Effective potential and warp factor dynamics

We define an effective potential describing all massless and massive modes in the supergravity limit of string/M theory compactification which is valid off-shell, i.e. without imposing the equations of motion. If we neglect the warp factor, it is unbounded below, as is the case for the action in Euclidean quantum gravity. By study of the constraint which determines the warp factor, we solve this problem, obtaining a physically satisfying and tractable description of the dynamics of the warp factor.Comment: 32 pages, JHEP3.cls. v4: added reference to hep-th/050715

Basic results in Vacuum Statistics

A review of recent work on constructing and finding statistics of string theory vacua, done in collaboration with Frederik Denef, Bogdan Florea, Bernard Shiffman and Steve Zelditch.Comment: 11 pages, 5 figures (Latex elsart.cls, included

Unifying discrete and continuous Weyl-Titchmarsh theory via a class of linear Hamiltonian systems on Sturmian time scales

In this study, we are concerned with introducing Weyl-Titchmarsh theory for a class of dynamic linear Hamiltonian nabla systems over a half-line on Sturmian time scales. After developing fundamental properties of solutions and regular spectral problems, we introduce the corresponding maximal and minimal operators for the system. Matrix disks are constructed and proved to be nested and converge to a limiting set. Some precise relationships among the rank of the matrix radius of the limiting set, the number of linearly independent square summable solutions, and the defect indices of the minimal operator are established. Using the above results, a classification of singular dynamic linear Hamiltonian nabla systems is given in terms of the defect indices of the minimal operator, and several equivalent conditions on the cases of limit point and limit circle are obtained, respectively. These results unify and extend certain classic and recent results on the subject in the continuous and discrete cases, respectively, to Sturmian time scales.Comment: 34 page

Enhanced Gauge Symmetry in M(atrix) Theory

We discuss the origin of enhanced gauge symmetry in ALE (and K3) compactification of M theory, either defined as the strong coupling limit of the type IIa superstring, or as defined by Banks et al. In the D-brane formalism, wrapped membranes are D0 branes with twisted string boundary conditions, and appear on the same footing with the Kaluza-Klein excitations of the gauge bosons. In M(atrix) theory, the construction appears to work for arbitrary ALE metric.Comment: 10 pp, harvma

Some Comments on QCD String

We try to draw lessons for higher dimensions from the string representations recently derived for large $N$ Yang-Mills theory by Gross and Taylor, Kostov, and others, and call attention to three characteristics that should be expected of a string theory precisely equivalent to a higher dimensional gauge theory: continuous world-sheets; strong coupling at short distances; and negative weights. To appear in the proceedings of the Strings '93 Berkeley conference.Comment: RU-94-9. (harvmac, 9 pp.