The Kerr/CFT correspondence is a possible route to gain insight into the quantum theory of gravity in the near-horizon region of a Kerr black hole via a dual holographic conformal field theory (CFT). Predictions of the black hole entropy, scattering cross section and the quasinormal modes from the dual holographic CFT corroborate this proposed correspondence. More recently, it has been suggested that quantum gravitational effects in the near-horizon region of a black hole may drastically modify the classical general relativistic description, leading to potential observable consequences. In this paper, we study the absorption cross section and quasinormal modes of a horizonless Kerr-like exotic compact object (ECO) in the dual CFT picture. Our analysis suggests that the near-horizon quantum modifications of the black hole can be understood as finite size and/or finite $N$ effects in the dual CFT. Signature of the near-horizon modification to a black hole geometry manifests itself as delayed echoes in the ringdown (i.e., the postmerger phase) of a binary black hole coalescence. From our dual CFT analysis we show how the length of the circle, on which the dual CFT lives, must be related to the echo time-delay that depends on the position of the near-horizon quantum structure. We further derive the reflectivity of the ECO membrane in terms of the CFT modular parameters, showing that it takes the Boltzmann form.

We studied the dynamics of the order parameter and the winding numbers $W$ formation of a quenched normal-to-superconductor state phase transition in a finite size holographic superconducting ring. There is a critical circumference $\tilde{C}$ below which no winding number will be formed; then, $\tilde{C}$ can be treated as the Kibble-Zurek mechanism (KZM) correlation length $\xi$, which is proportional to the fourth root of its quench rate ${\tau }_Q$, which is also the average size of independent pieces formed after a quench. When the circumference $C\ge 10\xi$, the key KZM scaling between the average value of absolute winding number and the quench rate $⟨|W|⟩\propto {\tau }_Q^{-1/8}$ is observed. At smaller sizes, the universal scaling will be modified; there are two regions. The middle size $5\xi <C<10\xi$ result $⟨|W|⟩\propto {\tau }_Q^{-1/5}$ agrees with a finite size experiment observation, while at $\xi <C\le 5\xi$, the average value of absolute winding number equals the variance of winding number, and there is no exponential relationship between the quench rate and the average value of absolute winding number. The winding number statistics can be derived from a trinomial distribution with $\tilde{N}=C/(f\xi )$ trials, and $f\simeq 5$ is the average number of adjacent pieces that are effectively correlated.

We investigate consistent charged black hole solutions to the Einstein-Maxwell-dilaton (EMD) equations that are asymptotically AdS. The solutions are gravity duals to phases of a nonconformal plasma at finite temperature and density. For the dilaton we take a quadratic ansatz, leading to linear confinement at zero temperature and density. We consider a grand canonical ensemble, where the chemical potential is fixed, and find a rich phase diagram involving the competition of small and large black holes. The phase diagram contains a critical line and a critical point similar to the van der Waals–Maxwell liquid-gas transition. As the critical point is approached, we show that the trace anomaly in the plasma phases vanishes, signifying the restoration of conformal symmetry in the fluid. We find that the heat capacity and charge susceptibility diverge as $C_V\propto (T-T^c{)}^{-\alpha }$ and $\chi \propto (T-T^c{)}^{-\gamma }$ at the critical point with universal critical exponents $\alpha =\gamma =2/3$. Our results suggest a description of the thermodynamics near the critical point in terms of catastrophe theories. In the limit $\mu \to 0$ we compare our results with lattice results for $SU(N_c)$ Yang-Mills theories.

We revisit the question whether the worldsheet theory of a string admits a global $O(d,d)$ symmetry. We consider the truncation of the target space theory in which fields are independent of $d$ coordinates, which is $O(d,d,\mathbb{R})$ invariant. The worldsheet theory is not $O(d,d,\mathbb{R})$ invariant, unless it is truncated by setting winding and center-of-mass momenta to zero. We prove consistency of this truncation and give a manifestly $O(d,d,\mathbb{R})$ invariant action, generalizing a formulation due to Tseytlin by including all external and internal target space fields. It is shown that, due to chiral bosons, this symmetry is anomalous. The anomaly is cancelled by a Green-Schwarz mechanism that utilizes the external $B$-field.

In the description of the ${\mathrm{AdS}}_5/{\mathrm{CFT}}_4$ duality by an integrable system the scattering matrix for bound states plays a crucial rôle: it was initially constructed for the evaluation of finite size corrections to the planar spectrum of energy levels/anomalous dimensions by the thermodynamic Bethe ansatz, and more recently it reappeared in the context of the gluing prescription of the hexagon approach to higher-point functions. In this work we present a simplified form of this scattering matrix and we make its pole structure manifest. We find some new relations between its matrix elements and also present an explicit form for its inverse. We finally discuss some of its properties including crossing symmetry. Our results will hopefully be useful for computing finite-size effects, in particular for simplifying the complicated sum integrals arising from the gluing of hexagons, as well as help towards understanding universal features of the ${\mathrm{AdS}}_5/{\mathrm{CFT}}_4$ scattering matrix.

I argue that a certain perturbative proximity exists between some supersymmetric and nonsupersymmetric theories (namely, pure Yang-Mills and adjoint QCD with two flavors, ${\mathrm{adjQCD}}_{N_f=2}$). I start with $\mathcal{N}=2$ super–Yang-Mills theory built of two $\mathcal{N}=1$ superfields: vector and chiral. In $\mathcal{N}=1$ language, the latter presents matter in the adjoint representation of $\mathrm{SU}(N)$. Then, I convert the matter superfield into a phantom one (in analogy with ghosts), breaking $\mathcal{N}=2$ down to $\mathcal{N}=1$. The global SU(2) acting between two gluinos in the original theory becomes graded. Exact results in thus deformed theory allow one to obtain insights in certain aspects of nonsupersymmetric gluodynamics. In particular, it becomes clear how the splitting of the $\beta$ function coefficients in pure gluodynamics, ${\beta }_1=(4-\frac{1}{3})N$ and ${\beta }_2=(6-\frac{1}{3})N^2$, occurs. Here, the first terms in the braces (4 and 6, always integers) are geometry related, while the second terms ($-\frac{1}{3}$ in both cases) are bona fide quantum effects. In the same sense, ${\mathrm{adjQCD}}_{N_f=2}$ is close to $\mathcal{N}=2$ SYM. Thus, I establish a certain proximity between pure gluodynamics and ${\mathrm{adjQCD}}_{N_f=2}$ with supersymmetric theories. (Of course, in both cases, we loose all features related to flat directions and Higgs/Coulomb branches in $\mathcal{N}=2$.) As a warmup exercise, I use this idea in the two-dimensional CP(1) sigma model with $\mathcal{N}=(2,2)$ supersymmetry, through the minimal heterotic $\mathcal{N}=(0,2)\to$ bosonic CP(1).

We propose a new inner product for scalar fields that are solutions of the Klein-Gordon equation with $m^2<0$. This inner product is nonlocal, bearing an integral kernel including Bessel functions of the second kind. The associated norm proves to be positive definite in the subspace of oscillatory solutions, as opposed to the conventional one, although some regularization procedure is required. Poincaré transformations are unitarily implemented on this subspace, which is the support of a unitary and irreducible representation of the proper orthochronous Poincaré group. We also provide a new Fourier transform between configuration and momentum spaces, which is unitary, and recover the projection onto the representation space. This new scenario suggests a revision of the corresponding quantum field theory.

We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic $\mathcal{O}(p^4)$ vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension $D=0$. For the case of a quartic $\mathcal{O}(p^6)$ vertex, classical conformal invariance constrains the theory to be the special Galileon in $D=-2$ dimensions. We also verify the conformal invariance of these theories by showing that their amplitudes are uniquely fixed by the conformal Ward identities. In these theories, conformal invariance is a much more stringent constraint than scale invariance.

We study the entanglement dynamics between two cavities when one of them is harmonically shaken in the context of quantum information theory. We find four different regimes depending on the frequency of the motion and the spectrum of the moving cavity. If the moving cavity is three dimensional only two modes inside get coupled and the entanglement can either degrade asymptotically with time or oscillate depending on the driving. On the other hand, if the cavity has an equidistant spectrum the entanglement can either vanish asymptotically if it is driven with its fundamental frequency or have a sudden death if it is driven with an uneven harmonic frequency.

Seven-point functions have two inequivalent topologies or channels. The comb channel has been computed previously, and here we compute scalar conformal blocks in the extended snowflake channel in $d$ dimensions. Our computation relies on the known action of the differential operator that sets up the operator product expansion in embedding space. The scalar conformal blocks in the extended snowflake channel are obtained as a power series expansion in the conformal cross-ratios whose coefficients are a triple sum of the hypergeometric type. This triple sum factorizes into a single sum and a double sum. The single sum can be seen as originating from the comb channel and is given in terms of a ${}_3{F}_2$-hypergeometric function, while the double sum originates from the snowflake channel which corresponds to a Kampé de Fériet function. We verify that our results satisfy the symmetry properties of the extended snowflake topology. Moreover, we check that the behavior of the extended snowflake conformal blocks under several limits is consistent with known results. Finally, we conjecture rules leading to a partial construction of scalar $M$-point conformal blocks in arbitrary topologies.

We study a series of the Wess-Zumino actions obtained by repeatedly integrating conformal anomalies with respect to the conformal-factor field that appear at higher loops. We show that they arise as physical quantities required to make nonlocal loop correction terms diffeomorphism invariant. Specifically, in a conformally flat spacetime $d{s}^2=e^{2\varphi }(-d{\eta }^2+d{\mathbf{x}}^2)$, we find that effective actions are described in terms of momentum squared expressed as a physical $Q^2=q^2/e^{2\varphi }$ for $q^2$ measured by the flat metric, which recalls the relationship between physical momentum and comoving momentum in cosmology. It is confirmed by calculating the effective action of QED in such a curved spacetime at the 3-loop level using dimensional regularization. The same applies to the case of QCD, in which we show that the effective action can be summarized in the form of the reciprocal of a running coupling constant squared described by the physical momentum. We also see that the same holds for renormalizable quantum conformal gravity and that conformal anomalies are indispensable for formulating the theory.

We study Hamiltonian form of unfree gauge symmetry where the gauge parameters have to obey differential equations. We consider the general case such that the Dirac-Bergmann algorithm does not necessarily terminate at secondary constraints, and tertiary and higher order constraints may arise. Given the involution relations for the first-class constraints of all generations, we provide explicit formulas for unfree gauge transformations in the Hamiltonian form, including the differential equations constraining gauge parameters. All the field theories with unfree gauge symmetry share the common feature: they admit sort of “global constants of motion” such that do not depend on the local degrees of freedom. The simplest example is the cosmological constant in the unimodular gravity. We consider these constants as modular parameters rather than conserved quantities. We provide a systematic way of identifying all the modular parameters. We demonstrate that the modular parameters contribute to the Hamiltonian constraints, while they are not explicitly involved in the action. The Hamiltonian analysis of the unfree gauge symmetry is precessed by a brief exposition for the Lagrangian analogue, including explicitly covariant formula for degrees of freedom number count. We also adjust the Batalin-Fradkin-Vilkovisky-Becchi-Rouet-Stora-Tyutin Hamiltonian quantization method for the case of unfree gauge symmetry. The main distinction is in the content of the nonminimal sector and gauge fixing procedure. The general formalism is exemplified by traceless tensor fields of irreducible spin $s$ with the gauge symmetry parameters obeying transversality equations.

We present the saddle-point approximation for the effective Hamiltonian of the quantum kink in two-dimensional linear sigma models to all orders in the time-derivative expansion. We show how the effective Hamiltonian can be used to obtain semiclassical soliton form factors, valid at momentum transfers of order the soliton mass. Explicit results, however, hinge on finding an explicit solution to a new wavelike partial differential equation, with a time-dependent velocity and a forcing term that depend on the solution. In the limit of small momentum transfer, the effective Hamiltonian reduces to the expected form, namely, $H=\sqrt{P^2+M^2}$, where $M$ is the one-loop corrected soliton mass, and soliton form factors are given in terms of Fourier transforms of the corresponding classical profiles.

We outline, test, and apply a new scheme for nonperturbative analyses of quantized field systems in contact with dynamical gravity. While gravity is treated classically in the present paper, the approach lends itself for a generalization to full quantum gravity. We advocate the point of view that quantum field theories should be regularized by sequences of quasiphysical systems comprising a well-defined number of the field’s degrees of freedom. In dependence on this number, each system backreacts autonomously and self-consistently on the gravitational field. In this approach, the limit which removes the regularization automatically generates the physically correct spacetime geometry, i.e., the metric the quantum states of the field prefer to “live” in. We apply the scheme to a Gaussian scalar field on maximally symmetric spacetimes, thereby confronting it with the standard approaches. As an application, the results are used to elucidate the cosmological constant problem allegedly arising from the vacuum fluctuations of quantum matter fields. An explicit calculation shows that the problem disappears if the pertinent continuum limit is performed in the improved way advocated here. A further application concerns the thermodynamics of de Sitter space where the approach offers a natural interpretation of the microstates that are counted by the Bekenstein-Hawking entropy.

This article is an addendum to a recent publication by Chandra et al. [Phys. Rev. D 102, 044035 (2020)]. We present updated results on upper limits on the merger of intermediate-mass black holes (IMBHs) with total mass between $210M_{\odot }$ and $500M_{\odot }$, mass ratio 1 to 7, and generic spins using data from the second Advanced LIGO observing run. Based on our analysis, we place the most stringent of our upper limits, of $0.28{\mathrm{Gpc}}^{-3}\mathrm{y}{\mathrm{r}}^{-1}$ on the merger rate density of precessing equal-mass intermediate-mass black holes with total masses of $210M_{\odot }$.

We present a global metric describing closed timelike curves embedded in Minkowski spacetime. Physically, the metric represents an Alcubierre warp drive on a rotating platform. The physical realizability of such a metric is uncertain due to the exotic matter required to produce it. Nevertheless we suggest that this metric will have applications in more rigorously studying the behavior of quantum fields interacting with closed timelike curves.

We investigate the escape probabilities of the photons near the horizon of the Kerr-Sen black hole. We find that the escape probabilities of the photons are nonzero in the event horizon limit of the extreme Kerr-Sen black hole if the light sources are near the equator. We show that the escape probability of a photon increases with the increasing radial position of the light source. It is also uncovered that the escape probability decreases if the light source with constant radius moves from the equatorial plane to the pole. Besides, we discover that the escape probability of a photon in the Carter frame is always greater than the one in the locally nonrotating frame, except on the pole, where they are equal.

We calculate gravitational perturbation quasinormal modes (QNMs) of nonsingular Bardeen black holes (BHs) and singularity-free BHs in conformal gravity and examine their spectra in wave dynamics comparing with standard BHs in general relativity. After testing the validity of the approximate signal-to-noise ratio (SNR) calculation for different space based interferometers, we discuss the SNR of nonsingular BHs in single-mode gravitational waveform detections in the Laser Interferometer Space Antenna (LISA), TianQin, and TaiJi. We explore the impact of the Bardeen parameter and the conformal factor on the behavior of the SNR and find that in comparison with the standard Schwarzschild BHs, the increase of nonsingular parameters leads to higher SNR for more massive nonsingular BHs. We also examine the effect of the galactic confusion noise on the SNR and find that a dip appears in SNR due to such noise. For nonsingular BHs, with the increase of the nonsingular parameters, the dip emerges for more massive BHs. It suggests a wider range of mass of nonsingular black holes whose SNR will not be lowered by galactic noise, which implies the SNR for the super massive black holes centered at our galaxy is less likely to be influenced by galactic noise in nonsingular black hole models than a singular case in general relativity. We conduct a Fisher analysis, which suggests that the nonsingular black holes parameters can be detected accurately with measurement errors as small as $\sim {10}^{-4}–{10}^{-5}$. The detections of nonsingular BHs are expected to be realized more likely by LISA or TaiJi.

We numerically study the next-to-leading order corrections of the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) 4-simplex amplitude in the large-$j$ expansions. We perform large-$j$ expansions of Lorentzian EPRL 4-simplex amplitudes with two different types of boundary states, the coherent intertwiners and the coherent spin-network, and numerically compute the leading-order and the next-to-leading order $O(1/j)$ contributions of these amplitudes. We also study the dependences of these $O(1/j)$ corrections on the Barbero-Immirzi parameter $\gamma$. We show that they, as functions of $\gamma$, stabilize to finite real constants as $\gamma \to \infty$. Lastly, we obtain the quantum corrections to the Regge action because of the $O(1/j)$ contribution to the spinfoam amplitude.

Spinning bosonic stars (SBSs) can form from the gravitational collapse of a dilute cloud of scalar/Proca particles with nonzero angular momentum, via gravitational cooling. The scalar stars are, however, transient due to a nonaxisymmetric instability which triggers the loss of angular momentum. By contrast, no such instability was observed for the fundamental ($m=1$) Proca stars. In [N. Sanchis-Gual et al., Phys. Rev. Lett. 123, 221101 (2019)] we tentatively related the different stability properties to the different toroidal/spheroidal morphology of the scalar/Proca models. Here, we continue this investigation, using three-dimensional numerical-relativity simulations of the Einstein-(massive, complex)Klein-Gordon system and of the Einstein-(complex)Proca system. First, we incorporate a quartic self-interaction potential in the scalar case to gauge its effect on the instability. Second, we investigate toroidal ($m=2$) Proca stars to assess their stability. Third, we attempt to relate the instability of SBSs to the growth rate of azimuthal density modes and the existence of a corotation point in the unstable models. Our results indicate that: (a) the self-interaction potential can only delay the instability in scalar SBSs but cannot quench it completely; (b) $m=2$ Proca stars always migrate to the stable $m=1$ spheroidal family; (c) unstable $m=2$ Proca stars and $m=1$ scalar boson stars exhibit a pattern of frequencies for the azimuthal density modes which crosses the angular velocity profile of the stars in the corotation point. This establishes a parallelism with rotating neutron stars affected by dynamical bar-mode instabilities. Finally, we compute the gravitational waves emitted by SBSs due to the nonaxisymmetric instability. We investigate the detectability of the waveforms comparing the characteristic strain of the signal with the sensitivity curves of a variety of detectors, computing the signal-to-noise ratio for different ranges of masses and for different source distances. Moreover, by assuming that the characteristic damping timescale of the bar-like deformation in SBSs is only set by gravitational-wave emission and not by viscosity (unlike in neutron stars), we find that the postcollapse emission could be orders of magnitude more energetic than that of the bar-mode instability itself. Our results indicate that gravitational-wave observations of SBSs might be within the reach of future experiments, offering a potential means to establish the existence of such stars and to place tight constraints on the mass of the bosonic particle.