International Journal of Modern Physics A

I discuss methods of calculation of propagator diagrams (massless, those of Heavy Quark Effective Theory, and massive on-shell diagrams) up to three loops. Integration-by-parts recurrence relations are used to reduce them to linear combinations of basis integrals. Nontrivial basis integrals have to be calculated by some other method, e.g. using Gegenbauer polynomial technique. Many of them are expressed via hypergeometric functions; in the massless and HQET cases, their indices tend to integers at ε→0. I discuss the algorithm of their expansion in ε, in terms of multiple ζ values.

The membrane instanton superpotential for M-theory on the G₂ holonomy manifold given by the cone on S³×S³ is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dilogarithm for the deformed conifold and to a flat bundle related to a conifold period, the Heisenberg group and the dilogarithm appearing in five-dimensional Seiberg/Witten theory.

We analyze possible cosmological scenarios on a brane where the brane acts as a dynamical boundary of various black holes with anti-de Sitter or de Sitter asymptotic. In many cases, the brane is found to describe the completely nonsingular universe. In some cases, quantum gravity era of the brane-universe can also be avoided by properly tuning bulk parameters. We further discuss the creation of a brane-universe by studying its wave function. This is done by employing Wheeler–De Witt equation in the mini superspace formalism.

We investigate several models described by real scalar fields, searching for topological defects, and investigating their linear stability. We also find bosonic zero modes and examine the thermal corrections at the one-loop level. The classical investigations are of direct interest to high energy physics and to applications in condensed matter, in particular to spatially extended systems where fronts and interfaces separating different phase states may appear. The thermal investigations show that the finite temperature corrections that appear in a specific model induce a second-order phase transition in the system, although the thermal effects do not suffice to fully restore the symmetry at high temperature.

The group embeddings used in orbifolding the AdS/CFT correspondence to arrive at quiver gauge field theories are studied for both supersymmetric and nonsupersymmetric cases. For an orbifold AdS₅×S⁵/Γ the conditions for embeddings of the finite group Γ in the SU(4)~O(6) isotropy of S⁵ are stated in the form of consistency rules, both for Abelian and non-Abelian Γ.

We discuss the hadroproductions of Λ_c, , D and in the framework of the constituent quark–diquark cascade model taking into account the valence quark annihilation. The spectra of Λ_c and in pA, Σ^-A and π^-A collisions are well explained by the model using the values of parameters used in hadroproductions of D and . It is shown that the role of valence diquark in the incident baryon is important for productions as well as for Λ_c production.

We propose an exact expression for the unintegrated form of the star gauge-invariant axial anomaly in an arbitrary even dimensional noncommutative gauge theory. The proposal is based on our earlier work,⁷ as well as on the inverse Seiberg–Witten map and identities related to it, obtained previously^15,18 by comparing Ramond–Ramond couplings in different descriptions. The integrated anomalies, found from the unintegrated ones, are expressed in terms of a simplified version of the Elliott formula involving the noncommutative Chern character. These anomalies, under the Seiberg–Witten transformation, reduce to the ordinary (integrated) axial anomalies. Compatibility with existing results of anomalies in noncommutative theories is established.