Forthcoming events in this series
In the absence of background fluxes and sources, the compactification of string theories on Calabi-Yau threefolds leads to supersymmetric solutions.Turning on fluxes, e.g. to lift the moduli of the compactification, generically forces the geometry to break the Calabi-Yau conditions, and to satisfy, instead, the weaker condition of reduced structure. In this talk I will discuss manifolds with SU(3) structure, and their relevance for heterotic string compacitications. I will focus on domain wall solutions and how explicit example geometries can be constructed.
Instantons and W-bosons in 5d N=2 Yang-Mills theory arise from a circle
compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding
self-dual strings, respectively. We study an index which counts BPS
instantons with electric charges in Coulomb and symmetric phases. We first
prove the existence of unique threshold bound state of U(1) instantons for
any instanton number. By studying SU(N) self-dual strings in the Coulomb
phase, we find novel momentum-carrying degrees on the worldsheet. The total
number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory.
We finally propose that our index can be used to study the symmetric phase of
this theory, and provide an interpretation as the superconformal index of the
sigma model on instanton moduli space.
String theory on a torus requires the introduction of dual coordinates
conjugate to string winding number. This leads to physics and novel geometry in a doubled space. This will be
compared to generalized geometry, which doubles the tangent space but not the manifold.
For a d-torus, string theory can be formulated in terms of an infinite
tower of fields depending on both the d torus coordinates and the d dual
coordinates. This talk focuses on a finite subsector consisting of a metric
and B-field (both d x d matrices) and a dilaton all depending on the 2d
doubled torus coordinates.
The double field theory is constructed and found to have a novel symmetry
that reduces to diffeomorphisms and anti-symmetric tensor gauge
transformations in certain circumstances. It also has manifest T-duality
symmetry which provides a generalisation of the usual Buscher rules to
backgrounds without isometries. The theory has a real dependence on the full
doubled geometry: the dual dimensions are not auxiliary. It is concluded
that the doubled geometry is physical and dynamical.
We establish a correspondence between generalized quiver gauge theories in
four dimensions and congruence subgroups of the modular group, hinging upon
the trivalent graphs which arise in both. The gauge theories and the graphs
are enumerated and their numbers are compared. The correspondence is
particularly striking for genus zero torsion-free congruence subgroups as
exemplified by those which arise in Moonshine. We analyze in detail the
case of index 24, where modular elliptic K3 surfaces emerge: here, the
elliptic j-invariants can be recast as dessins d'enfant which dictate the
Seiberg-Witten curves.
In this talk, I will focus on an infinite class of 3d N=4 gauge theories
which can be constructed from a certain set of ordered pairs of integer
partitions. These theories can be elegantly realised on brane intervals in
string theory. I will give an elementary review on such brane constructions
and introduce to the audience a symmetry, known as mirror symmetry, which
exchanges two different phases (namely the Higgs and Coulomb phases) of such
theories. Using mirror symmetry as a tool, I will discuss a certain
geometrical aspect of the vacuum moduli spaces of such theories in the
Coulomb phase. It turns out that there are certain infinite subclasses of
such spaces which are special and rather simple to study; they are complete intersections. I will mention some details and many interesting features of these spaces.
A simple formula is given for the $n$-field tree-level MHV gravitational
amplitude, based on soft limit factors. It expresses the full $S_n$ symmetry
naturally, as a determinant of elements of a symmetric ($n \times n$) matrix.
I will discuss some recent progress connecting different quiver gauge theories and some applications of these results.
The partition function of 3d N=2 superconformal theories on the
3-sphere can be computed exactly by localization methods. I will explain
some sublteties associated to that important result. As a by-product, this
analysis establishes the so-called F-maximization principle for N=2 SCFTs in
3d: the exact superconformal R-charge maximizes the 3-sphere free energy
F=-log Z.
The AdS/CFT correspondence is a powerful tool to analyse strongly coupled quantum field
theories. Over the past few years there has been a surge of activity aimed at finding
possible applications to condensed matter systems. One focus has been to holographically
realise various kinds of phases via the construction of fascinating new classes of black
hole solutions. In this framework, I will discuss the possibility of describing finite
temperature phase transitions leading to spontaneous breaking of translational invariance of
the dual field theory at strong coupling. Along with the general setup I will also discuss
specific string/M theory embeddings of the corresponding symmetry breaking modes leading to
the description of such phases.
In this talk we will review M-theory dualities and recent attempts to make these dualities manifest in eleven-dimensional supergravity. We will review the work of Berman and Perry and then outline a prescription, called non-linear realisation, for making larger duality symmetries manifest. Finally, we will explain how the local symmetries are described by generalised geometry, which leads to a duality-covariant constraint that allows one to reduce from generalised space to physical space.