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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