Strong evidence for dual superconformal symmetry in $\mathcal{N}=6$ superconformal Chern-Simons theory has fueled expectations that the $\mathrm{AdS}/\mathrm{CFT}$ dual geometry ${\mathrm{AdS}}_4\times \mathbb{C}{P}^3$ is self-dual under T duality. We revisit the problem to identify commuting bosonic and fermionic isometries in a systematic fashion and show that fermionic T duality, a symmetry originally proposed by Berkovits and Maldacena, inevitably leads to a singularity in the dilaton transformation. We show that TsT deformations commute with fermionic T duality and comment on T duality in the corresponding sigma model. Our results rule out self-duality based on fermionic T duality for ${\mathrm{AdS}}_4\times \mathbb{C}{P}^3$ or its TsT deformations but leave the door open for new possibilities.

We discuss an extension of the instanton-dyon liquid model that includes twisted light quarks in the fundamental representation with explicit $Z_{N_c}$ symmetry for the case with an equal number of colors $N_c$ and flavors $N_f$. We map the model on a three-dimensional quantum effective theory, and analyze it in the mean-field approximation. The effective potential and the vacuum chiral condensates are made explicit for $N_f=N_c=2$, 3. The low temperature phase is center symmetric but breaks spontaneously flavor symmetry with $N_f-1$ massless pions. The high temperature phase breaks center symmetry but supports finite and unequal quark condensates.

We discuss the instanton-dyon liquid model with $N_f$ Majorana quark flavors in the adjoint representation of color $S{U}_c(2)$ at finite temperature. We briefly recall the index theorem on $S^1\times R^3$ for twisted adjoint fermions in a Bogomolny-Prasad-Sommerfeld (BPS) dyon background of arbitrary holonomy and use the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction to derive the adjoint antiperiodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with $N_f$ light and antiperiodic adjoint quarks. We develop the model in details by mapping the theory on a three-dimensional quantum effective theory with adjoint quarks with manifest $SU(N_f)\times Z_{4N_f}$ symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for $N_f=1$. For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through $SU(N_f)\times Z_{4N_f}\to O(N_f)$. As the liquid dilutes with increasing temperature, center symmetry and chiral symmetry are restored. We present numerical and analytical estimates for the transition temperatures.

We discuss an extension of the instanton-dyon liquid model that includes light quarks at finite chemical potential in the center symmetric phase. We develop the model in details for the case of $S{U}_c(2)\times S{U}_f(2)$ by mapping the theory on a three-dimensional quantum effective theory. We analyze the different phases in the mean-field approximation. We extend this analysis to the general case of $S{U}_c(N_c)\times S{U}_f(N_f)$ and note that the chiral and diquark pairings are always comparable.

We give an exhaustive characterization of the complex saddle point configurations of the Gross-Witten-Wadia matrix model in the large-$N$ limit. In particular, we characterize the cases in which the saddles accumulate in one, two, or three arcs, in terms of the values of the coupling constant and of the fraction of the total unit density that is supported in one of the arcs, and derive an explicit condition for gap closing associated with nonvacuum saddles. By applying the idea of large-$N$ instanton we also give direct analytic derivations of the weak-coupling and strong-coupling instanton actions.

Quantum field theory—our basic framework for describing all nongravitational physics—conflicts with general relativity: the latter precludes the standard definition of the former’s essential principle of locality, in terms of commuting local observables. We examine this conflict more carefully, by investigating implications of gauge (diffeomorphism) invariance for observables in gravity. We prove a dressing theorem, showing that any operator with nonzero Poincaré charges, and in particular any compactly supported operator, in flat-spacetime quantum field theory must be gravitationally dressed once coupled to gravity, i.e., it must depend on the metric at arbitrarily long distances, and we put lower bounds on this nonlocal dependence. This departure from standard locality occurs in the most severe way possible: in perturbation theory about flat spacetime, at leading order in Newton’s constant. The physical observables in a gravitational theory therefore do not organize themselves into local commuting subalgebras: the principle of locality must apparently be reformulated or abandoned, and in fact we lack a clear definition of the coarser and more basic notion of a quantum subsystem of the Universe. We discuss relational approaches to locality based on diffeomorphism-invariant nonlocal operators, and reinforce arguments that any such locality is state-dependent and approximate. We also find limitations to the utility of bilocal diffeomorphism-invariant operators that are considered in cosmological contexts. An appendix provides a concise review of the canonical covariant formalism for gravity, instrumental in the discussion of Poincaré charges and their associated long-range fields.

In this paper we study cosmological signatures of modified gravity theories that can be written as a coupling between an extra scalar field and the electromagnetic part of the usual Lagrangian for the matter fields. In these frameworks, the electromagnetic sector of the theory is affected and variations of fundamental constants, of the cosmic distance-duality relation and of the evolution law of the cosmic microwave background (CMB) radiation, are expected and are related to each other. In order to search these variations we perform jointly analyses with angular diameter distances of galaxy clusters, luminosity distances of type Ia supernovae, and $T_{\mathrm{CMB}}(z)$ measurements. We obtain tight constraints with no significant indication of violation of the standard framework.

Surface asymmetries of accreting neutron stars are investigated for their mass quadrupole moment content. Though the amplitude of the gravitational waves from such asymmetries seems to be beyond the limit of detectability of the present generation of detectors, it appears that rapidly rotating neutron stars with strong magnetic fields residing in high-mass x-ray binaries would be worth considering for a targeted search for continuous gravitational waves with the next generation of instruments.

We calculated the dimensionless gyromagnetic ratio (“$g$-factor”) of self-gravitating, uniformly rotating disks of dust with a constant specific charge $\epsilon$. These disk solutions to the Einstein-Maxwell equations depend on $\epsilon$ and a “relativity parameter” $\gamma$ ($0<\gamma \le 1$) up to a scaling parameter. Accordingly, the $g$-factor is a function $g=g(\gamma ,\epsilon )$. The Newtonian limit is characterized by $\gamma \ll 1$, whereas $\gamma \to 1$ leads to a black-hole limit. The $g$-factor, for all $\epsilon$, approaches the values $g=1$ as $\gamma \to 0$ and $g=2$ as $\gamma \to 1$.

Gravitational effective field theories with nondynamical backgrounds explicitly break diffeomorphism and local Lorentz invariance. At the same time, to maintain observer independence the action describing these theories is required to be mathematically invariant under general coordinate transformations and changes of local Lorentz bases. These opposing effects of having broken spacetime symmetries but invariance under mathematical observer transformations can result in theoretical inconsistency unless certain conditions hold. The consistency constraints that must hold originate from Noether identities associated with the mathematical observer invariances in the action. These identities are examined in detail and are used to investigate gravity theories with nondynamical backgrounds, including when a Stückelberg approach is used. Specific examples include gravity theories with fixed scalar or tensor backgrounds, Einstein-Maxwell theory with a fixed external current, and massive gravity.

In this paper we show that there is a universal prediction for the Newtonian potential for a specific class of infinite derivative, ghost-free, quadratic curvature gravity. We show that in order to make such a theory ghost free at a perturbative level, the Newtonian potential always falls-off as $1/r$ in the infrared limit, while at short distances the potential becomes nonsingular. We provide examples which can potentially test the scale of gravitational nonlocality up to 0.004 eV.

Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters—the polytropic index $n$, the ratio of central pressure and central energy density of matter $\sigma$, and the ratio of energy density of vacuum and central density of matter $\lambda$. The static equilibrium configurations are determined by two coupled first-order nonlinear differential equations that are solved by numerical methods with the exception of polytropes with $n=0$ corresponding to the configurations with a uniform distribution of energy density, when the solution is given in terms of elementary functions. The geometry of the polytropes is conveniently represented by embedding diagrams of both the ordinary space geometry and the optical reference geometry reflecting some dynamical properties of the geodesic motion. The polytropes are represented by radial profiles of energy density, pressure, mass, and metric coefficients. For all tested values of $n>0$, the static equilibrium configurations with fixed parameters $n$, $\sigma$, are allowed only up to a critical value of the cosmological parameter ${\lambda }_{\mathrm{c}}={\lambda }_{\mathrm{c}}(n,\sigma )$. In the case of $n>3$, the critical value ${\lambda }_{\mathrm{c}}$ tends to zero for special values of $\sigma$. The gravitational potential energy and the binding energy of the polytropes are determined and studied by numerical methods. We discuss in detail the polytropes with an extension comparable to those of the dark matter halos related to galaxies, i.e., with extension $\ell >100\mathrm{kpc}$ and mass $M>10^{12}{\mathrm{M}}_{\odot }$. For such largely extended polytropes, the cosmological parameter relating the vacuum energy to the central density has to be larger than $\lambda ={\rho }_{\text{vac}}/{\rho }_{\mathrm{c}}\sim {10}^{-9}$. We demonstrate that the extension of the static general relativistic polytropic configurations cannot exceed the so-called static radius related to their external spacetime, supporting the idea that the static radius represents a natural limit on the extension of gravitationally bound configurations in an expanding universe dominated by the vacuum energy.

We examine the degree to which observations of large-scale cosmic microwave background (CMB) polarization can shed light on the puzzling large-scale power modulation in maps of CMB anisotropy. We consider a phenomenological model in which the observed anomaly is caused by modulation of large-scale primordial curvature perturbations and calculate Fisher information and error forecasts for future polarization data, constrained by the existing CMB anisotropy data. Because a significant fraction of the available information is contained in correlations with the anomalous temperature data, it is essential to account for these constraints. We also present a systematic approach to finding a set of normal modes that maximize the available information, generalizing the well-known Karhunen-Loève transformation to take account of the constraints from the temperature data. A polarization map covering at least $\sim 60\%$ of the sky should be able to provide a $3\sigma$ detection of modulation at the level favored by the temperature data. A significant fraction of the information in such a data set is contained in the single mode that optimally encapsulates the signal due to temperature-polarization correlation.

We consider limits on the local ($z=0$) density ($n_0$) of extragalactic neutrino sources set by the nondetection of steady high-energy neutrino sources producing $\gtrsim 50\mathrm{TeV}$ muon multiplets in the present IceCube data, taking into account the redshift evolution, luminosity function, and neutrino spectrum of the sources. We show that the lower limit depends moderately on source spectra and strongly on redshift evolution. We find $n_0\gtrsim {10}^{-8}–{10}^{-7}{\mathrm{Mpc}}^{-3}$ for standard candle sources evolving rapidly, $n_s\propto {(1+z)}^3$, and $n_0\gtrsim {10}^{-6}–{10}^{-5}{\mathrm{Mpc}}^{-3}$ for nonevolving sources. The corresponding upper limits on their neutrino luminosity are $L_{{\nu }_{\mu }}^{\mathrm{eff}}\lesssim 10^{42}–10^{43}\mathrm{erg}{\mathrm{s}}^{-1}$ and $L_{{\nu }_{\mu }}^{\mathrm{eff}}\lesssim 10^{41}–10^{42}\mathrm{erg}{\mathrm{s}}^{-1}$, respectively. Applying these results to a wide range of classes of potential sources, we show that powerful “blazar” jets associated with active galactic nuclei are unlikely to be the dominant sources. For almost all other steady candidate source classes (including starbursts, radio galaxies, and galaxy clusters and groups), an order of magnitude increase in the detector sensitivity at $\sim 0.1–1\mathrm{PeV}$ will enable a detection (as point sources) of the few brightest objects. Such an increase, which may be provided by next-generation detectors like IceCube-Gen2 and an upgraded KM3NET, can improve the limit on $n_0$ by more than 2 orders of magnitude. Future gamma-ray observations (by Fermi, the High-Altitude Water Cherenkov Observatory, and the Cherenkov Telescope Array) will play a key role in confirming the association of the neutrinos with their sources.

$P$-wave coupled channel effects arising from the $D\overline{D}$, $D{\overline{D}}^{*}+\mathrm{c}.\mathrm{c}.$, and $D^{*}{\overline{D}}^{*}$ thresholds in $e^{+}{e}^{-}$ annihilations are systematically studied. We provide an exploratory study by solving the Lippmann-Schwinger equation with short-ranged contact potentials obtained in the heavy quark limit. These contact potentials can be extracted from the $P$-wave interactions in the $e^{+}{e}^{-}$ annihilations, and then be employed to investigate possible isosinglet $P$-wave hadronic molecules. In particular, such an investigation may provide information about exotic candidates with quantum numbers $J^{\mathrm{PC}}=1^{-+}$. In the mass region of the $D\overline{D}$, $D{\overline{D}}^{*}+\mathrm{c}.\mathrm{c}.$, and $D^{*}{\overline{D}}^{*}$ thresholds, there are two quark model bare states, i.e. the $\psi (3770)$ and $\psi (4040)$, which are assigned as $(1^3{D}_1)$ and $(3^1{S}_1)$ states, respectively. By an overall fit of the cross sections of $e^{+}{e}^{-}\to D\overline{D}$, $D{\overline{D}}^{*}+\mathrm{c}.\mathrm{c}.$, $D^{*}{\overline{D}}^{*}$, we determine the physical coupling constants to each channel and extract the pole positions of the $\psi (3770)$ and $\psi (4040)$. The deviation of the ratios from that in the heavy quark spin symmetry (HQSS) limit reflects the HQSS breaking effect due to the mass splitting between the $D$ and the $D^{*}$. Besides the two poles, we also find a pole a few MeV above the $D{\overline{D}}^{*}+\mathrm{c}.\mathrm{c}.$ threshold which can be related to the so-called $G(3900)$ observed earlier by BABAR and Belle. This scenario can be further scrutinized by measuring the angular distribution in the $D^{*}{\overline{D}}^{*}$ channel with high luminosity experiments.

In this paper, we study the direct production of the diphoton resonance $X$, which was suggested by 2015 data at the LHC, in $e^{+}{e}^{-}\to X\gamma /XZ$ processes at the ILC. We derive an analytic expression for the scattering amplitudes of these processes and present a comprehensive analysis for determining the properties of $X$ at the ILC. A realistic simulation study for $e^{+}{e}^{-}\to X\gamma$ is performed based on the full detector simulation to demonstrate the capabilities of the ILC experiment. Complementary to the searches at the LHC, prospects for the measurement of the absolute values of the production cross section are obtained for the ILC using the recoil technique without assuming decay modes of $X$. In addition, we studied the searches for $X\to \text{invisible}$ and $X\to b\overline{b}$ modes, which are challenging at the LHC, and found that these decay modes can be discovered with high significance if their branching ratios are large enough.

Particles in a hidden sector can potentially acquire a small electric charge through their interaction with the Standard Model and can consequently be observed as millicharged particles. We systematically compute the production of millicharged scalar, fermion, and vector boson particles in collisions of polarized photons. The presented calculation is model independent and is based purely on the assumptions of electromagnetic gauge invariance and unitarity. Polarization observables are evaluated and analyzed for each spin case. We show that the photon polarization asymmetries are a useful tool for discriminating between the spins of the produced millicharged particles. Phenomenological implications for searches of millicharged particles in dedicated photon-photon collision experiments are also discussed.

Direct $CP$ violation in charmless three-body hadronic decays of $B$ mesons is studied within the framework of a simple model based on the factorization approach. Three-body decays of heavy mesons receive both resonant and nonresonant contributions. Dominant nonresonant contributions to tree-dominated and penguin-dominated three-body decays arise from the $b\to u$ tree transition and $b\to s$ penguin transition, respectively. The former can be evaluated in the framework of heavy meson chiral perturbation theory with some modification, while the latter is governed by the matrix element of the scalar density $⟨M_1{M}_2|{\overline{q}}_1{q}_2|0⟩$. Resonant contributions to three-body decays are treated using the isobar model. Strong phases in this work reside in effective Wilson coefficients, propagators of resonances, and the matrix element of scalar density. In order to accommodate the branching fraction and $CP$ asymmetries observed in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$, the matrix element $⟨K\pi |\overline{s}q|0⟩$ should have an additional strong phase, which might arise from some sort of power corrections such as final-state interactions. We calculate inclusive and regional $CP$ asymmetries and find that nonresonant $CP$ violation is usually much larger than the resonant one and that the interference effect between resonant and nonresonant components is generally quite significant. If nonresonant contributions are turned off in the $K^{+}{K}^{-}{K}^{-}$ mode, the predicted $CP$ asymmetries due to resonances will be wrong in sign when confronted with experiment. In our study of $B^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}$, we find that ${\mathcal{A}}_{CP}({\rho }^0{\pi }^{-})$ should be positive in order to account for $CP$ asymmetries observed in this decay. Indeed, both BABAR and LHCb measurements of $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ indicate positive $CP$ asymmetry in the $m({\pi }^{+}{\pi }^{-})$ region peaked at $m_{\rho }$. On the other hand, all theories predict a large and negative $CP$ violation in $B^{-}\to {\rho }^0{\pi }^{-}$. Therefore, the issue with $CP$ violation in $B^{-}\to {\rho }^0{\pi }^{-}$ needs to be resolved. Measurements of $CP$-asymmetry Dalitz distributions put very stringent constraints on the theoretical models. We check the magnitude and the sign of $CP$ violation in some (large) invariant mass regions to test our model.

The phase diagram of massless quantum electrodynamics in three space-time dimensions as a function of fermion flavor number $N$ exhibits two well-known phases: at large $N>N_{\mathrm{c}}^{\mathrm{conf}}$ the system is in a conformal gapless state, while for small $N<N_{\mathrm{c}}^{\chi \mathrm{SB}}$ the fermions are expected to develop a dynamical mass due to spontaneous chiral symmetry breaking. Using $\epsilon$ expansion near the lower critical dimension of 2, as well as the recent results on the generalization of the $F$ theorem to continuous dimension, we show that $N_{\mathrm{c}}^{\mathrm{conf}}>N_{\mathrm{c}}^{\chi \mathrm{SB}}$. There is therefore an intermediate range of values of $N$ at which a third phase is stabilized. We demonstrate that this phase is characterized by spontaneous breaking of Lorentz symmetry, in which a composite vector boson field acquires a vacuum expectation value with the fermions and the photon remaining massless.

We present a study of the isospin-violating one-pion strong decays of single heavy tetraquarks $X_Q=X(sq\overline{q}\overline{Q})$, $Q=c$, $b$, and $q=u$, $d$ with spin-parity $J^P=0^{+}$. We assume that the tetraquarks have the configuration of a color diquark and an antidiquark. Three mechanisms of isospin violation can contribute to the decay rate: (1) mixing of the $X(su\overline{u}\overline{Q})$ and $X(sd\overline{d}\overline{Q})$ tetraquark currents, (2) an explicit $m_d-m_u$ quark mass difference in the quark diagrams describing the corresponding decay transitions, and (3) ${\pi }^0-\eta$ mixing in the final state. Our main results are as follows: (1) It is quite likely that the investigated tetraquark states are isosinglet states with a small admixture of an isotriplet component; (2) The first isospin-breaking mechanism affects the decay rather more significantly than the others; (3) Our calculations contain a size parameter ${\mathrm{\Lambda }}_{X_Q}$, characterizing the distribution of the quarks in the tetraquark state $X_Q$. Absolute decay rates depend very much on the choice of ${\mathrm{\Lambda }}_{X_Q}$, varied from 1 to 2 GeV, reflecting the compactness of the multiquark system.