This series consists of talks in the area of Superstring Theory.
It has been known for twenty years that a class of
two-dimensional gauge theories are intimately connected to toric geometry, as
well as to hypersurfaces or complete intersections in a toric varieties, and to
generalizations thereof. Under renormalization
group flow, the two-dimensional gauge theory flows to a conformal field theory
that describes string propagation on the associated geometry. This provides a connection between certain
quantities in the gauge theory and topological invariants of the associated
Two-dimensional
models provide for a very attractive playground being a theory imitating some
of the main features of QCD. Those include the asymptotic freedom, mass gap,
confinement, chiral symmetry breaking and others. Furthermore, there is a correspondence between the spectra of
four-dimensional SQCD and N=(2,2) CP(N-1) sigma model which was discovered more
than a decade ago. This correspondence was explained later when it was found
that SQCD supports non-Abelian strings with confined monopoles. The kinks of
I discuss several recent efforts
in relating string field theory calculations of BMN BMN BMN and BMN BMN BPS
correlation functions to direct perturbative calculations and
integrability-assisted methods. I review the next-to-leading order agreement
between strings and perturbation theory in the SO(6) sector, a conjectured
extension of the integrability techniques by Escobedo, Gromov, Sever, Vieira from
the SU(2) to the full SO(6) sector and agreement with SFT and PT in it at the
In the study of the string/gauge theory duality (AdS/CFT), an important role is played by the relation between local operators and Wilson loops. Perhaps the most well known example is the relation between twist two operators and the light-like cusp Wilson loop. On the string side, the twist two operator is represented by a "long" string (GKP). In this talk I use T-duality to argue that such relation is also natural for "short" strings.
We propose a new
approach for the calculation of the spectrum of excitations of QCD flux tubes.
It relies on the fact that the worldsheet theory is integrable at low energies.
With this approach, energy levels can be calculated for much shorter flux tubes
than was previously possible, allowing for a quantitative comparison with
existing lattice data. The improved theoretical control makes it manifest that
existing lattice data provides strong evidence for a new pseudoscalar particle
I will discuss the conformal theories of N complex
scalars or fermions in 2+1 dimensions, coupled to a U(N) Chern-Simons (CS)
theory at level k. In the large N limit these theories have a high-spin
symmetry, and, as I will review, they are dual to Vasiliev's high-spin gravity
theories on four dimensional anti-de Sitter space. Maldacena and Zhiboedov
showed that the high-spin symmetry determines the 2-point and 3-point functions
of these theories at large N, up to two parameters. The duality to Vasiliev's
In this talk, we will describe our recent
work. Recently, we focus on the thermodynamical property and time
dependence of entanglement entropy. Using holography, we found that the
entanglement entropy for a very small subsystem obeys a property which is
analogous to the first law of thermodynamics when we excite the system. In
relativistic setups, its effective temperature is proportional to the inverse
of the subsystem size. This provides a universal relationship between the
We start with a one-slide review of the Kontsevich-Soibelman
(KS) solution to the wall-crossing problem and then proceed to direct and comprehensive physics counting of BPS states that eventually connects to KS. We also asks what input data is needed for either approaches to produce complete BPS spectra, and this naturally leads to the BPS quiver representation of BPS states and the new notion of quiver invariants.