Stephen H. Shenker

Strings in Less Than One-Dimension

Starting from the random triangulation definition of two-dimensional euclidean quantum gravity, we define the continuum limit and compute the partition function for closed surfaces of any genus. We discuss the appropriate way to define continuum string perturbation theory in these systems and show that the coefficients (as well as the critical exponents) are universal. The universality classes are just the multicritical points described by Kazakov. We show how the exact non-perturbative string theory is described by a non-linear ordinary differential equation whose properties we study. The behavior of the simplest theory, c = 0 pure gravity, is governed by the Painleve transcendent of the first kind.

D-branes and short distances in string theory

We study the behavior of D-branes at distances far shorter than the string length scale ls. We argue that short-distance phenomena are described by the IR behavior of the D-brane worldvolume quantum theory. This description is valid until the brane motion becomes relativistic. At weak string coupling gs this corresponds to momenta and energies far above string scale. We use 0-brane quantum mechanics to study 0-brane collisions and find structure at length scales corresponding to the eleven-dimensional Planck length (lp11 ∼ gs13 lss) and to the radius of the eleventh dimension in M-theory (R11, ∼ gsls). We use 0-branes to probe non-trivial geometries and topologies at sub-stringy scales. We study the 0-brane 4-brane system, calculating the 0-brane moduli space metric, and find the bound state at threshold, which has characteristic size lp11. We examine the blowup of an orbifold and are able to resolve the resulting S2 down to size lp11. A 0-brane with momentum approaching 1/R11 is able to explore a larger configuration space in which the blowup is embedded. Analogous phenomena occur for small instantons. We finally turn to 1-branes and calculate the size of a bound state to be ∼ gs12ls, the l-brane tension scale.

Dynamics of SU(N) supersymmetric gauge theory

We study the physics of the Seiberg-Witten and Argyres-Faraggi-Klemm-Lerche-Theisen-Yankielowicz solutions of D = 4, N = 2 and N = 1 SU(N) supersymmetric gauge theory. The N = 1 theory is confining and its effective Lagrangian is a spontaneously broken U(1)N−1 abelian gauge theory. We identify some features of its physics which see this internal structure, including a spectrum of different string tensions. We discuss the limit N → ∞, identify a scaling regime in which instanton and monopole effects survive, and give exact results for the crossover from weak to strong coupling along a scaling trajectory. We find a large hierarchy of mass scales in the scaling regime, including very light W bosons, and the absence of weak coupling. The light Ws leave a novel imprint on the effective dual magnetic theory. The effective Lagrangian appears to be inadequate to understand the conventional large N limit of the confining N = 1 theory

Branes from matrices

Abstract Various aspects of branes in the recently proposed matrix model for M-theory are discussed. A careful analysis of the supersymmetry algebra of the matrix model uncovers some central changes which can be activated only in the large N limit. We identify the states with non-zero charges as branes of different dimensions.

Microscopic and macroscopic loops in non-perturbative two dimensional gravity

Two-dimensional quantum gravity is relevant both for string theory and as a toy model of higher-dimensional quantum gravity. The definition of pure 2D quantum gravity and quantum gravity coupled to matter in terms of matrix models1 is very explicit and rigorous. Matrix realizations of pure gravity and gravity coupled to certain minimal conformai field theories (and their massive deformations) can be solved by the application of large-N techniques. Recently, an exact expression for the specific heat of some of these models was found in the continuum limit.2-6 In this chapter, we will show that the correlation functions of operators in these models can also be easily computed. We distinguish between two kinds of operators, microscopic and macroscopic loops. By microscopic loops we mean expressions like Tr M p in the matrix models with p finite. They contain all the information about integrals over the surface of local operators.

The Strength of Nonperturbative Effects in String Theory

We argue that the leading weak coupling nonperturbative effects in closed string theories should be of order exp(— C/κ) where κ 2 is the closed string coupling constant. This is the case in the exactly soluble matrix models. These effects are in principle much larger than the exp(—C/κ 2 ) effects typical of the low energy field theory. We argue that this behavior should be generic in string theory because string perturbation theory generically behaves like (2g)! at genus g.

The ising model coupled to 2D gravity. A nonperturbative analysis

Abstract We apply recently developed techniques to give an exact nonperturbative solution of the two matrix realization of the Ising model coupled to 2D lattice gravity. We demonstrate that the Ising model is different from multicritical matter. We conjecture that multicritical matter is described by certain non-unitary minimal models.

Proposal for a simple model of dynamical SUSY breaking

Abstract We discuss supersymmetric SU (2) gauge theory with a single matter field in the I = 3 2 representation. This theory has a moduli space of exactly degenerate vacua. Classically it is the complex plane with an orbifold singularity at the origin. There seem to be two possible candidates for the quantum theory at the origin. In both the global chiral symmetry is unbroken. The first is interacting quarks and gluons at a non-trivial infrared fixed point — a non-Abelian Coulomb phase. The second, which we consider more likely, is a confining phase where the singularity is simply smoothed out. If this second, more likely, possibility is realized, supersymmetry will dynamically break when a tree level superpotential is added. This would be the simplest known gauge theory which dynamically breaks supersymmetry.

Flow and instability in quantum gravity

Abstract We study the flow form the m = 3 multicritical matrix theory, unambiguously defined by Brezin, Marinari and Parisi, to the m = 2 pure gravity theory. We find behavior in the flow indicative of a non-perturbative instability in this definition of non-perturbative pure quantum gravity. We expect a similar situation for all m even theories. Other definitions of these theories are briefly discussed.

Issues in M(atrix) Theory Compactification

We discuss issues concerning M(atrix) theory compactifications on curved spaces. We argue from the form of the graviton propagator on curved space that excited string states do not decouple from the annulus D0-brane υ^4 amplitude, unlike the flat space case. This argurment shows that a large class of quantum mechanical systems with a finite number of degrees of freedom cannot reproduce supergravity answers. We discuss the specific example of an ALE space and suggest sources of possible higher derivative terms that might help reproduce supergravity results.