International Journal of Modern Physics A

We review the status of recent investigations on validating the gauge-gravity duality conjecture through numerical simulations of strongly coupled maximally supersymmetric thermal gauge theories. In the simplest setting, the gauge-gravity duality connects systems of D0-branes and black hole geometries at finite temperature to maximally supersymmetric gauged quantum mechanics at the same temperature. Recent simulations show that nonperturbative gauge theory results give excellent agreement with the quantum gravity predictions, thus proving strong evidence for the validity of the duality conjecture and more insight into quantum black holes and gravity.

Motivated by the experiments of heavy flavor physics at running LHC and upgrading SuperKEKB/Belle-II in the future, the nonleptonic $B_{(s)}^{\ast }\to M_1{M}_2$ $(M=D,D_s,\pi ,K)$ weak decays are studied in this paper. The amplitudes are calculated with factorization approach, and the transition form factors $A_0^{B_{(s)}^{\ast }\to M_1}(0)$ are evaluated within BSW model. With the reasonable approximation ${\Gamma }_{\mathrm{\text{tot}}}\left(\right.B_{(s)}^{\ast }\left)\right.\simeq \Gamma \left(\right.B_{(s)}^{\ast }\to B_{(s)}\gamma \left)\right.$, our predictions of branching fractions are presented. Numerically, the CKM-favored tree-dominated ${\bar{B}}^{\ast 0}\to D^{+}{D}_s^{-}$ and ${\bar{B}}_s^{\ast 0}\to D_s^{+}{D}_s^{-}$ decays have the largest branching fractions of the order $\sim {𝒪}(10^{-8})$, and hence will be firstly observed by forthcoming Belle-II experiment. However, most of the other decay modes have the branching fractions $<{𝒪}(10^{-9})$ and thus are hardly to be observed soon. Besides, for the possible detectable $B_{(s)}^{\ast }$ decays with branching fractions $\gtrsim {𝒪}(10^{-9})$, some useful ratios, such as $R_D$, etc. are presented and discussed in detail.

We study the problem of existence of finite energy monopole solutions in the Weinberg–Salam model starting with the most general ansatz for static axially-symmetric electroweak magnetic fields. The ansatz includes an explicit construction of field configurations with various topologies described by the monopole and Hopf charges. We introduce a unique $SU(2)$ gauge invariant definition for the electromagnetic field. It has been proved that the magnetic charge of any finite energy monopole solution must be screened at far distance. This implies nonexistence of finite energy monopole solutions with a nonzero total magnetic charge. In the case of a special axially-symmetric Dashen–Hasslacher–Neveu ansatz, we revise the structure of the sphaleron solution and show that sphaleron represents a nontrivial system of monopole and antimonopole with their centers located in one point. This is different from the known interpretation of the sphaleron as a monopole–antimonopole pair like Nambu’s “dumb-bell.” In general, the axially-symmetric magnetic field may admit a helical structure. We conjecture that such a solution exists and estimate an upper bound for its energy, $E_{\mathrm{\text{bound}}}=4.65\mathrm{\text{TeV}}$.

Unitarity of evolution in gravitational collapses implies existence of macroscopic stable horizonless objects. With such objects in mind, we study the effects of anisotropy of pressures on the stability of stars. We consider stars in four or higher dimensions and also stars in M theory made up of (intersecting) branes. Taking the stars to be static, spherically symmetric and the equations of state to be linear, we study “singular solutions” and the asymptotic perturbations around them. Oscillatory perturbations are likely to imply instability. We find that nonoscillatory perturbations, which may imply stability, are possible if an appropriate amount of anisotropy is present. This result suggests that it may be possible to have stable horizonless objects in four or any higher dimensions, and that anisotropic pressures may play a crucial role in ensuring their stability.

Since massive scalar field plays an important role in theoretical physics, we consider the interaction between a sphere and a plate due to the vacuum fluctuation of a massive scalar field. We consider combinations of Dirichlet and Neumann boundary conditions. There is a simple prescription to obtain the functional formulas for the Casimir interaction energies, known as TGTG formula, for the massive interactions from the massless interactions. From the TGTG formulas, we discuss how to compute the small separation asymptotic expansions of the Casimir interaction energies up to the next-to-leading order terms. Unlike the massless case, the results could not be expressed as simple algebraic expressions, but instead could only be expressed as infinite sums over some integrals. Nonetheless, it is easy to show that one can obtain the massless limits which agree with previously established results. We also show that the leading terms agree with that derive using proximity force approximation. The dependence of the leading order terms and the next-to-leading order terms on the mass of the scalar field is studied both numerically and analytically. In particular, we derive the small mass asymptotic expansions of these terms. Surprisingly, the small mass asymptotic expansions are quite complicated as they contain terms that are of odd powers in mass as well as logarithms of mass terms.

Branching ratios, lepton forward–backward asymmetries, and lepton polarization asymmetries for the flavor-changing neutral current (FCNC) dileptonic decays of the ${\Lambda }_b$ baryon to the ground state and a number of excited state $\Lambda$ baryons are calculated using form factors extracted using wave functions from a constituent quark model. The SM branching ratios for the transition to the ground state calculated using these quark model form factors are consistent with the recent measurement reported by the LHCb collaboration. It is shown that the lepton polarization asymmetries are largely insensitive to the transition form factors and, therefore, may also be insensitive to the effects of QCD in the nonperturbative regime. These observables could therefore provide somewhat model independent ways of extracting various combinations of the Wilson coefficients.

In this paper, we consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a symmetric global projection, which provides a symmetric form for the Green function. Based on this, we show that it is possible to end up with the propagator of the harmonic oscillator for one charged particle. After some transformations, we derive the normalized wave functions and the eigenvalues in terms of different physical parameters and quantum numbers. By interchanging quantum numbers, we show that our solutions have interesting properties. The density of current and the nonrelativistic limit are analyzed where different conclusions are obtained. Finally, the completeness of the Dirac oscillator eigenfunctions is proved by using the standard properties of the generalized Laguerre polynomials.

We show a possible way to construct a consistent formalism where the effective electric charge can change with space and time without destroying the gauge invariance. In the previous work${}^{1,2}$ we took the gauge coupling to be of the form $g(\varphi )j_{\mu }(A^{\mu }+{\partial }^{\mu }B)$ where $B$ is an auxiliary field, $\varphi$ is a scalar field and the current $j_{\mu }$ is the Dirac current. This term produces a constraint $({\partial }_{\mu }\varphi )j^{\mu }=0$ which can be related to MIT bag model by boundary condition. In this paper, we show that when we use the term $g(\varphi )j_{\mu }(A^{\mu }-{\partial }^{\mu }(\frac{1}{\square }{\partial }_{\rho }{A}^{\rho }))$, instead of the auxiliary field $B$, there is a possibility to produce a theory with dynamical coupling constant, which does not produce any constraint or confinement. The coupling $j_{\mu }^A(A^{\mu }-{\partial }^{\mu }(\frac{1}{\square }{\partial }_{\rho }{A}^{\rho }))$ where $j_{\mu }^A$ is an anomalous current is also discussed.

We study the Nambu–Jona-Lasinio model at finite temperature and finite density by using the functional renormalization group. The RG flows of the four-Fermi coupling constant in the NJL model are investigated. We obtain the chiral phase boundary in cases of the large-$N$ leading approximation and an improved approximation. The large-$N$ nonleading term at the vanishing temperature has a singularity at the Fermi surface. We show that the quantum corrections by the large-$N$ nonleading term largely influence the phase boundary at low temperature and high density region.

In this paper, we will study aspects relating to the gauge symmetry of the ABJM theory, in ${𝒩}=1$ superspace formalism. We will analyze the ABJM theory in a very general gauge by constructing a generalized gauge fixing term and a generalized ghost term for the ABJM theory. In a certain limit, these generalized gauge fixing and ghost terms will reduce to the gauge fixing and ghost terms for the ABJM theory in Maximal Abelian gauge. Furthermore, in a different limit they will reduce to the gauge fixing and ghost terms for the ABJM theory in Landau gauge. Thus, this very general gauge can be used to interpolates between the ABJM theory in Maximal Abelian gauge and the ABJM theory in Landau gauge. The connection between gauges is also established through generalized BRST approach.