arXiv subjects
Publications and source records attributed to H. B. Gao.
We propose a configuration of D-branes welded by analogous orbifold operation to be responsible for the enhancement of $SO(2N)$ gauge symmetry in type II string compactified on the $D_n$-type singular limit of K3. Evidences are discussed from the $D_n$-type ALE and D-manifold point of view. A subtlety regarding the ability of seeing the enhanced $SO(2N)$ gauge symmetry perturbatively is briefly addressed.
We construct more dual pairs of type II-heterotic strings in four dimensions with $N=2,1$ spacetime supersymmetry. On the type II side the construction utilizes the various possible choices of K3 automorphisms with fixed points which transform the holomorphic two-form nontrivially, and rotation plus translation on $T^2$. The Calabi-Yau orbifolds so obtained have non-zero Euler numbers, so quantum corrections exist on the type IIA strings. The heterotic string (asymmetric) orbifold duals are found which depend on going to the enhanced symmetry points. Some aspects of the construction are discussed including the role of the singularity and the possibility of going beyond the adiabatic argument. Many of these examples have also orientifold analogs.
In terms of the gauged nonlinear $σ$-models, we describe some results and implications of solving the following problem: Given a smooth symplectic manifold as target space with a quasi-free Hamiltonian group action, perform the symplectic blowing up of the point singularity and identify the blow-up modes in the corresponding (gauged) $σ$-model. Both classical and quantum aspects of the construction are explained, along with illustrating examples from the toric projective space and the Kähler manifold. We also discuss related problems such as the origin of Mirror symmetry and the quantum cohomologies.(Talk to be given at ICHEP94, Glasgow, July 20-27.)
In this paper a two dimensional non-linear sigma model with a general symplectic manifold with isometry as target space is used to study symplectic blowing up of a point singularity on the zero level set of the moment map associated with a quasi-free Hamiltonian action. We discuss in general the relation between symplectic reduction and gauging of the symplectic isometries of the sigma model action. In the case of singular reduction, gauging has the same effect as blowing up the singular point by a small amount. Using the exponential mapping of the underlying metric, we are able to construct symplectic diffeomorphisms needed to glue the blow-up to the global reduced space which is regular, thus providing a transition from one symplectic sigma model to another one free of singularities.
The renormalization group flow recently found by Brézin and Zinn- Justin by integrating out redundant entries of the $(N+1)\times (N+1)$ hermitian random matrix is studied. By introducing explicitly the RG flow parameter, and adding suitable counter terms to the matrix potential of the one matrix model, we deduce some interesting properties of the RG trajectories. In particular, the string equation for the general massive model interpolating between the UV and IR fixed points turns out to be a consequence of RG flow. An ambiguity in the UV regime of the RG trajectory is remarked to be related to the large order behavior of the one matrix model.