nonellipticity in BRST-invariant boundary value problems and when the use of gauge-fixing terms on the boundary can resolve the issue.

By examining the rate of growth of an invariant volume $\mathcal{V}$ of some spacetime region along a divergence-free vector field $v^{\alpha }$, we introduce the concept of a “vector volume” ${\mathcal{V}}_v$. This volume can be defined in various equivalent ways. For example, it can be given as $\mathrm{d}\mathcal{V}(\mu )/\mathrm{d}\mu$, where $v^{\alpha }{\partial }_{\alpha }=\mathrm{d}/\mathrm{d}\mu$ and $\mu$ is a parameter distance along the integral curve of $v$. Equivalently, it can be defined as $\int v^{\alpha }\mathrm{d}{\Sigma }_{\alpha }$, where $\mathrm{d}{\Sigma }_{\alpha }$ is the directed surface element. We find that this volume is especially useful for the description of black holes, but it can be used in other contexts as well. Moreover, this volume has several properties of interest. Among these is the fact that the vector volume is linear with respect to the the choice of vector $v^{\alpha }$. As a result, for example, in stationary axially symmetric spacetimes with timelike Killing vectors $t^{\alpha }$ and axially symmetric Killing vectors ${\varphi }^{\alpha }$, the vector volume of an axially symmetric region with respect to the vector $t^{\alpha }+\Omega {\varphi }^{\alpha }$ is equal for any value of $\Omega$, a consequence of the additional result that ${\varphi }^{\alpha }$ does not contribute to ${\mathcal{V}}_v$. Perhaps of most interest is the fact that in Kerr-Schild spacetimes the volume element for the full spacetime is equal to that of the background spacetime. We discuss different ways of using the vector volume to define volumes for black holes. Finally, we relate our work to the recent widespread thermodynamically motivated study of the “volumes” of black holes associated with nonzero values of the cosmological constant $\Lambda$.

The lambda-CDM model is the best fit to cosmological data and to the observed galactic rotation curves. However, in the absence of a direct detection of dark matter one should explore theories such as modified Newtonian dynamics (MOND), and perhaps also modified gravity theories like fourth order gravity and scalar-tensor-vector gravity (STVG) as possible explanations for the non-Keplerian behavior of galaxy rotation curves. STVG has a modified law for gravitational acceleration which attempts to fit data by fixing two free parameters. We show that, remarkably, the biharmonic equation which we get in the weak field limit of the field equations in a fourth order gravity theory implies a modification of Newtonian acceleration which is precisely of the same repulsive Yukawa form as in the STVG theory, and the corrections could in principle be large enough to try and explain the observed rotation curves. We also explain how our model provides a first principles understanding of MOND. We also show that STVG and fourth order gravity predict an acceleration parameter $a_0$ whose value is of the same order as in MOND.

We calculate the renormalized vacuum energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass $M$ and radius $R$. This study will take into account the static and spherically symmetric solution of Hořava-Lifshitz gravity found by Kehagias-Sfetsos (KS), in both weak field and infrared limits. A slight amplification of the Casimir force between the conducting plates is found. Thermal corrections to the Casimir energy are analyzed. Based on current Casimir effect measurements, a constraint on the $\omega$ parameter of KS metric is also obtained.

A tetrad field with spherical symmetry is applied to the charged field equations of $f(T)$ gravity theory. A special spherically symmetric charged-dS solution is obtained. The scalar torsion of this solution is a vanishing quantity. The spacetime of the derived solution is rewritten as a multiplication of three matrices: The first matrix is a special case of Euler’s angle “so(3),” the second matrix represents a boost transformation, while the third matrix is the square root of the spherically symmetric charged-dS metric. It is shown that the boost matrix is important because it plays an essential role in adjusting the spacetime to become a solution for $f(T)$ theory.

Recently, Lü and Pope proposed critical gravities in [Phys. Rev. Lett. 106, 181302 (2011)]. In this paper we construct analytic brane solutions in critical gravity with matter. The Gibbons-Hawking surface term and junction condition are investigated, and the thin and thick brane solutions are obtained. All these branes are embedded in five-dimensional anti–de Sitter spacetimes. Our solutions are stable against scalar perturbations, and the zero modes of scalar perturbations cannot be localized on the branes.

We study the power of current and future observational Hubble parameter data (OHD) on nonparametric estimations of the dark energy equation of state (EoS), $w(z)$. We propose a new method by conjunction of principal component analysis and the goodness of fit criterion to reconstruct $w(z)$, ensuring the sensitivity and reliability of the extraction of features in the EoS. We also give a new error model to simulate future OHD data, to forecast the power of future OHD on the EoS reconstruction. The result shows that current OHD, despite their lesser quantity, give not only a similar power of reconstruction of dark energy compared to the result given by type Ia supernovae, but also extend the constraint on $w(z)$ up to redshift $z\simeq 2$. Additionally, a reasonable forecast of future data in greater quantity and better quality greatly enhances the reconstruction of dark energy.

Primordial magnetic fields (PMFs), which were generated in the early Universe before recombination, affect the motion of plasma and then the cosmic microwave background and the matter power spectrum. We consider constraints on PMFs with a characteristic correlation length from the observations of the anisotropies of the cosmic microwave background and matter power spectrum. The spectrum of PMFs is modeled with multi-lognormal distributions rather than power-law distribution, and we derive constraints on the strength $|{\mathbf{B}}_k|$ at each wave number $k$ along with the standard cosmological parameters in the flat Universe and the foreground sources. We obtain upper bounds on the field strengths at $k={10}^{-1}$, ${10}^{-2}$, ${10}^{-4}$ and ${10}^{-5}{\mathrm{Mpc}}^{-1}$ as 4.7 nG, 2.1 nG, 5.3 nG, and 10.9 nG ($2\sigma$ C.L.) respectively, while the field strength at $k={10}^{-3}{\mathrm{Mpc}}^{-1}$ turns out to have a finite value as $|{\mathbf{B}}_{k={10}^{-3}}|=6.2\pm 1.3\mathrm{nG}$ ($1\sigma$ C.L.). This finite value is attributed to the finite values of the polarization with negative parity (BB mode) data at $\ell >300$ obtained from the QUAD experiment. If we do not include the BB mode data, we obtain only the upper bound on $B_{k={10}^{-3}}$.