802 publications from this institution
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.
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.
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.
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by twisting $N=2$ sigma models. This is mainly a review of old results, except for the discussion in \S7 of certain facts that may be relevant to constructing the ``mirror map'' between mirror moduli spaces.
I discuss certain surface operators in gauge theory and their relevance to the ramified case of the geometric Langlands program.
For vacua of string theory which leave unbroken N = 1 supersymmetry in the leading approximation, non-renormalization theorems guarantee that higher order (string or sigma model) perturbative corrections do not modify the space-time superpotential. If the low energy gauge group contains U(1) factors, this is not enough to ensure that the low energy physics is perturbatively stable. It is still possible to generate a Fayet-Iliopoulos D-term. We show that under certain conditions such a term is generated, and destabilizes the vacuum. This is a counterexample to various claims about the universal absence of quantum tadpoles when expanding around a classical solution with unbroken supersymmetry. Whether, in a given model, the generation of a D-term will destabilize the vacuum (or merely change the pattern of symmetry breaking) can be determined from properties of the low energy effective action.
The Gopakumar-Vafa (GV) formula expresses certain couplings that arise in Type IIA compactication to four dimensions on a Calabi-Yau manifold in terms of a counting of BPS states in M-theory. The couplings in question have applications to topological strings and supersymmetric black holes. In this paper, we reconsider the GV formula, taking a close look at the Schwinger-like computation that was suggested in the original GV work. The goal is to understand the background that must be used in this computation, the role played by the extended supersymmetry of this background, and how the computation gives a holomorphic result though supercially depending only on particle masses. We also examine in a similar way the Ooguri-Vafa (OV) formula, which is an extension of the GV formula to include D4-branes.
Synthesizing older ideas about the 1/N expansion in gauge theory, the quantum mechanics of black holes, and quantum field theory in Anti de Sitter space, a new correspondence between gauge theory and quantum gravity has illuminated both subjects.
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For various reasons, it seems necessary to include complex saddle points in the "Euclidean" path integral of General Relativity. But some sort of restriction on the allowed complex saddle points is needed to avoid various unphysical examples. In this article, a speculative proposal is made concerning a possible restriction on the allowed saddle points in the gravitational path integral. The proposal is motivated by recent work of Kontsevich and Segal on complex metrics in quantum field theory, and earlier work of Louko and Sorkin on topology change from a real time point of view.
We construct the gauge invariant supersymmetric nonlinear sigma model. Our results are expressed in the language of Kahler geometry. They lead to a new interpretation of the Fayet-Iliopoulos D-term.
No abstract is provided for this article.
Some properties of the anomaly-free O(32) superstring theory recently discovered by Green and Schwarz are discussed. With proper choice of ground state, the theory leads in four dimensions to an SU(5) theory with any desired number of standard generations (and no exotic or mirror fermions). It predicts axions and stable Nielsen-Olesen vortex lines. It can be consistently compactified only if certain topological conditions are imposed.
Superstring perturbation theory is traditionally carried out by using picture-changing operators (PCO's) to integrate over odd moduli. Naively the PCO's can be inserted anywhere on a string worldsheet, but actually a constraint must be placed on PCO insertions to avoid spurious singularities. Accordingly, it has been long known that the simplest version of the PCO procedure is valid only locally on the moduli space of Riemann surfaces, and that a correct PCO-based algorithm to compute scattering amplitudes must be based on piecing together local descriptions. Recently, was proposed as a relatively simple method to do this. Here, we spell out in detail what vertical integration means if carried out systematically. This involves a hierarchical procedure with corrections of high order. One might anticipate such a structure from the viewpoint of super Riemann surfaces.
The Feynman rules of gauge invariant open string field theory are shown to produce a triangulation of the moduli space of Riemann surfaces of arbitrary topology. If follows that the gauge invariant open string field theory is modular invariant.
