802 publications from this institution
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.
It is shown that ordinary baryons can be understood as solitons in current algebra effective lagrangians. The formation of color flux tubes can also be seen in current algebra, under certain conditions.
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.
The geometric Langlands correspondence was described some years ago in terms of S-duality of N = 4 super Yang–Mills theory. Some additional matters relevant to this story are described here. The main goal is to explain directly why an A-brane of a certain simple kind can be an eigenbrane for the action of 't Hooft operators. To set the stage, we review some facts about Higgs bundles and the Hitchin fibration. We consider only the simplest examples, in which many technical questions can be avoided.
We reconsider Chern-Simons gauge theory on a Seifert manifold M (the total space of a nontrivial circle bundle over a Riemann surface). When M is a Seifert manifold, Lawrence and Rozansky have shown from the exact solution of Chern-Simons theory that the partition function has a remarkably simple structure and can be rewritten entirely as a sum of local contributions from the flat connections on M. We explain how this empirical fact follows from the technique of non-abelian localization as applied to the Chern-Simons path integral. In the process, we show that the partition function of Chern-Simons theory on M admits a topological interpretation in terms of the equivariant cohomology of the moduli space of flat connections on M.
Some remarks are made about the nature and role of the search for higher symmetry in string theory. These symmetries are most likely to be uncovered in a mysterious ‘unbroken phase’, for which (2+ 1)-dimensional gravity provides an interesting and soluble model. New insights about conformal field theory, in which one gets ‘out of flatland’ to see a wider symmetry from a higher-dimensional vantage point, may offer clues to the unbroken phase of string theory
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).
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.
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 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.
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?
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.
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.
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.
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
