Elusive Worldsheet Instantons in Heterotic String Compactifications
Date
2012-01-01
Authors
Editors
Journal Title
Journal ISSN
Volume Title
Repository Usage Stats
views
downloads
Abstract
We compute the spectrum of massless gauge singlets in some heterotic string compactifications using Landau-Ginzburg, orbifold and non-linear sigma-model methods. This probes the worldsheet instanton corrections to the quadratic terms in the spacetime superpotential. Previous results predict that some of these states remain massless when instanton effects are included. We find vanishing masses in many cases not covered by these predictions. However, we discover that in the case of the Z-manifold the corrections do not vanish. Despite this, in all the examples studied, we find that the massless spectrum in the orbifold limit agrees with the nonlinear sigma-model computation.
Type
Department
Description
Provenance
Subjects
Citation
Permalink
Collections
Scholars@Duke
Paul Stephen Aspinwall
String theory is hoped to provide a theory of all fundamental physics encompassing both
quantum mechanics and general relativity. String theories naturally live in a large number of
dimensions and so to make contact with the real world it is necessary to ``compactify'' the
extra dimensions on some small compact space. Understanding the physics of the real
world then becomes a problem very closely tied to understanding the geometry of the space
on which one has compactified. In particular, when one restricts one's attention to
``supersymmetric'' physics the subject of algebraic geometry becomes particularly important.
Of current interest is the notion of ``duality''. Here one obtains the same physics by
compactifying two different string theories in two different ways. Now one may use our limited understanding of one
picture to fill in the gaps in our limited knowledge of the second picture. This appears to be an extremely powerful
method of understanding a great deal of string theory.
Both mathematics and physics appear to benefit greatly from duality. In mathematics one finds hitherto unexpected
connections between the geometry of different spaces. ``Mirror symmetry'' was an example of this but many more
remain to be explored. On the physics side one hopes to obtain a better understanding of nonperturbative aspects
of the way string theory describes the real world.
M. Ronen Plesser
My research is in String Theory, the most ambitious attempt yet at a comprehensive theory of the fundamental structure of the universe. In some (rather imprecise) sense, string theory replaces the particles that form the fundamental building blocks for conventional theories (the fields, or wave phenomena, we observe are obtained starting from particles when we apply the principles of quantum mechanics) with objects that are not point-like but extended in one dimension – strings. At present, the theory is not precisely formulated, as we still seek the conceptual and technical tools needed. The structures we do have in hand suggest that, when formulated precisely, the theory will provide a consistent framework encompassing the two greatest achievements of twentieth century theoretical physics: Einstein’s general theory of relativity, which describes gravitational forces objects in terms of deformations of the geometry of spacetime; and quantum mechanics, a model of fundamental physics in which microscopic objects exhibit the properties of particles under some circumstances and those of waves under others. Both of these theories have been tested with extraordinary precision and yield predictions that agree with our observations of the physical universe. Relativistic effects are manifest at the largest scales in the universe, in the interactions of stars, galaxies, etc. The differences between a quantum mechanical description and a classical nineteenth century description of these objects are so small they can be neglected. Quantum effects dominate at the smallest scales – atoms and their constituents. In this realm, the effects of gravitation can be completely neglected. And yet, under extreme conditions of density, such as may obtain in the final instant of the evaporation of a black hole, both kinds of effects are important. A universal theory of physics thus requires a consistent quantum theory of gravity. Thus far, string theory is the most promising candidate for producing such a theory. Investigations of this theory have already yielded rich insights, and continue to produce more.
My own research centers on the crucial role played in the theory by geometric structures. There is an obvious role for geometry in a theory that incorporates gravitation, which as discussed above is tantamount to the geometry of spacetime. Related to this are several other, less obvious, geometric structures that play an important role in determining the physics of the theory. Indeed, advances in mathematics and in the physics of string theory have often been closely linked. An example of how the two fields have interacted in a surprising way is the ongoing story of mirror symmetry.
Unless otherwise indicated, scholarly articles published by Duke faculty members are made available here with a CC-BY-NC (Creative Commons Attribution Non-Commercial) license, as enabled by the Duke Open Access Policy. If you wish to use the materials in ways not already permitted under CC-BY-NC, please consult the copyright owner. Other materials are made available here through the author’s grant of a non-exclusive license to make their work openly accessible.