This series consists of talks in the area of Superstring Theory.
theories with a U(1)_R symmetry, can be placed on a compact three manifold M
preserving some supersymmetry if and only if M admits a transversely
holomorphic foliation (THF). I will show that the partition function of the
resulting theory is independent of the metric and depends holomorphically on
the moduli of the THF. When applied to supersymmetric field theories on
manifolds diffeomorphic to S^3 and S^2 x S^1, this result explains many of the
In M-theory, the only AdS7 supersymmetric solutions are
AdS7 × S4 and its orbifolds. In this talk, I will describe a classification of
AdS7 supersymmetric solutions in type II supergravity. While in IIB none exist,
in IIA with Romans mass (which does not lift to M-theory) there are many new
ones. The classification starts from a pure spinor approach reminiscent of
generalized complex geometry. Without the need for any Ansatz, the method
determines uniquely the form of the metric and fluxes, up to solving a system
We study the
conformal bootstrap for 3D CFTs with O(N) global symmetry. We obtain rigorous
upper bounds on the scaling dimensions of the first O(N) singlet and symmetric
tensor operators appearing in the \phi_i x \phi_j OPE, where \phi_i is a
fundamental of O(N). Comparing these bounds to previous determinations of
critical exponents in the O(N) vector models, we find strong numerical evidence
that the O(N) vector models saturate the bootstrap constraints at all values of
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
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.