This series consists of talks in the area of Superstring Theory.
I will discuss the geometry of heterotic string compactifications with fluxes. The compactifications on 6 dimensional manifolds which preserve N=1 supersymmetry in 4 dimensions must be complex manifolds with vanishing first Chern class, but which are not in general Kahler (and therefore not Calabi-Yau manifolds) together with a vector bundle on the manifold which must satisfy a complicated differential equation. The flux, which can be viewed as a torsion, is the obstruction to the manifold being Kahler.
For stationary black holes it is universally agreed that entropy is proportional to horizon area. It is not so clear what the relationship is for dynamical black holes. In such spacetimes the event horizon is teleologically defined while the apparent horizon is non-unique. Thus even if one believes that entropy continues to be well-defined and proportional to horizon area, there are many possible areas to choose from. In this work I will review some recent work that I have done with M. Heller, G.
We perform an exact localization calculation for the expectation value of Wilson-'t Hooft line operators in N=2 gauge theories on S^1 x R^3.
The expectation values form a quantum mechanically deformed algebra of functions on the Hitchin moduli space by Moyal multiplication. We demonstrate that these expectation values are the Weyl transform of the Verlinde operators, which acts on conformal blocks as difference operators. Our results are also in exact match with the predictions from wall-crossing in the IR effective theory.
TBA
In recent years there has been a lot of interest in F-Theory GUTs, mostly considering local models. In this talk I first consider an SU(5) GUT locally at the "point of E_8". The requirements of proton stability and reasonable flavour structure single out exactly two models. However, both models cannot be embedded in a semilocal construction (via the spectral cover approach). This casts doubts on the predictivity of local models.
I will first summarize recent exact localization computations of supersymmetric gauge theories, and then discuss curious connections between SUSY/non-SUSY theories coming from 6d (2,0) theories. I particular, I will focus on our recent proposal relating 3d N=2 theories and 3d SL(2,R) Chern-Simons theories (or more mathematically, geometry of 3-manifolds).
Effective field theory is an indispensable tool for the analysis of emergent theories, in which we may know little about the UV degrees of freedom of the theory, and still tremendous amount of information can be revealed only by guessing the light degrees of freedom and symmetries. In this talk I will make use of this tool to describe the quantum theory of emergent long strings, open or closed, where the string need not be fundamental (thus not critical), nor it is strictly one dimensional.
The Polchinski equations for the Wilsonian renormalization group in the $D$--dimensional matrix scalar field theory can be written at large $N$ in a Hamiltonian form. The Hamiltonian defines evolution along one extra holographic dimension (energy scale) and can be found exactly for the subsector of $Tr\phi^n$ (for all $n$) operators. We show that at low energies independently of the dimensionality $D$ the Hamiltonian system in question reduces to the {\it integrable} effective theory.
The gauge/gravity duality may give a nonperturbative formulation of superstring/M theory, and hence, if one can study the nonperturbative dynamics of the gauge theory, it would be useful to understand the nonperturbative aspects of superstring theory.
The gauge/gravity duality may give a nonperturbative formulation of superstring/M theory, and hence, if one can study the nonperturbative dynamics of the gauge theory, it would be useful to understand the nonperturbative aspects of superstring theory.