The Abelian Chern-Simons gauge theory is constructed on the three-dimensional spacetime lattice. This proposal introduces both lattice and dual lattice, and the gauge field on the dual lattice is expressed in terms of the gauge field on the original lattice. This treatment circumvents the issue of forward/backward difference, which is the common problem that many previous proposals have, and also avoids the duplication problem, which prevents people from introducing the dual lattice. The form of the lattice action is very simple and is symmetric with respect to the three spacetime dimensions. These features make it straightforward to calculate the expectation values of Wilson loops, and the results agree with the topological field theory in continuous spacetime. Generalizations to multiple types of lattices are also discussed.

Triply heavy baryons are investigated in the framework of the relativistic quark model based on the quark-diquark picture in the quasipotential approach in QCD. Masses of the ground and excited states of the ${\mathrm{\Omega }}_{ccc}$, ${\mathrm{\Omega }}_{bbb}$, ${\mathrm{\Omega }}_{ccb}$, and ${\mathrm{\Omega }}_{cbb}$ baryons are calculated. Orbital and radial excitations between the diquark and quark as well as between quarks inside the diquark are considered. The diquark internal structure is consistently taken into account by the form factor of the diquark-gluon interaction expressed through the overlap integral of the diquark wave functions. A detailed comparison with previous calculations is given.

Studies of neutrino mixing and oscillations, solar neutrinos as background in dark matter searches involving electron detection, detection of sterile neutrino warm dark matter, and of possible electromagnetic properties of neutrinos, have generated interest in the low energy O(10 keV) scattering of electron neutrinos and antineutrinos by atomic electrons where the binding of the atomic electron cannot be ignored. Of particular interest is the ionization of atoms by neutrinos and antineutrinos. Most existing calculations are based upon modifications of the free electron differential cross section which destroy the relationship between the neutrino helicities and the orbital and spin angular momenta of the atomic electrons. The present calculations maintain the full collision dynamics by formulating the scattering in configuration space using the bound interaction picture, rather than the usual formulation in the interaction picture in momentum space as appropriate to scattering by free electrons. Energy spectra of ionization electrons produced by scattering of neutrinos and antineutrinos with energies of 5, 10, 20, and 30 keV by hydrogen, helium and neon have been calculated using Dirac central field eigenfunctions, and are presented as ratios to the spectra for scattering by free electrons. Binding effects increase strongly with atomic number, are largest for low neutrino energy and, for each neutrino energy, greatest at the high electron energy end of the spectrum. The most extreme effects of binding are for 5 keV scattering by Ne where the ratios are less than 0.1. The energy spectra have been calculated for both a Coulombic final electron state and a free final electron state. The results indicate that the binding effects from the continuum state of the final electron are significant and can be comparable to those arising from the bound initial electron state.

We present a comprehensive study of the electroweak interactions using the available Higgs and electroweak diboson production results from LHC runs 1 and 2 as well as the electroweak precision data in terms of the dimension-six operators. Under the assumption that no new tree-level sources of flavor violation or violation of the universality of the weak current are introduced, the analysis involves 21 operators. We assess the impact of the data on kinematic distributions for the Higgs production at the LHC by comparing the results obtained by including the simplified template cross-section data with those in which only total Higgs signal strengths are considered. We also compare the results obtained when including the dimension-six anomalous contributions to order $1/{\mathrm{\Lambda }}^2$ and to order $1/{\mathrm{\Lambda }}^4$. As an illustration of the LHC potential to indirectly learn about specific forms of new physics, we adapt the analysis to constrain the parameter space for a few simple extensions of the standard model which generate a subset of the dimension-six operators at tree level.

We study the spin-exotic $J^{PC}=1^{-+}$ amplitude in single-diffractive dissociation of $190\mathrm{GeV}/c$ pions into ${\pi }^{-}{\pi }^{-}{\pi }^{+}$ using a hydrogen target and confirm the ${\pi }_1(1600)\to \rho (770)\pi$ amplitude, which interferes with a nonresonant $1^{-+}$ amplitude. We demonstrate that conflicting conclusions from previous studies on these amplitudes can be attributed to different analysis models and different treatment of the dependence of the amplitudes on the squared four-momentum transfer and we thus reconcile these experimental findings. We study the nonresonant contributions to the ${\pi }^{-}{\pi }^{-}{\pi }^{+}$ final state using pseudodata generated on the basis of a Deck model. Subjecting pseudodata and real data to the same partial-wave analysis, we find good agreement concerning the spectral shape and its dependence on the squared four-momentum transfer for the $J^{PC}=1^{-+}$ amplitude and also for amplitudes with other $J^{PC}$ quantum numbers. We investigate for the first time the amplitude of the ${\pi }^{-}{\pi }^{+}$ subsystem with $J^{PC}=1^{--}$ in the $3\pi$ amplitude with $J^{PC}=1^{-+}$ employing the novel freed-isobar analysis scheme. We reveal this ${\pi }^{-}{\pi }^{+}$ amplitude to be dominated by the $\rho (770)$ for both the ${\pi }_1(1600)$ and the nonresonant contribution. These findings largely confirm the underlying assumptions for the isobar model used in all previous partial-wave analyses addressing the $J^{PC}=1^{-+}$ amplitude.

We study the microcanonical superconformal index of $\frac{1}{16}$-supersymmetric operators in 4d $\mathcal{N}=4$ $U(N)$ super Yang-Mills (SYM) theory. We show, numerically for $N\le 10$, that the large-charge asymptotics are consistent with the entropy of supersymmetric black holes in the dual anti de Sitter space. We then prove, using representation theory, that the index agrees precisely with the multigraviton index, when the charge is less than $2(N+1)$, and begins to deviate for larger values of charge. Thus the $U(N)$ SYM index interpolates between multigraviton values at small charges and black hole growth at large charges.

A novel mechanism for the primordial black hole (PBH) production is proposed as a natural and inevitable consequence of general first-order phase transitions without reference to specific underlying particle physics models. We obtain mutual predictions and constraints between primordial black holes and gravitational waves from phase transitions in the general case. For particular interest, our PBHs generated during a PeV-scale phase transition could make up all the dark matter, while PBHs generated during a MeV-scale phase transition could simultaneously account for LIGO-Virgo coalescence events and NANOGrav 12.5-yr result for the corresponding gravitational waves.

A family of deformed black branes is employed to examine the confinement/deconfinement phase transition in AdS/QCD. The holographic entanglement entropy (HEE) plays the role of the order parameter driving the confinement/deconfinement phase transition. The binding energy of quark-antiquark bound states and the critical length that makes a null variation of the HEE, together with the critical temperature separating the deconfined quark-gluon plasma to the confined hadronic phase, are discussed in the deformed black brane background, matching current experimental hadronic data.

Stochastic quantization provides an alternate approach to the computation of quantum observables, by stochastically sampling phase space in a path integral. Furthermore, the stochastic variational method can provide analytical control over the strong coupling regime of a quantum field theory—provided one has a decent qualitative guess at the form of certain observables at strong coupling. In the context of the holographic duality, the strong coupling regime of a Yang-Mills theory can capture gravitational dynamics. This can provide enough insight to guide a stochastic variational ansatz. We demonstrate this in the bosonic Banks-Fischler-Shenker-Susskind matrix theory. We compute a two-point function at all values of the coupling using the variational method showing agreement with lattice numerical computations and capturing the confinement-deconfinement phase transition at strong coupling. This opens up a new realm of possibilities for exploring the holographic duality and emergent geometry.

We develop an entanglement criterion with third- and fourth-order cumulants to detect the entanglement of non-Gaussian states. The efficiency of the entanglement criterion is investigated for gravitating mirrors in optomechanical systems. We show that the entangled regime of the mirrors is enlarged by the third- and fourth-order cumulants. We also discuss the limitations of the entanglement criterion for mirrors in a highly non-Gaussian state.

Using a nonperturbative approach based on the Cornwall-Jackiw-Tomboulis (CJT) effective action $\mathrm{\Gamma }(S)$ for composite operators ($S$ is the full fermion propagator), the phase structure of the simplest massless ($2+1$)-dimensional Gross-Neveu model is investigated. We have calculated $\mathrm{\Gamma }(S)$ and its stationary (or Dyson-Schwinger) equation in the first order of the bare coupling constant $G$ and have shown that there exist a well-defined dependence of $G\equiv G(\mathrm{\Lambda })$ on the cutoff parameter $\mathrm{\Lambda }$, such that the Dyson-Schwinger equation is renormalized. It has three different solutions for fermion propagator $S$ corresponding to possible dynamical appearance of three different mass terms in the model. One is a Hermitian, but two others are non-Hermitian and $\mathcal{P}\mathcal{T}$ even or odd. It means that two phases with spontaneous non-Hermiticity can be emerged in the system. Moreover, mass spectrum of quasiparticles is real in these non-Hermitian and $\mathcal{P}\mathcal{T}$ even/odd phases.

In the present paper, we show that a partially reflecting static mirror with time-dependent properties can produce, via dynamical Casimir effect in the context of a massless scalar field in $1+1$ dimensions, a larger number of particles than a perfectly reflecting one. As particular limits, our results recover those found in the literature for a perfect static mirror imposing a generalized or a usual time-dependent Robin boundary condition.

Recently, the notion of circuit complexity defined in symmetry group manifolds has been related to geometric actions which generally arise in the coadjoint orbit method in representation theory and play an important role in geometric quantization. On the other hand, it is known that there exists a precise relation between geometric actions and Berry phases defined in group representations. Motivated by these connections, we elaborate on a relation between circuit complexity and the group theoretic Berry phase. As the simplest setup relevant for holography, we discuss the case of two dimensional conformal field theories. In the large central charge limit, we identify the computational cost function with the Berry connection in the unitary representation of the Virasoro group. We then use the latter identification to express the Berry phase in terms of the Virasoro circuit complexity. The former can be seen as the holonomy of the Berry connection along the path in the group manifold which defines the protocol. In addition, we derive a proportionality relation between Virasoro circuit complexity and the logarithm of the inner product between a particularly chosen reference state and the prepared target state. In this sense, the logarithmic formula turns out to be approximating the complexity up to some additive constant if the building blocks of the circuit are taken to be the underlying symmetry gates. Predictions based on this formula have recently been shown to coincide with the holographic complexity proposals and the path integral optimization procedure. The found connections may therefore help to better understand such coincidences. We also discuss that our findings, put together with earlier observations, may suggest a connection between the Virasoro Berry phase and the complexity measure in the path integral optimization proposal.

The treatment of higher order perturbations of branes is considered using a covariant variational approach. This covariant variational approach brings to the forefront the geometric structure of the underlying perturbation theory, as opposed to a more commonly used “direct approach,” that ignores the variational origin. In addition, it offers a clear calculational advantage with respect to so-called “gauge fixed” treatments that distinguish tangential and normal modes, as it emphasizes the symmetries of the geometric models that describe the brane dynamics. We restrict our attention to a brane action that depends at most on first derivatives of the embedding functions of the world volume spanned by the brane in its evolution. We consider first and second variations of the action that describes the brane dynamics. The first variation produces the equations of motion, as is well known. In the second variation we derive the Jacobi equations for these kind of models, and we emphasize the role of the Hessian matrix. This is extended to third order in variations, first in a flat and then in a curved spacetime background. Further, we specialize to the relevant case of the Dirac-Nambu-Goto action that describes extremal branes. The proper setting of a covariant variational approach allows to go in principle to geometric models that depend on higher derivatives of the embedding functions, and higher order perturbations, with the due complications involved, but with a solid framework in place.

This paper describes a model for baby Skyrme crystal chunks with arbitrary potential by considering energy contributions from the bulk and surface of a crystal chunk. We focus on two potentials which yield distinct Skyrme lattices: the standard potential $V=m^2(1-{\phi }^3)$ and the easy plane potential $V=\frac{1}{2}{m}^2({\phi }^1{)}^2$. In both models, the static energy functional is minimized over all two-dimensional period lattices, yielding the minimal-energy crystal structure(s). For the standard potential, the Skyrmions form a hexagonal crystal structure, whereas, for the easy plane potential, the minimal-energy crystal structure is a square lattice of half-charge lumps. We find that square crystal chunks are the global minima in the easy plane model for charges $B>6$, with $2B$ being a perfect square ($m^2=1$). In contrast, we observe that hexagonal crystal chunks in the standard model become the global minima for surprisingly large charges, $B>954$ ($m^2=0.1$).

A broad class of forces, $P$, is identified, for which the Abraham-Lorentz-Dirac (ALD) and Newton-like equations have solutions in common. Moreover, these solutions do not present preacceleration or escape into infinity (runaway behavior). Any continuous or piecewise continuous force can be represented in terms of functions belonging to this class $P$. It was also argued that the set of common solutions of both sets of equations is wider, and it was proved that these solutions could be formulated in terms of generalized functions. The existence of such generalized functions motions is explicitly demonstrated for the relevant example of the instantaneously applied constant force, for which the respective solution of the ALD equation exhibits a lack of causality and runaway motion. In this case, the expressions for the position and velocity of the particle are formulated in terms of generalized functions of time, having only a point support at the time that the force is applied. Thus, both the velocity and the position are discontinuous at the instant that the force was applied. The solution for a particle moving between the plates of a capacitor reproduces the one obtained by A. Yaghjian from his discussion for extended particles. This outcome suggests a possible link or equivalence between both studies. A solution, common to the Newton-like and the ALD equations, for a constant homogeneous magnetic field is also presented. The extension of the results obtained to a relativistic context will be studied in future works.

We present a discontinuous Galerkin internal-penalty scheme that is applicable to a large class of linear and nonlinear elliptic partial differential equations. The unified scheme can accommodate all second-order elliptic equations that can be formulated in first-order flux form, encompassing problems in linear elasticity, general relativity, and hydrodynamics, including problems formulated on a curved manifold. It allows for a wide range of linear and nonlinear boundary conditions, and accommodates curved and nonconforming meshes. Our generalized internal-penalty numerical flux and our Schur-complement strategy of eliminating auxiliary degrees of freedom make the scheme compact without requiring equation-specific modifications. We demonstrate the accuracy of the scheme for a suite of numerical test problems. The scheme is implemented in the open-source spectre numerical relativity code.

The construction of general derivative self-interactions for a massive Proca field relies on the well-known condition for constrained systems of having a degenerate Hessian. The nature of the existing constraints algebra will distinguish among different classes of interactions. Proca-Nuevo interactions enjoy a nontrivial constraint by mixing terms of various order whereas generalized Proca interactions satisfy the degeneracy condition order by order for each individual Lagrangian. In both cases the vector field propagates at most 3 degrees of freedom. It has been shown that the scattering amplitudes of Proca-Nuevo arising at the tree level always differ from those of the generalized Proca, implying their genuinely different nature and a lack of relation by local field redefinitions. In this work, we show the quantum stability of the Proca-Nuevo theory below a specific UV cutoff. Although Proca-Nuevo and generalized Proca are different inherently in their classical structure, both have the same high energy behavior when quantum corrections are taken into account. The arising counterterms have the exact same structure and scaling. This might indicate that whatever UV completion they may come from, we expect it to be of similar nature.

The implication of Ruppeiner thermodynamic geometry theory to spherically symmetric black holes in anti–de Sitter (AdS) spacetime produces an unavoidable singularity in the line element of thermodynamic geometry. The singularity occurs due to the nonindependence of volume and entropy of black holes (BH) in AdS spacetime. In this work, we present an efficient and easy approach to deal the thermodynamic geometry of AdS BH in Einstein-Maxwell-scalars theory. We show that enthalpy instead of internal energy is central thermodynamic quantity. We develop the particular forms of the line element of thermodynamic geometry in different phase spaces. We find out that the curvatures in different phase spaces are identical and positive which leads to the repulsive interaction information between black hole molecules. We also analyze the thermal stability of AdS BH in Einstein-Maxwell-scalars theory and regularized Lovelock theory in the presence of thermal fluctuations. We observed that momentum relaxation parameter and coupling constants of Lovelock theory increase the thermal stability of the BHs. Finally, we also study the Joule-Thomson expansion for black hole in regularized Lovelock theory.

We revisit Wyman’s “other” scalar field solution of the Einstein equations and its Sultana generalization to positive cosmological constant, which has a finite 3-space and corresponds to a special case of a stiff fluid solution proposed by Buchdahl and Land and, later, by Ibañez and Sanz to model relativistic stars. However, there is a hidden cosmological constant and the peculiar geometry prevents the use of this spacetime to model relativistic stars.