International Journal of Modern Physics A

By applying the renormalization group equation, it has been shown that the effective potential V in the massless model and in massless scalar quantum electrodynamics is independent of the scalar field. This analysis is extended here to the massive model, showing that the effective potential is independent of ϕ here as well.

Based on the observations that there exists an analogy between the Reissner–Nordström–Anti-de Sitter (RN–AdS) black holes and the van der Waals–Maxwell liquid-gas system, in which a correspondence of variables is (ϕ,q) ↔ (V,P), we study the Ruppeiner geometry, defined as Hessian matrix of black hole entropy with respect to the internal energy (not the mass) of black hole and electric potential (angular velocity), for the RN, Kerr and RN–AdS black holes. It is found that the geometry is curved and the scalar curvature goes to negative infinity at the Davies' phase transition point for the RN and Kerr black holes. Our result for the RN–AdS black holes is also in good agreement with the one about phase transition and its critical behavior in the literature.

We argue the existence of a universal open-string interaction induced by open-string singlet exchange from the universality of gravity diagram involving open strings. At the tree level, the interaction is induced by stringy massive excitations of spin-1 and spin-2 at the leading order. The origin of this interaction is purely stringy in nature with the massless contributions canceling each other at the tree level and therefore has no field theory correspondence. The effective dimension-8 interactions at low energies for both spin-1 and spin-2 are given for the four-fermion processes. The spin-2 piece of the interaction to a pair of vector bosons is twice as strong as when it couples to a pair of fermions as a result of the SUSY constraint on the amplitudes and angular momentum decomposition. The massive spin-2 piece of the interaction is separately universal for fermions and vector bosons, in contrast to conventional massive gravity.

We investigate quasilocal tachyon condensation by using gravity/gauge duality. In order to cure the IR divergence due to a tachyon, we introduce two regularization schemes: AdS space and a d = 10 Schwarzschild black hole in a cavity. These provide stable canonical ensembles and thus are good candidates for the end point of tachyon condensation. Introducing the Cardy–Verlinde formula, we establish the on-shell gravity/gauge duality. We propose that the stringy geometry resulting from the off-shell tachyon dynamics matches onto the off-shell AdS black hole, where "off-shell" means nonequilibrium configuration. The instability induced by condensation of a tachyon behaves like an off-shell black hole and evolves toward a large stable black hole. The off-shell free energy and its derivative (β-function) are used to show the off-shell gravity/gauge duality for the process of tachyon condensation. Further, d = 10 Schwarzschild black hole in a cavity is considered for the Hagedorn transition as a possible explanation of the tachyon condensation.

It is discussed how a limiting procedure of conformal field theories may result in logarithmic conformal field theories with Jordan cells of arbitrary rank. This extends our work on rank-two Jordan cells. We also consider the limits of certain three-point functions and find that they are compatible with known results. The general construction is illustrated by logarithmic limits of minimal models in conformal field theory. Characters of quasirational representations are found to emerge as the limits of the associated irreducible Virasoro characters.

We show that we can construct a model in 3+1 dimensions where it is necessary that composite vector particles take place in physical processes as incoming and outgoing particles. Cross-section of the processes in which only the constituent spinors take place goes to zero. While the spinor–spinor scattering goes to zero, the scattering of composites gives nontrivial results.

A q-deformed version of classical analysis is given to quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. The subject is presented in a rather complete and self-contained way. All relevant notions are introduced and explained in detail. The different possibilities to realize the objects of q-deformed analysis are discussed and their elementary properties are studied. In this manner attention is focused on star products, q-deformed tensor products, q-deformed translations, q-deformed partial derivatives, dual pairings, q-deformed exponentials, and q-deformed integration. The main concern of this work is to show that these objects fit together in a consistent framework, which is suitable to formulate physical theories on quantum spaces.

Motivated by string gas cosmology, we investigate the stability of moduli fields coming from compactifications of string gas on torus with background flux. It was previously claimed that moduli are stabilized only at a single fixed-point in moduli space, a self-dual point of T-duality with vanishing flux. Here, we show that there exist other stable fixed-points on moduli space with nonvanishing flux. We also discuss the more general target space dualities associated with these fixed-points.

We generalize the Endo formula¹ originally developed for the computation of the heat kernel asymptotic expansion for nonminimal operators in commutative gauge theories to the noncommutative case. In this way, the first three nonzero heat trace coefficients of the nonminimal U(N) gauge field kinetic operator on the Moyal plane taken in an arbitrary background are calculated. We show that the nonplanar part of the heat trace asymptotics is determined by U(1) sector of the gauge model. The nonplanar or mixed heat kernel coefficients are shown to be gauge-fixing dependent in any dimension of space–time. In the case of the degenerate deformation parameter the lowest mixed coefficients in the heat expansion produce nonlocal gauge-fixing dependent singularities of the one-loop effective action that destroy the renormalizability of the U(N) model at one-loop level. Such phenomenon was observed at first in Ref. 2 for spacelike noncommutative ϕ⁴ scalar and U(1) gauge theories. The twisted-gauge transformation approach is discussed.

The asymptotic iteration method is used to calculate the eigenenergies for the asymmetrical quantum anharmonic oscillator potentials , with (α = 2) for quartic, and (α = 3) for sextic asymmetrical quantum anharmonic oscillators. An adjustable parameter β is introduced in the method to improve its rate of convergence. Comparing the present results with the exact numerical values, and with the numerical results of the earlier works, it is found that asymptotically, this method gives accurate results over the full range of parameter values A_j.