802 publications from this institution
This article is devoted to an overview of superstring perturbation theory from the point of view of super Riemann surfaces. We aim to elucidate some of the subtleties of superstring perturbation that caused difficulty in the early literature, focusing on a concrete example—the $SO(32)$ heterotic string compactified on a Calabi–Yau manifold, with the spin connection embedded in the gauge group. This model is known to be a significant test case for superstring perturbation theory. Supersymmetry is spontaneously broken at 1-loop order, and to treat correctly the supersymmetry-breaking effects that arise at 1- and 2-loop order requires a precise formulation of the procedure for integration over supermoduli space. In this paper, we aim as much as possible for an informal explanation, though at some points we provide more detailed explanations that can be omitted on first reading.
I would like to explain some applications of quantum field theory methods to Donaldson theory. But first, perhaps, I should explain what Donaldson theory is. We start with an oriented four-manifold M,and a compact gauge group, say G = SU (2) We pick a principal G bundle P over M, and let A denote a connection on P The space of such connections will be called A.
We consider the possibility that the neutral-current neutrino detector recently proposed by Drukier and Stodolsky could be used to detect some possible candidates for the dark matter in galactic halos. This may be feasible if the galactic halos are made of particles with coherent weak interactions and masses 1--${10}^{6}$ GeV; particles with spin-dependent interactions of typical weak strength and masses 1--${10}^{2}$ GeV; or strongly interacting particles of masses 1--${10}^{13}$ GeV.
We consider the interpretation in classical geometry of conformal field theories constructed from orbifolds with discrete torsion. In examples we can analyze, these spacetimes contain “tringy regions” that from a classical point of view are singularities that are to be neither resolved nor blown up. Some of these models also give particularly simple and clear examples of mirror symmetry.
No abstract is provided for this article.
It is shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian.Some of the implications of modern ideas in mathematics for supersymmetric theories are discussed.
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from cla
We define the (1 + 1)-dimensional supersymmetry algebra of type (p, q) to be that generated by p right-handed Majorana-Weyl supercharges and q left-handed ones. We construct the non-linear sigma models with supersymmetry of type (1,0) and (2,0) and discuss their geometry and their relevance to compactifications of the heterotic superstring. The sigma-model anomalies can be cancelled by a mechanism closely related to that used by Green and Schwarz to cancel gravitational and Yang-Mills anomalies for the superstring.
In most field theories that enter physics, the energy is defined as the integral of a gauge invariant physically meaningful energy density T00(x):
ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTUnusually strong antiferromagnetic coupling in unsymmetrical diiron(III).mu.-oxo complexesPedro Gomez-Romero, E. H. Witten, William Michael Reiff, and Geoffrey B. JamesonCite this: Inorg. Chem. 1990, 29, 26, 5211–5217Publication Date (Print):December 1, 1990Publication History Published online1 May 2002Published inissue 1 December 1990https://pubs.acs.org/doi/10.1021/ic00351a015https://doi.org/10.1021/ic00351a015research-articleACS PublicationsRequest reuse permissionsArticle Views204Altmetric-Citations23LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-AlertscloseSupporting Info (1)»Supporting Information Supporting Information Get e-Alerts
In the first of these two lectures, I use a comparison to symplectic Khovanov homology to motivate the idea that the Jones polynomial and Khovanov homology of knots can be defined by counting the solutions of certain elliptic partial differential equations in 4 or 5 dimensions. The second lecture is devoted to a description of the rather unusual boundary conditions by which these equations should be supplemented. An appendix describes some physical background. (Versions of these lectures have been presented at various institutions including the Simons Center at Stonybrook, the TSIMF conference center in Sanya, and also Columbia University and the University of Pennsylvania.)
In the twenty-five years since the original publication of these two Volumes, there have been numerous developments in string theory. The curious twists and turns that marked its pre-1987 evolution have continued apace, and current research makes contact with a wide range of areas of mathematics and physics. In the following we will mention briefly some of these developments and then explain why we believe that these volumes are still useful.
In a certain strong coupling limit, compactification of the E 8 × E 8 heterotic string on a Calabi-Yau manifold X can be described by an eleven-dimensional theory compactified on X × S 1/Z 2 . In this limit, the usual relations among low-energy gauge couplings hold, but the usual (problematic) prediction for Newton's constant does not. In this paper, the equations for unbroken supersymmetry are expanded to the first non-trivial order, near this limit, verifying the consistency of the description and showing how, in some cases, if one tries to make Newton's constant too small, strong coupling develops in one of the two E 8's. The lower bound on Newton's constant (beyond which strong coupling develops) is estimated and is relatively close to the actual value.
The topological phase of two-dimensional gravity is re-examined. The correlation functions of the naturally occuring operators in the minimal topological model are computed, using topological methods, in genus zero and genus one. The genus-zero results agree with recent results obtained in exact solutions of “matrix models”, suggesting that the two approaches to two-dimensional gravity are equivalent. The coupling of two-dimensional topological gravity to topological sigma models is investigated. The CP1 model appears to be almost as simple as the pure topological gravity theory. General, model-independent properties of the correlation functions are obtained which hold in coupling to arbitrary topological field theories and can serve as a qualitative definition of the topological phase of two-dimensional gravity. A number of facts that are familiar in the usual phase of string theory, such as the relation between vanishing of the canonical line bundle of a Kähler manifold and scale invariance of the corresponding field theory, have simpler echoes in the topological phase.
The description of superstrings given in chapter 4 suffers from one striking drawback. It is extremely difficult to understand the origins of spacetime supersymmetry. Bosonic strings are described by choosing one set of boundary conditions and fermionic ones by choosing another set. Then, lo and behold, there is a symmetry relating the two sets of states. It is certainly necessary to have this symmetry, as we have already argued, to have consistent interactions of the gravitino field contained in the massless closed-string multiplet. We also showed that when the GSO conditions are imposed there are an equal number of bosons and fermions at every mass level, as is necessary for a linear realization of the supersymmetry.
This note is devoted to a detail concerning the work of Albert Einstein and Peter Bergmann on unied theories of electromagnetism and gravitation in ve dimensions. In their paper of 1938, Einstein and
We derive a holomorphic anomaly equation for the Vafa-Witten partition function for twisted four-dimensional N = 4 super Yang-Mills theory on CP 2 for the gauge group SO(3) from the path integral of the effective theory on the Coulomb branch.The holomorphic kernel of this equation, which receives contributions only from the instantons, is not modular but 'mock modular'.The partition function has correct modular properties expected from S-duality only after including the anomalous nonholomorphic boundary contributions from anti-instantons.Using M-theory duality, we relate this phenomenon to the holomorphic anomaly of the elliptic genus of a two-dimensional noncompact sigma model and compute it independently in two dimensions.The anomaly both in four and in two dimensions can be traced to a topological term in the effective action of six-dimensional (2, 0) theory on the tensor branch.We consider generalizations to other manifolds and other gauge groups to show that mock modularity is generic and essential for exhibiting duality when the relevant field space is noncompact.
