This series consists of talks in the area of Superstring Theory.
I will describe a method to compute from first principles the anomalous dimension of short operators in N=4 super Yang-Mills theory at strong coupling, where they are described in terms of superstring vertex operators in an anti-de Sitter background. I will focus on the Konishi multiplet, dual to the first massive level of the superstring, and compute the one-loop correction to its anomalous dimension at strong coupling, using the pure spinor formalism for the superstring.
The 4D rotating black hole described by the Kerr geometry possesses many of what was called by Chandrasekhar "miraculous" properties. Most of them are related to the existence of a fundamental hidden symmetry of a principal conformal Killing-Yano (PCKY) tensor. In my talk I shall demonstrate that hidden symmetry of the PCKY tensor plays exceptional role also in higher dimensions.
ABJM theory is a world-volume theory for an arbitrary number of M2-branes. One of the unique features of ABJM theory is its characteristic scaling behaviour, exhibited for example by the free energy and correlation functions of chiral primary operators. In more detail, ABJM theory has a holographic dual where thermodynamics at strong coupling is determined by a system of black M2-branes. The zero-coupling (black-body radiation) free energy disagrees with the strong coupling result. Even the scaling in the 't Hooft coupling is different (strongly suppressed at strong coupling).
We describe a classification of 4d N=2 superconformal theories
obtained from the compactification of 6d N=(2,0) A_N theories on
punctured Riemann surfaces. We show the basic building blocks to
construct any such theory and its various S-dual frames. A host of new
S-dualities and interacting (non-Lagrangian) superconformal theories are
unconvered. We also compute various properties of these interacting
I will discuss a novel approach to time-dependent background fields of string theory, which allows the identification of configurations which satisfy the conformal invariance conditions to all orders in the Regge slope parameter alpha'.
Gauge/gravity duality, a concept which emerged from string theory,
holds promise for revealing the secrets of certain strongly
interacting real world condensed matter systems. Historically, string
theorists presented their subject as a promising framework for a
quantum theory of gravity. More recently, the AdS/CFT correspondence
and gauge/gravity dualities have emerged as powerful tools for using
what we already know about gravity to investigate the properties of
strongly interacting field theories. I will cherry pick and discuss a
Mathematics and physics can come together to the benefit of both fields, particularly in the case of Calabi-Yau spaces and string theory---our leading attempt to explain the universe to date. The audience will gain a sense of how mathematicians think and approach the world and realize that mathematics does not have to be a wholly abstract discipline, disconnected from everyday phenomena, but it is instead crucial to our understanding of the physical world.