International Journal of Modern Physics A

Compactifications of the heterotic string are a viable route to phenomenologically realistic vacua and interesting new mathematics. While supergravity aspects of heterotic compactifications are largely well-understood their worldsheet description remains largely unexplored. We review recent work in developing linear sigma model techniques aimed at elucidating the underlying worldsheet description.

We study the nature of the covariant thermodynamic geometry arising from the free energy of hot QCD. We systematically analyze the underlying equilibrium thermodynamic configurations of the free energy of two- and three-flavor hot QCD with or without the inclusion of thermal fluctuations in the neighborhood of the QCD transition temperature. We show that there exists a well-defined thermodynamic geometric notion for the QCD thermodynamics. The geometry thus obtained has no singularity as an intrinsic Riemannian manifold. We further show that there is a close connection of this geometric approach with the existing studies of correlations and quark number susceptibilities.

We consider an imaginary time functional integral formulation of a two-flavor, 3+1 lattice QCD model with Wilson's action and in the strong coupling regime (with a small hopping parameter, κ > 0, and a much smaller plaquette coupling, , so that the quarks and glueballs are heavy). The model has local SU(3)_c gauge and global SU(2)_f flavor symmetries, and incorporates the corresponding part of the eightfold way particles: baryons (mesons) of asymptotic mass ≈-3 ln κ(≈-2 ln κ). We search for pentaquark states as meson–baryon bound states in the energy–momentum spectrum of the model, using a lattice Bethe–Salpeter equation. This equation is solved within a ladder approximation, given by the lowest nonvanishing order in κ and β of the Bethe–Salpeter kernel. It includes order κ² contributions with a exchange potential together with a contribution that is a local-in-space, energy-dependent potential. The attractive or repulsive nature of the exchange interaction depends on the spin of the meson–baryon states. The Bethe–Salpeter equation presents integrable singularities, forcing the couplings to be above a threshold value for the meson and the baryon to bind in a pentaquark. We analyzed all the total isospin sectors, I = 1/2, 3/2, 5/2, for the system. For all I, the net attraction resulting from the two sources of interaction is not strong enough for the meson and the baryon to bind. Thus, within our approximation, these pentaquark states are not present up to near the free meson–baryon energy threshold of ≈-5 ln κ. This result is to be contrasted with the spinless case for which our method detects meson–baryon bound states, as well as for Yukawa effective baryon and meson field models. A physical interpretation of our results emerges from an approximate correspondence between meson–baryon bound states and negative energy states of a one-particle lattice Schrödinger Hamiltonian.

The canonical Hamiltonian path integral measure obeys certain rule which relates such measure on the paths defined on the whole time axis to the measures on the paths defined on the regions constituting the time axis. We show that this "gluing" rule can be reproduced without referring to Hamiltonian formalism, by substituting field configurations with arbitrarily fast change of the fields at the boundary points of these regions into action and viewing the path integral in the sense of generalized function. Now the coordinate along which gluing proceeds can be not only the time.

The piecewise-flat (simplicial) minisuperspace gravity system is considered. Arbitrarily fast change of the (tangential component of) metric between the two 4-simplices with common 3-face is studied. That is, we generalize piecewise-flat anzats by allowing tangential metric to be function of the distance from the 3-face in the neighborhood of this 3-face. The action is nondegenerate (nonsingular) with respect to these additional generalized coordinates. The rule for gluing the path integral measures on separate 4-simplices is found. The resulting general expression covers a large variety of the measures including those usually used in numerical calculations and allows one to specify the measure in some applications.

In this paper we study some aspects of closed string theories in the Nappi–Witten space–time. The effects of spectral flow on the geodesics are studied in terms of an explicit parametrization of the group manifold. The worldsheets of the closed strings under the spectral flow of the geodesics can be classified into four classes, each with a geometric interpretation. We also obtain a free field realization of the Nappi–Witten affine Lie algebra in the most general conditions using a different but equivalent parametrization of the group manifold.

A model is built in which the main global properties of classical and quasiclassical black holes become local. These are the event horizon, "no hair," temperature and entropy. The construction is based on the features of a quantum collapse, discovered when studying some quantum black hole models. But the model is purely classical, and this allows one to use self-consistently the Einstein equations and classical (local) thermodynamics and explain in this way the "log 3" puzzle.