MOST06: Workshop Titles and Abstract
Speaker: Jacek Brodzki (University of Southampton, UK)
Title: D-brane charges and Poincare duality on noncommutative manifolds
Abstract:
In classical differential geometry, one of the main properties of a compact diffierentiable manifold M of dimension n is the Poincare duality, which establishes an isomorphism between cohomology in degree k and homology in degree n-k, or equivalently, it provides a non degenerate complex valued pairing between cohomology groups in degree k and n-k. An analogue of this property, expressed in terms of Poincare duality in Kasparov's KK-theory, has found a place in Connes' axiomatic description of differentiable manifolds in noncommutative geometry. In this talk we shall give an introduction to the notion of Poincare duality in bivariant K-theory and provide applications of this formalism in the D-brane theory. We propose a general formula for D-brane charge.
Speaker: Gil Cavalcanti (Oxford University, UK)
Title: T-duality with NS-flux and generalized complex structures
Abstract: Using the construction of T-dual spaces
with NS-flux due to Bouwknegt, Evslin and Mathai, I will show
that T-duality can be interpreted as an isomorphism of Courant
algebroids. This interpretation allows us transport generalized
structures between T-dual spaces, including generalized complex, generalized Kahler and strong KT structures. I'll also recover the isomorphism of Courant algebroids in terms of a reduction of a
Courant algebroid over the correspondence space.
Speaker: Anna Ceresole (AC, INFN and University of Turin, Italy)
Title: Domain walls in the landscape
Abstract:
We present a theory of static BPS domain walls that is suitable for
studying the landscape of string/M-theory vacua. We illustrate it by a
number of examples, where the BPS walls interpolate between different
supersymmetric vacua, such as KKLT models, STU models, type IIB multiple
flux vacua and KL racetrack models. Upon uplifting, we generate dS vacua
and near-BPS walls, that may serve as bubble walls in the theory of
vacuum decay. As an interesting application of cosmological relevance, we
find channels of irreversible vacuum decay that work as "sinks" of
probabilities in the landscape.
Speaker: Alex Flournoy (ANU, Canberra)
Title: Nongeometric strings and the worldsheet
Abstract:
I will review the worldsheet construction of certain “nongeometric” string
theories which correspond to string propagation on backgrounds which
incorporate the duality twists of Hull. The aim is to test the quantum
consistency of strings on these spaces by checking the modular invariance
of the partition functions in each case. We distinguish between “truly”
and “pseudo” nongeometric string backgrounds via their relation to
standard geometric backgrounds through T-duality.
Speaker: Omar Foda (University of Melbourne)
Title: Bethe ansatz, plane partitions and topological strings
Abstract:
Generating functions of random plane partitions are related
to topological string vertices (Okounkov et al, 2003, and
many others after that).
They are also scalar products in the algebraic Bethe ansatz
view of integrable vertex models in statistical mechanics
(Bogoliubov, 2005).
This establishes yet another (to me unexpected) link between
integrable models and string theory, this time via algebraic
combinatorics.
I would like to review the above connections, with particular
emphasis on the Bethe ansatz/plane partition part.
Speaker: Jim Gates (University of Maryland, USA)
Title: Adinkras: New Mathematical Objects in Supersymmetrical Representation Theory
Abstract:
An introduction is given to the concept that
for supersymmetric theories, the concept of the
Wigner little group may be replaced by a certain
class of Clifford Algebra that can be discerned
by reduction of ALL supersymmetrical theories
on 0-branes.
Speaker: Nick Halmagyi (University of Chicago, USA)
Title: Special Lagrangians and IIA/Hetreotic Duality
Abstract: --
Speaker: Keith Hannabuss (Oxford University, UK)
Title: T-duality and tensor categories
Abstract:
There are many examples of physical systems which can be
described by apparently different models related by rather
non-obvious symmetries. In string theory T-duality related
spaces with group actions and H-fields. The simplest cases
can be described in purely geometric terms, but others are harder to
describe. One approach is to use the methods of non-commutative
geometry, but in some cases even that is insufficient because the
algebras are not associative. This talk will survey some of the ideas.
Speaker: Sergei Kuzenko (UWA, Perth)
Title: Superpotentials for nonlinear sigma-models with eight supercharges
Abstract (from hep-th/0602050):
Using projective superspace techniques, we consider 4D N = 2 and 5D N = 1 gauged supersymmetric nonlinear sigma-models for which the hyper-Kahler target space is (an open domain of the zero section of) the cotangent bundle of a real-analytic Kahler manifold. As in the 4D N = 1 case, one may gauge those holomorphic isometries of the base Kahler manifold (more precisely, their lifting to the cotangent bundle) which are generated by globally defined Killing potentials. In the U(1) case, by freezing the background vector (tropical) multiplet to a constant value of its gauge-invariant superfield strength, we demonstrate the generation of a chiral superpotential, upon elimination of the auxiliary superfields and dualisation of the complex linear multiplets into chiral ones. Our analysis uncovers a N = 2 superspace origin for the results recently obtained in hep-th/0601165.
Speaker: Sunil Mukhi (TIFR, Mumbai, India)
Title: Noncritical strings and topological strings
Abstract: --
Speaker: Nuno Romao (University of Adelaide)
Title: Spectral curves and the mass of hyperbolic monopoles
Abstract:
Monopoles in hyperbolic space have a very intricate structure and do
provide a promising stage to study the AdS/CFT correspondence, which
is already manifest at the classical level. There are two basic
invariants that one can associate to them: an integer magnetic charge
k and a positive real mass m. To a hyperbolic monopole with given (k,m),
one can associate a spectral curve, which is (generically) a compact
Riemann surface of genus (k-1)2 encoding all the gauge-invariant
information about the fields. In this talk, I will describe joint work
with Paul Norbury clarifying how one can compute the mass m from a given
spectral curve. I shall be discussing two classes of examples for which
this calculation can be made quite explicit: (i) monopoles of charge k=2;
(ii) monopoles with the symmetries of a platonic solid.
Speaker: Annamaria Sinkovics (DAMTP, Cambridge, UK)
Title: Topological membranes
Abstract:
We review the status of topological theories on G2 target spaces as possible fundamental
descriptions of topological M-theory. We formulate a topological theory of membranes wrapping associative three-cycles in a seven-dimensional target space with G2 holonomy. The topological BRST rules and BRST invariant action are constructed via the Mathai-Quillen formalism. We construct a set of local and non-local observables for the topological membrane theory. As the BRST cohomology of local operators turns out to be isomorphic to the de Rham cohomology of the G2 manifold, our observables agree with the spectrum of d=4, N=1 G2 compactifications of M-theory. We also consider an effective target space description of topological M-theory, constructed as a ‘G2 quantum foam’ in terms of an abelian two-form gauge field.
Speaker: Mathai Varghese (University of Adelaide)
Title: T-duality via noncommutative geometry
Abstract: --
Speaker: Bryan Wang (ANU, Canberra)
Title: Differential twisted K-theory and its Chern character
Abstract:
It is known that the group of charges in string theory
is a generalized cohomology group, fields and current are geometric
objects in generalized differential cohomology theory as developed by
Hopkins-Singer. I will discuss charges of D-branes in Type IIB
strings in terms of differential twisted K-theory class and its
Chern character.
Speaker: Katrin Wendland (Warwick, UK/UNC, USA/Augsburg, Germany, ... ;-)
Title: A family of superconformal field theories hosting all "very attractive" relatives of the (2)4 Gepner model
Abstract:
A construction of a four-parameter family of superconformal field theories (SCFTs) associated to certain smooth quartic K3 surfaces is given by combining orbifold techniques and a non-classical duality. At rational parameters, these quartic K3 surfaces exhaust all "very attractive" K3s, i.e. all quartic hypersurfaces in CP3 with defining polynomial given by the sum of two polynomials in two variables each with maximal Picard number. In particular, the SCFT associated to the Fermat quartic is the Gepner model (2)4, and our family of SCFTs can be viewed as a pure complex structure deformation of this model.
All steps in the construction are entirely explicit, yielding the first known example of a smooth family of SCFTs which both from a conformal field theorist's and from an algebraic geometer's point of view is completely under control.
Speaker: Siye Wu (University of Colorado, Boulder and University of Hong Kong)
Title: Fiber Integration of Deligne Cohomology Classes
Abstract: We begin with a review of how to integrate differential forms and cohomology classes along the fiber. Then we discuss the geometry of gerbes and Deligne cohomology classes. Finally we give an intrinsic definition of fiber integration of such objects and explain its significance, relating it to various types of fiber integration reviewed earlier. We complete the talk with an outlook of future development.
Student Talks
Speaker: Peggy Kao (ANU)
Title: Generalized Geometry and T-duality
Speaker: Josh Garretson (ANU)
Title: Generalized Geometry and T-duality
Speaker: Rishni Ratnam (ANU)
Title: T-duality a la Noncommutative Geometry
Speaker: Richard Green (Adelaide)
Title: G-structures and Distributions
Speaker: Rongmin Lu (Adelaide)
Title: The equivariant cohomology of the free loop space
Speaker: Madeleine Smith (ANU)
Title: Exact Solution of String Field Equation of Motion
Speaker: Marni Sheppeard (Canterbury)
Title: Categories and Logic for Spin Foams: An Introduction
