The chiral phase transition of the quark sector of QCD is investigated within the Hamiltonian approach in Coulomb gauge. Finite temperature $T$ is introduced by compactifying one spatial dimension, which makes all thermodynamical quantities accessible from the ground state on the spatial manifold ${\mathbb{R}}^2\times S^1(1/T)$. Neglecting the coupling between quarks and transversal gluons, the equations of motion of the quark sector are solved numerically and the chiral quark condensate is evaluated and compared to the results of the usual canonical approach to finite-temperature Hamiltonian QCD based on the density operator of the grand canonical ensemble. For zero bare quark masses, we find a second-order chiral phase transition with a critical temperature of about 92 MeV. If the Coulomb string tension is adjusted to reproduce the phenomenological value of the quark condensate, the critical temperature increases to 118 MeV.

Results from a search for supersymmetry in events with four or more charged leptons (electrons, muons and taus) are presented. The analysis uses a data sample corresponding to $36.1{\mathrm{fb}}^{-1}$ of proton–proton collisions delivered by the Large Hadron Collider at $\sqrt{s}=13\mathrm{TeV}$ and recorded by the ATLAS detector. Four-lepton signal regions with up to two hadronically decaying taus are designed to target a range of supersymmetric scenarios that can be either enriched in or depleted of events involving the production and decay of a $Z$ boson. Data yields are consistent with Standard Model expectations and results are used to set upper limits on the event yields from processes beyond the Standard Model. Exclusion limits are set at the 95% confidence level in simplified models of general gauge mediated supersymmetry, where Higgsino masses are excluded up to 295 GeV. In $R$-parity-violating simplified models with decays of the lightest supersymmetric particle to charged leptons, lower limits of 1.46, 1.06, and 2.25 TeV are placed on wino, slepton and gluino masses, respectively.

We study dilaton-gravity theories in two dimensions obtained by dimensional reduction of higher-dimensional nonrelativistic theories. Focusing on certain families of extremal charged hyperscaling violating Lifshitz black branes in Einstein-Maxwell-scalar theories with an extra gauge field in four dimensions, we obtain ${\mathrm{AdS}}_2$ backgrounds in the near-horizon throats. We argue that these backgrounds can be obtained in equivalent theories of two-dimensional dilaton-gravity with an extra scalar, descending from the higher-dimensional scalar, and an interaction potential with the dilaton. A simple subcase here is the relativistic black brane in Einstein-Maxwell theory. We then study linearized fluctuations of the metric, dilaton and the extra scalar about these ${\mathrm{AdS}}_2$ backgrounds. The coefficient of the leading Schwarzian derivative term is proportional to the entropy of the (compactified) extremal black branes.

Recently, a rotating black hole solution was found in vector-tensor Galileon modified gravity that has some significant differences from the Kerr black hole solution. We study the iron line shape that is part of the reflection spectrum of accretion disks around black holes in this new black hole solution. We simulate and compare the iron lines of this solution with those of the Kerr solution to see if the technique of iron line spectroscopy can be used as a tool to test vector-tensor Galileon modified gravity. Our analysis shows that current x-ray facilities can, in principle, be used to test and place constraints on vector-tensor Galileon modified gravity in the strong-coupling and ultraspinning regimes.

A way to obtain a correspondence between the first order and second order formalism is studied. By introducing a Lagrange multiplier coupled to the covariant derivative of the metric, a metricity constraint is implemented. The new contributions which comes from the variation of the Lagrange multiplier transforms the field equations from the first order to the second order formalism, yet the action is formulated in the first order. In this way all the higher derivatives terms in the second order formalism appear as derivatives of the Lagrange multiplier. Using the same method for breaking metricity condition and building conformal invariant theory is briefly discussed, so the method goes beyond just the study of first order or second formulations of gravity, in fact vast new possible theories of gravity are envisioned this way.

There has been a striking realization that physics resolving the black hole information paradox could imply postmerger gravitational wave echoes. We here report on evidence for echoes from the LIGO compact binary merger events, GW151226, GW170104, GW170608, GW170814, as well as the neutron star merger GW170817. There is a signal for each event with a $p$-value of order 1% or sometimes significantly less. Our study begins with the comparison of echoes from a variety of horizonless exotic compact objects. Next we investigate the effects of spin. The identification of the more generic features of echoes then leads to the development of relatively simple windowing methods, in both time and frequency space, to extract a signal from noise. The time delay between echoes is inversely related to the spacing between the spectral resonances, and it is advantageous to look directly for this resonance structure. We find time delays for the first four events that are consistent with a simple model that accounts for mass and spin of the final object, while for the neutron star merger the final mass and spin are constrained.

The generalized Chaplygin gas is usually defined as a barotropic perfect fluid with an equation of state $p=-A{\rho }^{-\alpha }$, where $\rho$ and $p$ are the proper energy density and pressure, respectively, and $A$ and $\alpha$ are positive real parameters. It has been extensively studied in the literature as a quartessence prototype unifying dark matter and dark energy. Here, we consider an extended family of generalized Chaplygin gas models parametrized by three positive real parameters $A$, $\alpha$, and $\beta$, which, for two specific choices of $\beta$ [$\beta =1$ and $\beta =(1+\alpha )/(2\alpha )$], is described by two different Lagrangians previously identified in the literature with the generalized Chaplygin gas. We show that, for $\beta >1/2$, the linear stability conditions and the maximum value of the sound speed $c_s$ are regulated solely by $\beta$, with $0\le c_s\le 1$ if $\beta \ge 1$. We further demonstrate that in the non-relativistic regime the standard equation of state $p=-A{\rho }^{-\alpha }$ of the generalized Chaplygin gas is always recovered, while in the relativistic regime this is true only if $\beta =(1+\alpha )/(2\alpha )$. We present a regularization of the ($\alpha \to 0$, $A\to \infty$) limit of the generalized Chaplygin gas, showing that it leads to a logarithmic Chaplygin gas model with an equation of state of the form $p=\mathcal{A}\ln (\rho /{\rho }_{*})$, where $\mathcal{A}$ is a real parameter and ${\rho }_{*}>0$ is an arbitrary energy density. We finally derive its Lagrangian formulation.

We revisit the question of how to calculate correlations of the curvature perturbation, $\zeta$, using the $\delta N$ formalism when one cannot employ a truncated Taylor expansion of $N$. This problem arises when one uses lattice simulations to probe the effects of isocurvature modes on models of reheating. Working in real space, we use an expansion in the cross-correlation between fields at different positions and present simple expressions for observables such as the power spectrum and the reduced bispectrum, $f_{\mathrm{NL}}$. These take the same form as those of the usual $\delta N$ expressions, but with the derivatives of $N$ replaced by nonperturbative $\delta N$ coefficients. We test the validity of this expansion and, when compared to others in the literature, argue that our expressions are particularly well suited for use with simulations.

Gravitational wave detectors in the LIGO/Virgo frequency band are able to measure the individual masses and the composite tidal deformabilities of neutron-star binary systems. This paper demonstrates that high accuracy measurements of these quantities from an ensemble of binary systems can in principle be used to determine the high density neutron-star equation of state exactly. This analysis assumes that all neutron stars have the same thermodynamically stable equation of state, but does not use simplifying approximations for the composite tidal deformability or make additional assumptions about the high density equation of state.

Equation (19) of Phys. Rev. D 67, 094003 (2003) turns out to contain mistakes, as pointed out recently in Phys. Rev. D 97, 074019 (2018) by H. H. Matevosyan et al. In particular, Eq. (19) contains an erroneous explicit dependence on the angle ${\varphi }^l$, and the terms linear in $\widehat{g}$ have an opposite sign with respect to what one would deduce from Fig. 1. As a result, the expressions for the projection of the $\cos (2({\varphi }_R-{\varphi }_{\overline{R}}))$ azimuthal dependence are incorrect. Specifically, Eqs. (34), (37), and (38) should all vanish, which means that the $\cos (2({\varphi }_R-{\varphi }_{\overline{R}}))$ projection is not a measure of the di-hadron fragmentation function $G_1^{\perp }$, as concluded in the paper. The vanishing of the projection explains the nonobservation of the related asymmetry in the recent experimental search by the BELLE Collaboration (A. Abdesselam et al., arXiv:1505.08020). We refer to Phys. Rev. D 97, 074019 (2018) for the correct version of Eq. (19) and for an alternative nonzero projection of the asymmetry that does probe the function $G_1^{\perp }$.

Electric fields may decay by quantum tunneling: as calculated by Schwinger, an electron-positron pair may be summoned from the vacuum. In this paper, I calculate the pair-production rate at nonzero temperatures. I find that, at high temperatures, the decay rate is dominated by a new instanton that involves both thermal fluctuation and quantum tunneling; this decay is exponentially faster than the rate in the literature. I also calculate the decay rate when the electric field wraps a compact circle (at zero temperature). The same new instanton also governs this rate: I find that, for small circles, decay is dominated by a process that drops the electric field by one unit, but does not produce charged particles.

The small-$x$ evolution of protons is determined from numerical solutions of the JIMWLK equations, starting from an initial condition at moderate $x$ for a finite size proton. The resulting dipole amplitude is used to calculate the total reduced cross section ${\sigma }_r$ and charm reduced cross section ${\sigma }_{rc}$, as well as diffractive vector meson production. We compare results to experimental data from HERA and discuss fundamental problems arising from the regime sensitive to nonperturbative physics. We emphasize that information on the gluonic content of the proton, gluon spatial distributions and correlations over wide ranges in $x$, which can in principle be constrained by our study, are essential ingredients for describing the initial state in proton-proton and proton-ion collisions. Future electron nucleus collisions at an electron-ion collider will provide important additional insight for heavier nuclei. We further demonstrate that it is not possible to rigorously probe the saturation regime of the color glass condensate framework in electron-proton collisions at HERA energies and that electron-heavy ion collisions will be essential to access its regime of validity.

We have measured the cross section and single-spin asymmetries from forward $W^{\pm }\to {\mu }^{\pm }\nu$ production in longitudinally polarized $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$ using the PHENIX detector at the Relativistic Heavy Ion Collider. The cross sections are consistent with previous measurements at this collision energy, while the most forward and backward longitudinal single spin asymmetries provide new insights into the sea quark helicities in the proton. The charge of the $W$ bosons provides a natural flavor separation of the participating partons.

Using $\zeta$-function regularization, we study the one-loop effective action of fundamental strings in $Ad{S}_5\times S^5$ dual to the latitude $\frac{1}{4}$-BPS Wilson loop in $\mathcal{N}=4$ super-Yang-Mills theory. To avoid certain ambiguities inherent to string theory on curved backgrounds we subtract the effective action of the holographic $\frac{1}{2}$-BPS Wilson loop. We find agreement with the expected field theory result at first order in the small latitude angle expansion but discrepancies at higher order.

The dimensional reduction of a generic theory on a curved internal space such as a sphere does not admit a consistent truncation to a finite set of fields that includes the Yang-Mills gauge bosons of the isometry group. In rare cases, e.g., the $S^7$ reduction of 11-dimensional supergravity, such a consistent “Pauli reduction” does exist. In this paper, we study this existence question in two examples of $S^2$ reductions of supergravities. We do this by making use of a relation between certain $S^2$ reductions and group manifold $S^3=SU(2)$ reductions of a theory in one dimension higher. By this means, we establish the nonexistence of a consistent $S^2$ Pauli reduction of five-dimensional minimal supergravity. We also show that a previously discovered consistent Pauli reduction of six-dimensional Salam-Sezgin supergravity can be elegantly understood via a group-manifold reduction from seven dimensions.

We study the four-dimensional (4D) scalar potential arising from a generalized type IIA flux superpotential including the (non)geometric fluxes. First, we show that using a set of peculiar flux combinations, the 4D scalar potential can be formulated into a very compact form. This is what we call the “symplectic formulation” from which one could easily anticipate the ten-dimensional origin of the effective scalar potential. We support our formulation through an alternate derivation of the scalar potential via considering the double field theory reduction on a generic Calabi-Yau orientifold. In addition, we also exemplify the insights of our formulation with explicit computations for two concrete toroidal examples using orientifolds of the complex threefolds ${\mathbb{T}}^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ and ${\mathbb{T}}^6/{\mathbb{Z}}_4$.

The lack of energy conservation introduces new particle processes in curved spacetime that are forbidden in flat space. Therefore, one has to be very cautious about using the results calculated in Minkowskian space in early Universe applications. This is true for particle decay rates in particular, which need to be calculated using quantum field theory in curved spacetime. Previous studies are usually restricted to using minimal or conformal coupling for the decaying particle, while using a more general coupling would give deeper insight into particle decay. This paper presents the results we obtained for a massive particle decaying in a general power-law universe with arbitrary coupling to gravity. We find that, depending on the value of the gravitational coupling, the effect of gravitation may either strengthen or weaken the decay. The analysis further reveals that, apart from radiation-dominated universe, there are values of the coupling constant for which the decay rate is exactly Minkowskian for all universe types. Because the decay rate may be considerably modified in curved space, these issues need to be considered when doing precise cosmological calculations.

We exhibit simple lattice systems, motivated by recently proposed cold atom experiments, whose continuum limits interpolate between real and $p$-adic smoothness as a spectral exponent is varied. A real spatial dimension emerges in the continuum limit if the spectral exponent is negative, while a $p$-adic extra dimension emerges if the spectral exponent is positive. We demonstrate Hölder continuity conditions, both in momentum space and in position space, which quantify how smooth or ragged the two-point Green’s function is as a function of the spectral exponent. The underlying discrete dynamics of our model is defined in terms of a Gaussian partition function as a classical statistical mechanical lattice model. The couplings between lattice sites are sparse in the sense that as the number of sites becomes large, a vanishing fraction of them couple to one another. This sparseness property is useful for possible experimental realizations of related systems.

We study canonical transformations of general relativity (GR) to provide a novel matter coupling to gravity. Although the transformed theory is equivalent to GR in vacuum, the equivalence no longer holds if a matter field minimally couples to the canonically transformed gravitational field. We find that a naive matter coupling to the transformed field leads to the appearance of an extra mode in the phase space, rendering the theory inconsistent. We then find a consistent and novel way of matter coupling: after imposing a gauge fixing condition, a matter field can minimally couple to gravity without generating an unwanted extra mode. As a result, the way matter field couples to the gravitational field determines the preferred time direction and the resultant theory has only two gravitational degrees of freedom. We also discuss the cosmological solution and linear perturbations around it, and confirm that their dynamics indeed differ from those in GR. The novel matter coupling can be used for a new framework of modified gravity theories.