802 publications from this institution
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 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.
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.
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.
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 condition under which (0,2) linear sigma models possess a “left-moving” conformal stress tensor in Q + cohomology (i.e. which leaves invariant the “right-moving” ground states) even away from their critical points. At the classical level this enforces quasihomogeneity of the superpotential terms. The persistence of this structure at the quantum level on the worldsheet is obstructed by an anomaly unless the charges and superpotential degrees satisfy a condition which is equivalent to the condition for the cancellation of the anomaly in a particular “right-moving” U(1) R-symmetry.
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.
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.
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.
These are notes on the theory of supermanifolds and integration on them, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
No abstract is provided for this article.
No abstract is provided for this article.
Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of $\N=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the $\N=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.
We analyze the u-plane contribution to Donaldson invariants of a four-manifold X. For $b_2^+(X)>1$, this contribution vanishes, but for $b_2^+=1$, the Donaldson invariants must be written as the sum of a u-plane integral and an SW contribution. The u-plane integrals are quite intricate, but can be analyzed in great detail and even calculated. By analyzing the u-plane integrals, the relation of Donaldson theory to N=2 supersymmetric Yang-Mills theory can be described much more fully, the relation of Donaldson invariants to SW theory can be generalized to four-manifolds not of simple type, and interesting formulas can be obtained for the class numbers of imaginary quadratic fields. We also show how the results generalize to extensions of Donaldson theory obtained by including hypermultiplet matter fields.
Modulo some highly plausible assumptions, we show that vector-like global symmetries (like isospin or baryon number) are not spontaneously broken in vector-like gauge theories with θ = 0 (like QCD). We also show that in these theories massless bound states do not form from massive constituents.
It is shown that in compactification of superstrings on manifolds of SU(3) holonomy, the superpotential receives no string theoretic corrections from the form it takes in the field theoretic limit, at least to all finite orders in sigma model perturbation theory. Modulo nonperturbative effects, this implies that those manifolds do indeed obey the exact classical equations of superstring theory, as has been argued on other grounds. Also, it is pointed out that the superpotential — even in the field theory limit — contains terms coupling charged fields to E6 singlets as well as self-couplings of the charged fields. A slightly tentative argument is given that on certain manifolds of SU(3) holonomy — though not all — it is possible to find conformally invariant sigma models that, while keeping unbroken supersymmetry, break E8 to SO(10) or SU(5) rather than E6. Including the effects of Wilson lines this would mean that E8 could be broken precisely to SU(3) × SU(2) × U(1) while keeping unbroken supersymmetry. These facts may open avenues for solving the problems associated with neutrino masses, proton decay, and renormalization group calculations of coupling constants. They also may lead to models with fewer unknown parameters than have been present in previous quasi-realistic models.
No abstract is provided for this article.
This note is devoted to a detail concerning the work of Albert Einstein and Peter Bergmann on unified theories of electromagnetism and gravitation in five dimensions. In their paper of 1938, Einstein and Bergmann were among the first to introduce the modern viewpoint in which a four-dimensional theory that coincides with Einstein-Maxwell theory at long distances is derived from a five-dimensional theory with complete symmetry among all five dimensions. But then they drew back, modifying the theory in a way that spoiled the five-dimensional symmetry and looks contrived to modern readers. Why? According to correspondence of Peter Bergmann with the author, the reason was that the more symmetric version of the theory predicts the existence of a new long range field (a massless scalar field). In 1938, Einstein and Bergmann did not wish to make this prediction. (Based on a lecture at the Einstein Centennial Celebration at the Library of Alexandria, June, 2005.
