K-theory and strings - titles and abstracts of talks

IGA Workshop
"Strings and Mathematics 2003"

26-28 May 2003

Titles and Abstracts of Talks

Speaker : Michael Eastwood (University of Adelaide)
Title : How long is a piece of string?
Abstract : Of course, it depends on the string. Perhaps your string is a circle but then what is a circle intrinsically? Well, as a smooth manifold, it has no well-defined length but, once endowed with a Riemannian metric, a circle has preferred parameterisations by arc-length and a well-defined length. Between these extremes, however, there is another possibility. In this talk I shall answer the question: how can the circle be a homogeneous space? The answer to this question has implications for the structure of distinguished curves in Cartan geometries. This is joint work with Jan Slovak. Whether it has anything to do with "String Theory" is unclear.

Speaker : Jarah Evslin (University of Pisa, Italy)
Title : Fields and Charges in String Theory
Abstract : This introductory talk will review the fields and charges of type IIA and IIB string theory, and the dualities which relate them.

Speaker : Jarah Evslin (University of Pisa, Italy)
Title : K-Theory from String Theory, parts I and II (Two talks)
Abstract : I will review several arguments indicating that the fields and charges of type II string theories are classified by K-theory. I will then argue that they are in fact classified by mysterious equivalence classes of a subset of K-theory.

Speaker : Simon Gindikin (Rutgers University, New Brunswick, USA)
Title : Manifolds of rational curves, twistors, and solitons.
Abstract : Some manifolds of rational curves participate in nonlinear equations which can be integrated by the inverse problem's method. I will discuss examples of how some manipulations with such manifolds are connected with soliton type solutions. The basic example will be right-flat metrics.

Speaker : Stuart Johnson (University of Adelaide)
Title : B-fields, Chern-Simons and bundle 2-gerbes
Abstract : In recent years many authors have recognised that generalisations of line bundles, such as gerbes and other related objects, have some relevance to string theory. I shall explain how bundle gerbes, which shall be described in Michael Murray's talk, are relevant to the study of B-fields and Chern-Simons Theory. This will require consideration of bundle gerbe holonomy and bundle 2-gerbes.

Speaker : Michael Murray (University of Adelaide)
Title : Introduction to bundle gerbes
Abstract : I will explain what a bundle gerbe is, what the Dixmier-Douady class, connection, curving and three curvature of a bundle gerbe are and give some examples in particular the lifting bundle gerbe. This lecture will be assumed knowledge for the lectures of Stuart Johnson and Danny Stevenson.

Speaker : Hisham Sati (University of Michigan, Ann Arbor, USA)
Title : E8 gauge theory in 11 dimensions
Abstract : An E8 gauge bundle arises in the topological part of the M-theory partition function. One might view this as a natural extension of the Horava-Witten construction to the bulk. One can try to shed some light on the nature of the "gauge theory" described by such a bundle and on whether it is supersymmetric by constructing the supergravity fields as condensates of the gauge fields. We discuss the implications of such a construction for the gravitino field.

Speaker : Hisham Sati (University of Michigan, Ann Arbor, USA)
Title : M-theory
Abstract : I will review eleven dimensional supergravity and M-theory, the theory that arises as the strong coupling limit of string theories.

Speaker : Eric Sharpe (University of Illinois, Urbana-Champagne, USA)
Title : BRST = Ext
Abstract : In this talk we shall review some recent work relevant to understanding the role derived categories play in physics. In particular, we shall answer one of the most basic questions one can ask -- how to see explicitly that Ext groups count massless states in open strings? We shall see this is secretly an exercise in solving thorny physics questions by translating them into comparatively easy math questions. Along the way we shall outline a rudimentary math-physics dictionary that we hope will help clarify some of the physics language.

Speaker : Eric Sharpe (University of Illinois, Urbana-Champagne, USA)
Title : Discrete torsion
Abstract : Discrete torsion is a mysterious-looking degree of freedom arising in string orbifolds. Often mischaracterized as an `inherently stringy' degree of freedom, discrete torsion was the subject of numerous failed attempts at a geometric understanding until just a couple of years ago, when the physical properties of discrete torsion were finally derived from an intellectually simple basis. In this talk we shall outline how the physical properties of discrete torsion can be derived from nothing more than the choice of equivariant structure on a physical field known as the ``B field.'' Specifically, we shall describe how equivariant structures on the B field not only classify both discrete torsion as well as a more obscure degree of freedom (known as a `shift' orbifold), but also reproduces twisted sector phase factors, and actions on D-branes (yielding projectivized equivariant K-theory, as well as a generalization). We shall also discuss M-theory duals of discrete torsion and shift orbifolds, as well as analogues of discrete torsion (and their corresponding twisted sector phase factors) for other tensor field potentials.

Speaker : Danny Stevenson (University of Adelaide)
Title : String classes and bundle gerbes
Abstract : If K is a compact Lie group then it is well known that there is a central extension U(1) -> L(K)^ -> L(K) of the group L(K) of smooth maps from the circle to K. If P -> M is a principal L(K) bundle then there is a class in H^3(M;Z) (called the string class of the bundle P) which measures the obstruction to lifting the structure group of P to L(K)^. In this talk I will describe how, using the differential geometry of bundle gerbes, one can write down a closed 3-form on M representing the image of the string class in real cohomology. This is joint work with Michael Murray.

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