Modern Physics Letters A

Over the past few years the understanding of the microscopic theory of black hole entropy has made important conceptual progress by recognizing that the degeneracies are encoded in partition functions which are determined by higher rank automorphic representations, in particular in the context of Siegel modular forms of genus two. In this review, some of the elements of this framework are highlighted. One of the surprising aspects is that the Siegel forms that have appeared in the entropic context are geometric in origin, arising from weight two cusp forms, hence from elliptic curves.

We study the quantization of a free scalar field when the background metric satisfies Einstein's equations and develops gravitational shock waves.

We construct (m, n)-type holographic dark energy models at a phenomenological level, which can be viewed as a generalization of agegraphic models with the conformal-like age as the holographic characteristic size. For some values of (m, n) the holographic dark energy can automatically evolve across ω = -1 into a phantom phase even without introducing an interaction between the dark energy and background matter. Our construction is also applicable to the holographic dark energy with generalized future event horizon as the characteristic size. Finally, we address the issue on the stability of our model and show that they are generally stable under the scalar perturbation.

The recent results from Daya Bay and RENO reactor neutrino experiments have firmly established that the smallest reactor mixing angle θ₁₃ is nonvanishing at the 5 σ level, with a relatively large value, i.e. θ₁₃ ≈ 9°. Using the fact that the neutrino mixing matrix can be represented as , where U_l and U_ν result from the diagonalization of the charged lepton and neutrino mass matrices and P_ν is a diagonal matrix containing the Majorana phases and assuming the tri-bimaximal (TBM) form for U_ν, we investigate the possibility of accounting for the large reactor mixing angle due to the corrections of the charged lepton mixing matrix. The form of U_l is assumed to be that of CKM mixing matrix of the quark sector. We find that with this modification it is possible to accommodate the large observed reactor mixing angle θ₁₃. We also study the implications of such corrections on the other phenomenological observables.

We consider the problem of a relativistic particle with position-dependent mass in the presence of a Coulomb and a scalar potentials in the background spacetime generated by a cosmic string. The scalar potential arises from the self-interaction potential which is induced by the conical geometry of the spacetime under consideration. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle. The behavior of the energy levels on the parameters associated with the presence of the cosmic string and with the fact that the mass of the particle depends on its position is also analyzed.

We study a model of scalar quantum field theory (QFT) in which spacetime is a discrete set of points obtained by repeatedly subdividing a triangle into three triangles at the centroid. By integrating out the field variable at the centroid we get a renormalized action on the original triangle. The exact renormalization map between the angles of the triangles is obtained as well. The map can be used to find the partition function in scalar field theories in a recursive manner. A fixed point of this map is the cotangent formula in Finite Element Method which is used to find the energy stored in fields on a plane due to a Laplacian.

We examine the sensitivity to anomalous couplings of the Higgs boson to neutral gauge bosons in a model-independent way at the Large Hadron electron Collider (LHeC). We have obtained the constraints on anomalous couplings for HZZ vertex via the process e^-p→e^-HqX. We find the accessible limits on the CP-conserving coupling b_Z as (-0.12,0.43) and (-0.10,0.33), while the limits on CP-violating coupling β_Z as (-0.32,0.32) and (-0.24,0.24) at the electron beam energy E_e = 60 GeV and E_e = 140 GeV, respectively.