International Journal of Modern Physics A

Using a nonperturbative approach based on the Cornwall–Jackiw–Tomboulis (CJT) effective action ${\Gamma }(S)$ for composite operators, the phase structure of the simplest massless $(2+1)$-dimensional Gross–Neveu model is investigated. We have calculated ${\Gamma }(S)$ in the first-order of the bare coupling constant $G$ and have shown that there exist three different specific dependences of $G\equiv G(\mathrm{\Lambda })$ on the cutoff parameter $\mathrm{\Lambda }$, and in each case, the effective action and its stationarity equations have been obtained. The solutions of these equations correspond to the fact that three different masses of fermions can arise dynamically and, respectively, three different nontrivial phases can be observed in the model.

This paper investigates the new definition of complexity factor for the case of irrotational spherical relativistic structure in the Rastall theory of gravity (RTG). To do so, we assumed static spherically symmetric metric with anisotropic self-gravitating fluid. We studied Rastall field equations, generalized nonconservation equation, mass function and physical impacts of Rastall parameter $\alpha$ on various material variables by employing certain observational data of compact objects like PSR J1614-2230, 4U1608-52, SAX J 1808.4-3658, 4U1820-30 and Vela X-1. We obtained structure scalars through orthogonal decomposition of the curvature tensor and then utilize these scalars to find the complexity factor of the self-gravitating spherical structure. We examined that the vanishing complexity factor condition is an effective energy density inhomogeneity and an effective anisotropy of pressure which must cancel each other, employed the condition $Y_{TF}=0$. Moreover, we also depicted the solutions of interior formation of spherical stellar object regarding to this vanishing complexity condition. Finally, it is found that the complexity of the system enhances due to the presence of nonminimal to curvature matter couple parameter $\alpha$. It is very fascinating to report here that these outcomes could be recovered back to former solutions about complexity factor in General Relativity (GR) by imposing $\alpha =0$.

A Gaussian approximation to the bosonic part of M-(atrix) theory with mass deformation is considered at large values of the dimension $d$. From the perspective of the gauge/gravity duality this action reproduces with great accuracy the stringy Hagedorn phase transition from a confinement (black string) phase to a deconfinement (black hole) phase whereas from the perspective of the matrix/geometry approach this action only captures a remnant of the geometric Yang–Mills-to-fuzzy-sphere phase where the fuzzy sphere solution is only manifested as a three-cut configuration termed the “baby fuzzy sphere” configuration. The Yang–Mills phase retains most of its characteristics with two exceptions: (i) the uniform distribution inside a solid ball suffers a crossover at very small values of the gauge coupling constant to a Wigner’s semicircle law, and (ii) the uniform distribution at small values of the temperatures is nonexistent.

A bonus of the framed Standard Model (FSM), constructed initially to explain the mass and mixing patterns of quarks and leptons, is a solution (without axions) of the strong CP problem by cancelling the theta-angle term ${𝜃}_I\mathrm{Tr}(H^{\mu \nu }{H}_{\mu \nu }^{\ast })$ in colour by a chiral transformation on a quark zero mode which is inherent in FSM, and produces thereby a CP-violating phase in the CKM matrix similar in size to what is observed.¹ Extending here to flavour, one finds that there are two terms proportional to $\mathrm{Tr}(G^{\mu \nu }{G}_{\mu \nu }^{\ast })$: (a) in the action from flavour instantons with unknown coefficient, say ${𝜃}_I^{\prime }$, (b) induced by the above FSM solution to the strong CP-problem with therefore known coefficient ${𝜃}_C^{\prime }$. Both terms can be cancelled in the FSM by a chiral transformation on the lepton zero mode to give a Jarlskog invariant $J^{\prime }$ in the PMNS matrix for leptons of order $10^{-2}$, as is hinted by the experiment. But if, as suggested in Ref. 2, the term ${𝜃}_I^{\prime }$ is to be cancelled by a chiral transformation in the predicted hidden sector to solve the strong CP problem therein, leaving only the term ${𝜃}_C^{\prime }$ to be cancelled by the chiral transformation on leptons, then the following prediction results: $J^{\prime }\sim -0.012$ $({\delta }_{\mathrm{\text{CP}}}^{\prime }\sim (1.11)\pi )$ which is (i) of the right order, (ii) of the right sign and (iii) in the range favoured by the present experiment. Together with the earlier result for quarks, this offers an attractive unified treatment of all known CP physics.

A unified treatment of CP physics for quarks and leptons in the framed Standard Model (FSM) is extended to include the predicted hidden sector giving as consequences: (i) that an earlier part estimate of the Jarlskog invariant $J^{\prime }$ for leptons is turned into a prediction for its actual value, i.e. $J^{\prime }\sim -0.012$ $({\delta }_{\mathrm{\text{CP}}}^{\prime }\sim 1.11\pi )$, which is of the right order of magnitude, of the right sign, and in the range of values favoured by the present experiment, (ii) some novel twists to the effects of CP-violation on the material content of the universe.

In this paper, the thermodynamics of Gauss–Bonnet black hole is investigated. We calculate the analytical solutions of corresponding thermodynamic variables, e.g. the Hawking temperature, entropy of the black hole at its event horizon. In addition, we derive the heat capacity to analyze the thermal stability of the black hole. We also compute the rate of emission in terms of photons through tunneling. By adopting a numerical method to analyze their properties, an obvious phase transition behavior is found. Furthermore, according to the general uncertainty principle, we study the quantum corrections to these thermodynamic quantities and obtain the quantum-corrected entropy containing the logarithmic term. At last, we investigate the effects of the Gauss–Bonnet coupling parameter $\sigma$ and generalized uncertainty principle parameter $\alpha$ on the thermodynamics of Gauss–Bonnet black hole.

In physics, the application of the regular cases of spacelike fronts has been studied extensively; however, under the gravitational influence, the spacelike fronts can be singular. In this paper, we will consider the traveling trajectories of a set of parallel light rays as spacelike fronts with singularities in null de Sitter sphere. It is of great significance to investigate and explore the spacelike fronts which may have singularities in null de Sitter sphere. We also characterize the singularities of the nullcone dual worldsheets generated by spacelike fronts via the spherical curvature. Then we define the nullcone caustics and analyze the geometric properties of the nullcone caustics at singular points. Moreover, we establish the dual relationship between spacelike fronts and the nullcone dual worldsheets.

In the QCD sum rules for the tetraquark (molecular) states, the higher-dimensional vacuum condensates play an important role in extracting the tetraquark masses. We carry out the operator product expansion up to the vacuum condensates of dimension-10 and observe that the vacuum condensates of dimensions 6, 8 and 10 have the same expressions but opposite signs for the $C{\gamma }_5\otimes {\gamma }_{\mu }C$-type and $C\otimes {\gamma }_{\mu }C$-type four-quark currents, which make their influences distinguishable, and they are excellent channels to examine the vacuum saturation approximation. We introduce a parameter $\kappa$ to parametrize the derivation from the vacuum saturation or factorization approximation, and choose two sets of parameters to examine the influences on the predicted tetraquark masses, which can be confronted to the experimental data in the future. In all the channels, smaller value of the $\kappa$ leads to better convergent behavior in the operator product expansion, which favors the vacuum saturation approximation.