802 publications from this institution
The SO(32) heterotic superstring on a Calabi-Yau manifold can spontaneously break supersymmetry at one-loop order even when it is unbroken at tree-level. It is known that calculating the supersymmetry-breaking effects in this model gives a relatively accessible test case of the subtleties of superstring perturbation theory in the RNS formalism. In the present paper, we calculate the relevant amplitudes in the pure spinor approach to superstring perturbation theory, and show that the regulator used in computing loop amplitudes in the pure spinor formalism leads to subtleties somewhat analogous to the more familiar subtleties of the RNS approach.
No abstract is provided for this article.
String theory may provide the best clues yet about how to obtain a unified theory that describes all the laws of nature, but do we even understand what string theory is?
It was recently proposed (by Candelas, Horowitz, Strominger and the author) that compact manifolds of SU(3) holonomy are an interesting starting point for superstring phenomenology. Some aspects of such models are explored in this paper. Possible low-energy gauge groups are classified. It is shown that these theories have a mechanism to produce extra massless Higgs doublets unaccompanied by light color triplets. The SU(3) × SU(2) × U(1) couplings obey the standard relations after E6 breaking, so the standard computation of sin2θ is valid. These models lead typically to discrete global symmetries, but a model in which these symmetries forbid all baryon-violating dimension-four operators may be hard to find. An alternative possibility (involving O(6) holonomy) is discussed in the last section.
These notes are based on lectures at the PSSCMP/PiTP summer school that was held at Princeton University and the Institute for Advanced Study in July, 2015. They are devoted largely to topological phases of matter that can be understood in terms of free fermions and band theory. They also contain an introduction to the fractional quantum Hall effect from the point of view of effective field theory.
This article is devoted to an overview of some of the subtleties of superstring perturbation theory in the RNS framework, focusing on a concrete example { the SO(32) heterotic string compactied on a Calabi-Yau manifold, with the spin connection embedded in the gauge group. This model is known to be a signicant test case for superstring
This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The article is based on a lecture at the conference on the Mathematics of Gauge Theory and String Theory, University of Auckland, January 2020)
We propose an explanation via string theory of the correspondence between the Coulomb branch of certain three-dimensional supersymmetric gauge theories and certain moduli spaces of magnetic monopoles. The same construction also gives an explanation, via SL(2, Z ) duality of Type IIB superstrings, of the recently discovered “mirror symmetry” in three dimensions. New phase transitions in three dimensions as well as new infrared fixed points and even new coupling constants not present in the known Lagrangians are predicted from the string theory construction. An important role in the construction is played by a novel aspect of brane dynamics in which a third brane is created when two branes cross.
Let $G$ be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal $G$ bundles over an elliptic curve $E$. In particular we give a new proof of a theorem of Looijenga and Bernshtein-Shvartsman, that the moduli space is a weighted projective space. The method of proof is to study the deformations of certain unstable bundles coming from special maximal parabolic subgroups of $G$. We also discuss the associated automorphism sheaves and universal bundles, as well as the relation between various universal bundles and spectral covers.
A version of conformal gravity is formulated with a local fermionic symmetry that is reminiscent of BRST invariance. It may have mathematical applications (gravitational counterpart of Donaldson theory) or physical ones (unbroken phase of general relativity).
No abstract is provided for this article.
This paper is devoted to a systematic discussion of the supersymmetric index Tr (-1)^F for the minimal supersymmetric Yang-Mills theory -- with any simple gauge group G -- primarily in four spacetime dimensions. The index has refinements that probe confinement and oblique confinement and the possible spontaneous breaking of chiral symmetry and of global symmetries, such as charge conjugation, that are derived from outer automorphisms of the gauge group. Predictions for the index and its refinements are obtained on the basis of standard hypotheses about the infrared behavior of gauge theories. The predictions are confirmed via microscopic calculations which involve a Born-Oppenheimer computation of the spectrum as well as mathematical formulas involving triples of commuting elements of G and the Chern-Simons invariants of flat bundles on the three-torus.
Let $G$ be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal $G$ bundles over an elliptic curve $E$. In particular we give a new proof of a theorem of Looijenga and Bernshtein-Shvartsman, that the moduli space is a weighted projective space. The method of proof is to study the deformations of certain unstable bundles coming from special maximal parabolic subgroups of $G$. We also discuss the associated automorphism sheaves and universal bundles, as well as the relation between various universal bundles and spectral covers.
DOE Final Report “Strings 2014” PI: Edward Witten, Institute for Advanced Study, Princeton, NJ 08540 CO-PI: Igor Klebanov, Princeton University, Princeton, NJ 08540 DOE Grant Number: DE-SC0011919 The Strings 2014 meeting was held at Princeton University in June 2014, co-sponsored by Princeton University and the Institute for Advanced Study. Plenary lectures at Strings 2014 were held in Richardson Auditorium of Princeton University. This comfortable and spacious facility easily accommodated the 616 participants registered participants at Strings 2014. The rental fee for the auditorium was $11,000. This grant provided $5,500 from the Department of Energy to pay for one-half of the cost of the facility rental and videotaping. Speakers were supported with funds from the National Science Foundation Clay Mathematics Institute, the Institute for Advanced Study and Princeton University. The organization of Strings 2014 consisted of an International Organizing Committee of 60 prominent scientists around the world, and a Local Advisory Committee consisting of an additional 15 distinguished scientists from neighboring institutions. Additionally, the Local Organizing Committee assisted them with about 15 members (mostly faculty at Princeton University and the Institute for Advanced Study). These groups (which are listed at the end of this narrative) offered important input concerning the selectionmore » of speakers and helped to ensure that the speakers were selected from the broadest possible pool. The conference was held on June 23-7 at Princeton University and the Institute for Advanced Study. The 616 registered participants included 272 participants from the United States and 344 from 32 institutions outside of the U.S. We believe that we were successful at providing a stimulating and up-to-date overview of research in string theory and its relations to other areas of physics and mathematics, ranging from geometry to quantum field theory, condensed matter physics, and more. There were a total of 45 plenary speakers and 27 speakers at parallel sessions. (Parallel sessions were held at the Institute for Advanced Study.) Overall the speakers did an excellent job of presenting their topics and some presented surprising and novel results. The talks at Strings 2014 were videotaped and are available on the conference website: http://physics.princeton.edustrings2014/Talk_titles.shtml. One important facet of Strings 2014 and one of the reasons it was so well-attended was that it had a strong educational component. The week before the meeting, there was a summer school, Prospects in Theoretical Physics (PiTP), held at the Institute for Advanced Study on the subject of string theory. 260 graduate students attended both PiTP and Strings 2014. The group consisted of 25 females and 235 males; 208 graduate students and 52 postdocs. 129 participants were from the United States, and 131 participants came from institutions in 25 countries outside of the U.S. The Institute for Advanced Study substantially subsidized the summer school for students. Over two dozen students had the chance to give short (six minute) talks at the “gong shows” that were held at PiTP and Strings 2014, and nearly 60 students and postdocs made poster presentations at Strings 2014.« less
The particle spectrum of a string theory consists of a finite number of massless states and an infinite tower of massive excitations at a mass scale characterized by a fundamental parameter – the string tension or Regge slope. As has been explained in previous chapters, this parameter must be of order the Planck mass (1019 GeV) in order that the graviton interact with the usual Newtonian strength. If one wishes to give a phenomenological description of the consequences of string theory for lowenergy physics, it should not be necessary to describe explicitly what the massive states are doing. It is natural, instead, to formulate an effective action based entirely on fields that correspond to massless, or at least very light, degrees of freedom only. Such a description turns out to be useful not only for a phenomenological analysis, but even as a framework for addressing certain theoretical issues, such as the occurrence of anomalies.
We study four dimensional $N=2$ supersymmetric gauge theories on $R^3 \times S^1$ with a circle of radius $R$. They interpolate between four dimensional gauge theories ($R=\infty$) and $N=4$ supersymmetric gauge theories in three dimensions ($R=0$). The vacuum structure can be determined quite precisely as a function of $R$, agreeing with three and four-dimensional results in the two limits.
