We study entanglement entropy (EE) in conformal field theories (CFTs) in Minkowski space with a planar boundary or with a planar defect of any codimension. In any such boundary CFT or defect CFT (DCFT), we consider the reduced density matrix and associated EE obtained by tracing over the degrees of freedom outside of a (hemi)sphere centered on the boundary or defect. Following Casini, Huerta, and Myers, we map the reduced density matrix to a thermal density matrix of the same theory on hyperbolic space. The EE maps to the thermal entropy of the theory on hyperbolic space. For boundary CFTs and DCFTs dual holographically to Einstein gravity theories, the thermal entropy is equivalent to the Bekenstein–Hawking entropy of a hyperbolic black brane. We show that the horizon of the hyperbolic black brane coincides with the minimal area surface used in Ryu and Takayanagi’s conjecture for the holographic calculation of EE. We thus prove their conjecture in these cases. We use our results to compute the Rényi entropies and EE in DCFTs in which the defect corresponds to a probe brane in a holographic dual.

We investigate the problem of counting $1/16$ Bogomol’nyi-Prasad-Sommerfield (BPS) operators in $\mathcal{N}=4$ super-Yang-Mills theory at weak coupling. We present the complete set of $1/16$ BPS operators in the infinite-$N$ limit, which agrees with the counting of free BPS multigraviton states in the gravity dual ${\mathrm{AdS}}_5\times S^5$. Further, we conjecture that all $1/16$ BPS operators in $\mathcal{N}=4$ super-Yang-Mills theory are of the multigraviton form, and give numerical evidence for this conjecture. We discuss the implication of our conjecture and the seeming failure in reproducing the entropy of large $1/16$ BPS black holes in ${\mathrm{AdS}}_5$.

We present a new computational method for smoothly matching general relativistic ideal magnetohydrodynamics (MHD) to its force-free limit. The method is based on a flux-conservative formalism for MHD and its force-free limit and a vector potential formulation for the induction equation to maintain the zero divergence constraint for the magnetic field. The force-free formulation we adopt evolves the magnetic field and the Poynting vector, instead of the magnetic and electric fields. We show that our force-free code passes a robust suite of tests, performed both in one-dimensional flat spacetime and in three-dimensional black hole spacetimes. We also demonstrate that our matching technique successfully reproduces the aligned rotator force-free solution. Our new techniques are suitable for studying electromagnetic effects and predicting electromagnetic signals arising in many different curved spacetime scenarios. For example, we can treat spinning neutron stars, either in isolation or in compact binaries, that have MHD interiors and force-free magnetospheres.

We evaluated the scattering amplitude of neutral scalar particles at one-loop order in the context of effective field theory of quantum gravity in the presence of a cosmological constant. Our study suggests that quantum gravitational corrections induce an asymptotic freedom behavior to the $\lambda {\varphi }^4$ theory, for a positive cosmological constant. This result hints that a complete theory of quantum gravity can play an important role in avoiding the issue of triviality in quantum field theory.

Many generic arguments support the existence of a minimum spacetime interval $L_0$. Such a “zero-point” length can be naturally introduced in a locally Lorentz invariant manner via Synge’s world function biscalar $\Omega (p,P)$ which measures squared geodesic interval between spacetime events $p$ and $P$. I show that there exists a nonlocal deformation of spacetime geometry given by a disformal coupling of metric to the biscalar $\Omega (p,P)$, which yields a geodesic interval of $L_0$ in the limit $p\to P$. Locality is recovered when $\Omega (p,P)\gg L_0^2/2$. I discuss several conceptual implications of the resultant small-scale structure of spacetime for QFT propagators as well as spacetime singularities.

We present three-dimensional simulations of the dynamical bar-mode instability in magnetized and differentially rotating stars in full general relativity. Our focus is on the effects that magnetic fields have on the dynamics and the onset of the instability. In particular, we perform ideal-magnetohydrodynamics simulations of neutron stars that are known to be either stable or unstable against the purely hydrodynamical instability, but to which a poloidal magnetic field in the range of ${10}^{14}–{10}^{16}\mathrm{G}$ is superimposed initially. As expected, the differential rotation is responsible for the shearing of the poloidal field and the consequent linear growth in time of the toroidal magnetic field. The latter rapidly exceeds in strength the original poloidal one, leading to a magnetic-field amplification in the stars. Weak initial magnetic fields, i.e., $\lesssim {10}^{15}\mathrm{G}$, have negligible effects on the development of the dynamical bar-mode instability, simply braking the stellar configuration via magnetic-field shearing. On the other hand, strong magnetic fields, i.e., $\gtrsim {10}^{16}\mathrm{G}$, can suppress the instability completely, with the precise threshold being dependent also on the amount of rotation. As a result, it is unlikely that very highly magnetized neutron stars can be considered as sources of gravitational waves via the dynamical bar-mode instability.

In Einstein-Maxwell gravity with a conformally coupled scalar field, the black hole found by Bocharova, Bronnikov, Melnikov, and Bekenstein (BBMB) breaks when embedded in the external magnetic field of the Melvin universe. The situation improves in the presence of acceleration, allowing one to build a magnetized and accelerating BBMB black hole with a thin membrane. But to overcome this and other disadvantages of BBMB spacetimes, a new class of black holes, including the rotating case, is proposed for the conformal matter coupling under consideration.

In the context of the Randall-Sundrum braneworld, the minimal geometric deformation approach is used to generate an analytic interior solution to four-dimensional effective Einstein field equations for a spherically symmetric compact distribution. This solution represents the braneworld version of the well-known Tolman IV solution in general relativity. By using this analytic solution, an exhaustive analysis of the braneworld effects on realistic stellar interiors is developed, finding strong evidence in favor of the hypothesis that compactness is reduced due to bulk effects on stellar configurations.

We present a model for determining the dimensionless spin parameter and mass of the black hole remnant of black hole-neutron star mergers with parallel orbital angular momentum and initial black hole spin. This approach is based on the Buonanno, Kidder, and Lehner method for binary black holes, and it is successfully tested against the results of numerical-relativity simulations: the dimensionless spin parameter is predicted with absolute error $\lesssim 0.02$, whereas the relative error on the final mass is $\lesssim 2\%$, its distribution in the tests being pronouncedly peaked at 1%. Our approach and the fit to the torus remnant mass reported in [57] thus constitute an easy-to-use analytical model that accurately describes the remnant of black hole-neutron star mergers. The space of parameters consisting of the binary mass ratio, the initial black hole spin, and the neutron star mass and equation of state is investigated. We provide indirect support to the cosmic censorship conjecture for black hole remnants of black hole-neutron star mergers. We show that the presence of a neutron star affects the quasinormal mode frequency of the black hole remnant, thus suggesting that the ringdown epoch of the gravitational wave signal may virtually be used to (1) distinguish black hole-black hole from black hole-neutron star mergers and to (2) constrain the neutron star equation of state.

We develop a formalism for general relativistic $N$-body simulations in the weak field regime, suitable for cosmological applications. The problem is kept tractable by retaining the metric perturbations to first order, the first derivatives to second order, and second derivatives to all orders, thus taking into account the most important nonlinear effects of Einstein gravity. It is also expected that any significant “backreaction” should appear at this order. We show that the simulation scheme is feasible in practice by implementing it for a plane-symmetric situation and running two test cases, one with only cold dark matter, and one which also includes a cosmological constant. For these plane-symmetric situations, the deviations from the usual Newtonian $N$-body simulations remain small and, apart from a nontrivial correction to the background, can be accurately estimated within the Newtonian framework. The correction to the background scale factor, which is a genuine backreaction effect, can be robustly obtained with our algorithm. Our numerical approach is also naturally suited for the inclusion of extra relativistic fields and thus for dark energy or modified gravity simulations.

We investigate the main features of the flat Friedmann-Lemaître-Robertson-Walker cosmological models in the $f(T)$ modified gravity regime. In particular, a general approach to find out exact cosmological solutions in $f(T)$ gravity is discussed. Instead of taking into account phenomenological models, we consider as a selection criterion, the existence of Noether symmetries in the cosmological $f(T)$ pointlike Lagrangian. We find that only the $f(T)=f_0{T}^n$ model admits extra Noether symmetries. The existence of extra Noether integrals can be used in order to simplify the system of differential equations (equations of motion) as well as to determine the integrability of the $f(T)=f_0{T}^n$ cosmological model. Within this context, we can solve the problem analytically and thus we provide the evolution of the main cosmological functions such as the scale factor of the Universe, the Hubble expansion rate, the deceleration parameter, and the linear matter perturbations. We show that the $f(T)=f_0{T}^n$ cosmological model suffers from two basic problems. The first problem is related to the fact that the deceleration parameter is constant which means that it never changes sign, and therefore the Universe always accelerates or always decelerates depending on the value of $n$. Second, we find that the clustering growth rate remains always equal to unity implying that the recent growth data disfavor the $f(T)=f_0{T}^n$ gravity. Finally, we prove that the $f(T)=f_0{T}^n$ gravity can be cosmologically equivalent with the $f(R)=R^n$ gravity model and the time varying vacuum model $\Lambda (H)=3\gamma H^2$ (for $n^{-1}=1-\gamma$) because the above cosmological scenarios share exactly the same Hubble expansion, despite the fact that the three models have a different geometrical origin. Finally, some important differences with power-law $f(R)$ gravity are pointed out.

We study numerical evolutions of nonlinear gravitational waves in moving-puncture coordinates. We adopt two different types of initial data—Brill and Teukolsky waves—and evolve them with two independent codes producing consistent results. We find that Brill data fail to produce long-term evolutions for common choices of coordinates and parameters, unless the initial amplitude is small, while Teukolsky wave initial data lead to stable evolutions, at least for amplitudes sufficiently far from criticality. The critical amplitude separates initial data whose evolutions leave behind flat space from those that lead to a black hole. For the latter we follow the interaction of the wave, the formation of a horizon, and the settling down into a time-independent trumpet geometry. We explore the differences between Brill and Teukolsky data and show that for less common choices of the parameters—in particular negative amplitudes—Brill data can be evolved with moving-puncture coordinates and behave similarly to Teukolsky waves.

We study the thermodynamics of higher-dimensional singly spinning asymptotically AdS black holes in the canonical (fixed $J$) ensemble of extended phase space, where the cosmological constant is treated as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Along with the usual small/large black hole phase transition, we find a new phenomenon of reentrant phase transitions for all $d\ge 6$ dimensions, in which a monotonic variation of the temperature yields two phase transitions from large to small and back to large black holes. This situation is similar to that seen in multicomponent liquids.

Studies of the QCD phase diagram must properly include nucleonic degrees of freedom and their thermodynamics in the range of baryon chemical potentials characteristic of nuclear matter. A useful framework for incorporating relevant nuclear physics constraints in this context is a chiral nucleon-meson effective Lagrangian. In the present paper, such a chiral nucleon-meson model is extended with systematic inclusion of mesonic fluctuations using the functional renormalization group approach. The resulting description of the nuclear liquid-gas phase transition shows a remarkable agreement with three-loop calculations based on in-medium chiral effective field theory. No signs of a chiral first-order phase transition and its critical endpoint are found in the region of applicability of the model, i.e. up to twice the density of normal nuclear matter and at temperatures $T\lesssim 100\mathrm{MeV}$. Fluctuations close to the critical point of the first-order liquid-gas transition are also examined with a detailed study of chiral and baryon number susceptibilities.

We discuss the role of the $U(1)$ axial symmetry for the scalar and pseudoscalar meson mass spectrum of QCD at finite temperature, above the chiral transition at $T_c$, using a chiral effective Lagrangian model, which, in addition to the usual chiral condensate $⟨\overline{q}q⟩$, also includes a (possible) genuine $U(1{)}_A$-breaking condensate that (possibly) survives across the chiral transition. The motivations for considering this Lagrangian (and a critical comparison with other effective Lagrangian models existing in the literature) are presented. A detailed comparison between the case $N_f\ge 3$ and the (remarkably different) case $N_f=2$ is performed. The results obtained in the case $N_f=2$ are also critically compared with the available lattice results.

We study the low energy implications, especially the particle spectroscopy, of SO(10) grand unification in which the SO(10) symmetry is broken to the Standard Model gauge group with a single pair of ($144+\overline{144}$)-dimensional Higgs multiplet (unified Higgs sector). In this class of models, the asymptotic relation $Y_b\approx Y_{\tau }\approx Y_t/6$ among the third generation quark and lepton Yukawa couplings can be derived. This relation leads to the prediction $\tan \beta \approx 14$, where $\tan \beta$ is the well known Minimal Supersymmetric Standard Model parameter. We find that this type of Yukawa coupling unification (YU) is realized only by employing nonuniversal soft supersymmetry breaking terms, dictated by SO(10) symmetry, for the gauginos. A 125 GeV Higgs boson mass is also found to be consistent with YU at the $\sim 5\%$ level. Without imposing a constraint on the relic abundance of dark matter in these models, the squark and slepton masses, with the exception of the top squark, exceed 2 TeV and the gluino is heavier than 1 TeV. We show that the neutralino in this model is an acceptable dark matter candidate through the neutralino–top squark coannihilation scenario, with the top squark being relatively light ($\gtrsim 500\mathrm{GeV}$).

Current searches for direct production of scalar top quarks, or stops, in supersymmetry focus on their decays into $b{W}^{+}{\tilde{\chi }}^0$ by way of $t{\tilde{\chi }}^0$ and $b{\tilde{\chi }}^{+}$. While the polarization of the top quark depends on the stop mixing, the chargino turns out to be fully polarized when the bottom Yukawa coupling can be neglected relative to the top Yukawa coupling. We compute the energy and angular spectra of the charged lepton in the chargino channel, which could serve as the spin analyzer of the chargino. In addition, we demonstrate the top polarization could have a significant impact on the selection efficiencies in direct stop samples at the LHC, while the effect from the chargino polarization is less pronounced. Two observables in the laboratory frame, the opening angle between the charged lepton and the $b$ quark and the energy of the $b$ quark, are also proposed to optimize searches in the chargino channel versus the top channel.

We explore the phase space spanned by the temperature and the chemical potential for four-flavor lattice QCD using the Wilson-clover quark action. In order to determine the order of the phase transition, we apply finite-size scaling analyses to gluonic and quark observables, including plaquette, Polyakov loop, and quark number density, and examine their susceptibility, skewness, kurtosis, and Challa-Landau-Binder cumulant. Simulations were carried out on lattices of a temporal size fixed at $N_{\mathrm{t}}=4$ and spatial sizes chosen from $6^3$ up to ${10}^3$. Configurations were generated using the phase-reweighting approach, while the value of the phase of the quark determinant was carefully monitored. The $\mu$-parameter reweighting technique is employed to precisely locate the point of the phase transition. Among various approximation schemes for calculating the ratio of quark determinants needed for $\mu$ reweighting, we found the Taylor expansion of the logarithm of the quark determinant to be the most reliable. Our finite-size analyses show that the transition is first order at $(\beta ,\kappa ,\mu /T)=(1.58,0.1385,0.584\pm 0.008)$, where $(m_{\pi }/m_{\rho },T/m_{\rho })=(0.822,0.154)$. It weakens considerably at $(\beta ,\kappa ,\mu /T)=(1.60,0.1371,0.821\pm 0.008)$, where $(m_{\pi }/m_{\rho },T/m_{\rho })=(0.839,0.150)$, and a crossover rather than a first-order phase transition cannot be ruled out.

A two-component model (TCM) for single-particle $p_t$ spectra describes 200 GeV $p$-$p$ data accurately. Based on that TCM a spectrum hard component was isolated that is related quantitatively to pQCD predictions for jet fragmentation down to low jet energies ($\approx 3\mathrm{GeV}$). Here we address jet-related structure in 2D trigger-associated (TA) correlations as a more-detailed method to explore the kinematic limits of low-energy jet production and low-momentum jet fragment structure in $p$-$p$ collisions. We derive a TCM for $p$-$p$ TA correlations that can be used to isolate 2D jet-related structure. Inferred minimum-bias (mainly low-energy) jet-related TA correlations may challenge several major assumptions about jet production in $p$-$p$ (and A-A) collisions. These results should be relevant to $p$-$p$ underlying-event studies and Monte Carlo predictions of multiple parton interactions.

In highly improved staggered quark simulations by the HPQCD, MILC, and Fermilab Lattice collaborations, both the light quarks and the charm quark are staggered. We extend chiral perturbation theory for staggered quarks to include such all-staggered heavy-light mesons. We assume that the heavy quark action is sufficiently improved that we may take $a{m}_Q\ll 1$ (where $m_Q$ is the heavy quark mass), but also that $m_Q\gg {\Lambda }_{\mathrm{QCD}}$ so that a continuum heavy quark expansion is appropriate. We develop this effective chiral theory through next-to-leading order, and use it to study the pattern of taste splittings in the heavy-light meson and to compute the leptonic decay constant of the heavy-light meson to one loop in the chiral expansion.