Igor R. Klebanov

Baryon Masses in the Bound State Approach to Strangeness in the Skyrme Model

Abstract We diagonalize exactly the O( N 0 c ) hamiltonian relevant to the bound state approach to strangeness in the Skyrme model. The hyperfine splitting of strange baryons computed within this framework agree well with the experimental values.

Wormholes and the cosmological constant

We review Colemans wormhole mechanism for the vanishing of the cosmological constant. We show that in a minisuperspace model wormhole-connected universes dominate the path integral. We also provide evidence that the euclidean path integral over geometries with spherical topology is unstable with respect to formation of infinitely many wormhole-connected 4-spheres. Consistency is restored by summing over all topologies, which leads to Colemans result. Colemans argument for determination of other parameters is reviewed and applied to the mass of the pion. A discouraging result is found that the pion mass is driven to zero. We also consider qualitatively the implications of the wormhole theory for cosmology. We argue that a small number of universes containing matter and energy may exist in contact with infinitely many cold and empty universe. Contact with the cold universe insures that the cosmological constant in the warm ones in zero.

Continuum strings from discrete field theories

Abstract We demonstrate that one of the phases of a light-cone lattice gauge theory with an infinite number of colors exactly describes free fundamental strings. The lattice spacing does not have to be taken to zero. Thus, exact rotation and translation invariance can coexist with discrete space.

SIZE AND SHAPE OF STRINGS

We study numerically and analytically spatial properties of the ground state of a fundamental string in the light-cone gauge. We find that strings are smooth and have divergent average size. Their properties are very different from what is expected from particles in a conventional field theory.

Renormalization Group and String Amplitudes

Abstract We define β-functions for open-string tachyons away from the perturbative fixed point. We show that solutions of the renormalization-group fixed-point equations generate open-string scattering amplitudes.

Quantum Mechanics of the Googolplexus

«La formulation euclidienne de la gravitation est un sujet qui na pas de fondements solides ni de regles de procedure claires; elle ressemble en effet a un marais sans pistes. Je pense men etre sorti sain et sauf, mais il est toujours possible que, sans le savoir, je sois dans des sables mouvants jusquau cou et que je menfonce rapidement.» Sidney Coleman

The role of a massive strange quark in the Large-N Skyrme model

Abstract We analyze the rigid rotator treatment of the three-flavor Skyrme model in the limit of a large number of colors. This is an approximation to the bound state approach to strangeness. The dynamical picture of baryons that emerges is similar to that of the non-relativistic quark model. In particular, we find a collective excitation of the q q background with all the properties of a constituent strange quark. We calculate the nucleon mass and the matrix element 〈N| s s |N〉 as functions of the mass of the strange quark.

String loop divergences and effective lagrangians

Abstract We isolate logarithmic divergences from bosonic string amplitudes on a disc. These divergences are compared with “tadpole” divergences in the effective field theory, with a covariant cosmological term implied by the counting of string coupling constants. We find an inconsistency between the two. This might be a problem in eliminating divergences from the bosonic string.

Strings in Space

String theory was originally invented to describe hadrons.* Ultimately this idealized mathematical theory of hadrons failed, owing in part to the inability to couple strings to the external local fields, such as the electromagnetic field. The reason for this failure is the infinity of normal mode zero point fluctuations spreading the string over all space [2]. In this chapter we will examine in detail the spatial properties of fundamental strings. We will also speculate on how they compare with the strings of large-N color gauge theory.† We will be particularly interested in the following characteristics of the ground state of the fundamental string: n n1. n nWhat is the average size of the spatial region occupied by the string? n n n n n2. n nWhat is the average length of the string? n n n n n3. n nIs the string smooth on small scales or does it exhibit rough or fractal-like behavior? n n n n n4. n nHow densely is space filled with string?

String Perturbation Theory and Effective Lagrangians

We isolate logarithmic divergences from bosonic string amplitudes on a disc. These divergences are compared with ‘tadpole’ divergences in the effective field theory with a cosmological term, which also contains an effective potential for the dilaton. Also, corrections to β-functions are compared with variations of the effective action. In both cases we find an inconsistency between the two. This is a serious problem which could undermine our ability to remove divergences from the bosonic string.