International Journal of Modern Physics A

Diaconescu, Moore and Witten proved that the partition function of type IIA string theory coincides (to the extent checked) with the partition function of M-theory. One of us (Kriz) and Sati proposed in a previous paper a refinement of the IIA partition function using elliptic cohomology and conjectured that it coincides with a partition function coming from F-theory. In this paper, we define the geometric term of the F-theoretical effective action on type IIA compactifications. In the special case when the first Pontrjagin class of space–time vanishes, we also prove a version of the Kriz–Sati conjecture by extending the arguments of Diaconescu–Moore–Witten. We also briefly discuss why even this special case allows interesting examples.

A class of solutions for phantom field corresponding to a generalized k-essence Lagrangian has been presented, employing a simple method which provides the scope to explore many such. All the solutions having dynamical state parameter are found to touch the magic line w = -1 asymptotically. The solutions with constant equation of state can represent phantom, quitessence or an ordinary scalar field cosmologies depending on the choice of a couple of parameters of the theory. For w ≈ -1, quintessence and phantom models are indistinguishable through the Hubble parameter. Finally, it appears that inflation rather than big-rip is the generic feature of phantom cosmology.

In this paper I discuss connections between the noncommutative geometry approach to the Standard Model on one side, and the internal space coming from strings on the other. The Standard Model in noncommutative geometry is described via the spectral action. I argue that an internal noncommutative manifold compactified at the renormalization scale, could give rise to the almost commutative geometry required by the spectral action. I then speculate how this could arise from the noncommutative geometry given by the vertex operators of a string theory.

By making use of the gauge potential decomposition theory and ϕ-mapping theory, the topological structure and the topological quantization of dislocations and disclinations are studied in the framework of Riemann–Cartan space–time manifold. The evolution of dislocation strings and disclination points is also studied from the topological properties of the order parameter field. The dislocations and disclinations are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the order parameter field.

We consider the supergravity backgrounds that correspond to supersymmetric Wilson line operators in the context of AdS/CFT correspondence. We study the gravitino and dilatino conditions of the IIB supergravity under the appropriate ansatz, and obtain some necessary conditions for a supergravity background that preserves the same symmetry as the supersymmetric Wilson lines. The supergravity solutions are characterized by continuous version of Maya diagrams. This diagram is related to the eigenvalue distribution of the Gaussian matrix model. We also consider the similar backgrounds of the 11-dimensional supergravity.

Two-dimensional string theory is known to contain the set of discrete states that are the SU(2) multiplets generated by the lowering operator of the SU(2) current algebra. Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. In this paper we show that the interaction of d = 2 superstrings with the superconformal β - γ ghosts enlarges the actual algebra of the dimension 1 currents and hence the new ghost-dependent discrete states appear. Generally, these states are the SU(N) multiplets if the algebra includes the currents of ghost numbers n : -N ≤ n ≤ N - 2, not related by picture changing. We compute the structure constants of these ghost-dependent discrete states for N = 3 and express them in terms of SU(3) Clebsch–Gordan coefficients, relating this operator algebra to the volume preserving diffeomorphisms in d = 3. For general N, the operator algebra is conjectured to be isomorphic to SDiff(N). This points at possible holographic relations between two-dimensional superstrings and field theories in higher dimensions.

We compute the quantum string entropy S_s(m, H) from the microscopic string density of states ρ_s(m, H) of mass m in Anti-de Sitter space–time. For high m, (high Hm → c/α′), no phase transition occurs at the Anti-de Sitter string temperature T_s = (1/2πk_B)L_clc²/α′, which is higher than the flat space (Hagedorn) temperature t_s. (L_cl = c/H, the Hubble constant H acts as producing a smaller string constant α′ and thus, a higher tension). T_s is the precise quantum dual of the semiclassical (QFT) Anti-de Sitter temperature scale T_sem = ℏc/(2πk_BL_cl). We compute the quantum string emission σ_string by a black hole in Anti-de Sitter (or asymptotically Anti-de Sitter) space–time (bhAdS). For T_{sem bhAdS} ≪ T_s (early evaporation stage), it shows the QFT Hawking emission with temperature T_{sem bhAdS} (semiclassical regime). For T_{sem bhAdS} → T_s, it exhibits a phase transition into a Anti-de Sitter string state of size , and Anti-de Sitter string temperature T_s. New string bounds on the black hole emerge in the bhAdS string regime. The bhAdS string regime determines a maximal value for H : H_max = 0.841c/l_s. The minimal black hole radius in Anti-de Sitter space–time turns out to be r_{g min} = 0.841l_s, and is larger than the minimal black hole radius in de Sitter space–time by a numerical factor equal to 2.304. We find a new formula for the full AdS entropy S_sem(H), as a function of the usual Bekenstein–Hawking entropy . For L_cl ≫ ℓ_Planck, i.e. for low H ≪ c/ℓ_Planck, or classical regime, is the leading term with its logarithmic correction, but for high H ≥ c/ℓ_Planck or quantum regime, no phase transition operates, in contrast to de Sitter space, and the entropy S_sem(H) is very different from the Bekenstein–Hawking term .

We propose an alternative unification scenario where the Higgs self-coupling (λ) is determined by imposing its unification with the electroweak gauge couplings. An attractive feature of models within this scenario is the possibility to determine the Higgs boson mass by evolving λ from the electroweak–Higgs unification scale M_GH down to the electroweak scale. The unification condition for the gauge (g₁, g₂) and Higgs couplings is written as g₁ = g₂ = f(λ), where being the normalization constant. Two variants for the unification condition are discussed; scenario I is defined through the linear relation: g₁ = g₂ = k_Hλ(M_GH), while scenario II assumes a quadratic relation: . Fixing k_H = O(1) and the standard normalization (k_Y = 5/3), we obtain a Higgs boson mass value m_H ≃ 190 GeV, with similar results for other normalizations such as k_Y = 7/4 and 3/2. However, the unification scale M_GH depends on the value of k_Y, going from 1.8 ×10¹²GeV up to 4.9 ×10¹⁴GeV for 7/4 > k_Y > 3/2. Possible tests of this idea at a future linear collider and its application for determining the Higgs spectrum in the two-Higgs doublet model are also discussed. We also elaborate on these unification scenarios within the context of a six-dimensional SU(3)_c×SU(3)_w Gauge–Higgs unified model, where the Higgs boson arises as the extra-dimensional components of the 6D gauge fields.

We prove the existence of a strong coupling expansion for a classical λϕ⁴ field theory in agreement with the duality principle in perturbation theory put forward in a paper: M. Frasca, Phys. Rev. A58, 3439 (1998). The leading order solution is a snoidal wave taking the place of plane waves of the free theory. We compute the first-order correction and show that higher-order terms do renormalize the leading order solution.