802 publications from this institution
The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct explanation of the relationship of the A-model to quantum mechanics; such a relationship has been explored from several points of view in the last few years. These phenomena have an analog for Chern-Simons gauge theory in three dimensions: integration cycles in the path integral of this theory can be derived from N=4 super Yang-Mills theory in four dimensions. Hence, under certain conditions, a Chern-Simons path integral in three dimensions is equivalent to an N=4 path integral in four dimensions.
The geometric Langlands correspondence has been interpreted as the mirror symmetry of the Hitchin fibrations for two dual reductive groups.This mirror symmetry, in turn, reduces to T -duality on the generic Hitchin fibers, which are smooth tori.In this paper, we study what happens when the Hitchin fibers on the B-model side develop orbifold singularities.These singularities correspond to local systems with finite groups of automorphisms.In the classical Langlands program, local systems of this type are called endoscopic.They play an important role in the theory of automorphic representations, in particular, in the stabilization of the trace formula.Our goal is to use the mirror symmetry of the Hitchin fibrations to expose the special role played by these local systems in the geometric theory.The study of the categories of A-branes on the dual Hitchin fibers allows us to uncover some interesting phenomena associated with the endoscopy in the geometric Langlands correspondence.We then follow our predictions back to the classical theory of automorphic functions.This enables us to test and confirm them.The geometry we use is similar to that which is exploited in recent work by Ngô, a fact which could be significant for understanding the trace formula.
No abstract is provided for this article.
Conformal operators for partially massless states
The quantization law for the antisymmetric tensor field of M-theory contains a gravitational contribution not known previously. When it is included, the low energy effective action of M-theory, including one-loop and Chern-Simons contributions, is well defined. The relation of M-theory to the E 8 × E 8 heterotic string greatly facilitates the analysis.
We consider two-dimensional supergravity theories with four supercharges constructed from compactification of Type II string theory on a generic Calabi–Yau four-fold. In type IIA and type IIB cases, respectively, new superspace formulations of N=(2,2) and N=(0,4) dilaton supergravities are found and their coupling to matter multiplets is discussed.
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.
We study four dimensional N = 2 supersymmetric gauge theories with matter multiplets. For all such models for which the gauge group is SU(2), we derive the exact metric on the moduli space of quantum vacua and the exact spectrum of the stable massive states. A number of new physical phenomena occur, such as chiral symmetry breaking that is driven by the condensation of magnetic monopoles that carry global quantum numbers. For those cases in which conformal invariance is broken only by mass terms, the formalism automatically gives results that are invariant under electric-magnetic duality. In one instance, this duality is mixed in an interesting way with SO(8) triality.
The conjecture that N=2 minimal models in two dimensions are critical points of a superrenormalizable Landau-Ginzburg model can be tested by computing the path integral of the Landau-Ginzburg model with certain twisted boundary conditions. This leads to simple expressions for certain characters of the N=2 models which can be verified at least at low levels. An N=2 superconformal algebra can in fact be found directly in the noncritical Landau-Ginzburg system, giving further support for the conjecture.
This paper is devoted to the construction of a family of linear sigma models with (0,4) supersymmetry which should flow in the infrared to the stringy version of Yang-Mills instantons on R 4. The family depends on the full set of expected parameters and is obtained by using the data that appear in the ADHM construction of instantons.
No abstract is provided for this article.
This lecture surveys a few loosely related topics, ranging from the scarcity of quantum field theories -- and the role that this has played, and still plays, in physics -- to paradoxes involving black holes in soluble two dimensional string theory and the question of whether naked singularities might be of even greater interest to string theorists than black holes.
More general constructions are given of six-dimensional theories that look at low energy like six-dimensional super Yang-Mills theory.The constructions start with either parallel fivebranes in Type IIB, or M-theory on (C 2 x § 1 )/r for T a suitable finite group.Via these constructions, one can obtain six-dimensional theories with any simple gauge group, and SU(r) theories with any rational theta angle.A matrix construction of these theories is also possible.
Symmetry-protected phases of matter have been at the forefront of condensed matter physics in recent years. Bosonic symmetry-protected phases have been interpreted in terms of anomalies and group cohomology. The present article aims to develop an analogous description of fermionic symmetry-protected phases, such as the topological insulators that have been seen experimentally in 2 or 3 space dimensions. The relevant mathematical concepts include the Atiyah-Singer index theorem and the Atiyah-Patodi-Singer eta invariant.
The goal of these notes is to give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six dimensions.
