This series consists of talks in the area of Superstring Theory.
In this talk, I will describe a new form of hidden simplicity in the planar scattering amplitudes of N=4 super-Yang-Mills theory, notably that the loop integrands can be expressed in dlog form. I will explain how this form arises geometrically from computing the scattering amplitudes using a holomorphic Wilson loop in twistor space. I will also describe a systematic method for evaluating such integrals and use it to obtain a new formula for the 1-loop MHV amplitude.
We discuss a partition function of 3d supersymmetric gauge
theories on the (p, -1) Lens space.
In 3d the partition function is directly used to check dualities though the normalization is not seriously treated, especially, the phase is usually
ignored. However, when we consider the partition function on the orbifold the partition function consists of the sum of factors labeled by holonomies
Hexagon functions are a class of iterated integrals, depending on three variables (dual conformal cross ratios) which have the correct branch cut structure and other properties to describe the scattering of six gluons in planar N=4 super-Yang-Mills theory. We classify all hexagon
functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. As an example, the three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined
previously.
I will describe recent results obtained for N=4 superconformal field
theories in four dimensions by means of the conformal bootstrap.
This talk will be related to the content of arXiv:1304.1803, as well as
some additional work in progress.
We show explicitly how the exact renormalization group
equation of interacting vector models in the large N limit can be
mapped into certain higher-spin equations of motion. The equations of
motion are generalized to incorporate a multiparticle extension of the
higher-spin algebra, which reflects the "multitrace" nature of the
interactions in the dual field theory from the holographic point of view.
We discuss how bipartite graphs on Riemann surfaces encapture a wealth of information about the physics of large classes of supersymmetric gauge theories, especially those with quiver structure and arising from the AdS/CFT context. The correspondence between the gauge theory, the underlying algebraic geometry of it space of vacua, the combinatorics of dimers and toric varieties, as well as the number theory of dessin d'enfants becomes particular intricate under this light.
We reconstruct the experience of an infalling observer
using the AdS/CFT correspondence.
We write operators both outside and inside the black hole
in terms of CFT operators.
Our construction provides a natural realization of black
hole complementarity, and a way of preserving information without the need for
firewalls.
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