This series consists of talks in the area of Superstring Theory.
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.
Hints for the possibility of two times emerged in M-theory in 1995. If taken seriously this required new concepts that could solve unitarity
(ghost) and causality problems so that physics could be described sensibly in a spacetime with two times. The necessary concept turned out to be a gauge symmetry in phase space. This is an unfamiliar concept, but is one that extends Einstein's approach to the formulation of fundamental equations of physics, by removing the perspective of the observer, not only in position space but more generally in phase space.
We show how to extract from conjectured S-dualities the dimensions and flavor symmetry transformation properties of certain Higgs branches (hypermultiplet flat directions) of strongly coupled N=2 d=4 superconformal field theories. This leads to an expansion and refinement of the exact data (conformal dimensions, central charges) that can be computed for N=2 SCFTs.
The properties of a superfluid phase transition with a d-wave order parameter in a strongly interacting field theory with gravity dual are considered. In the context of the AdS/CFT correspondence, this amounts to writing down an action for a charged, massive spin two field on a background, and I will discuss all technical problems. In the second part I will show that coupling bulk fermions to the spin two field and studying the fermionic two-point function, one recovers interesting features of d-wave superconductors, like d-wave gap, Dirac nodes and Fermi arcs.
We derive a holographic dual description of free quantum field theory in arbitrary dimensions, by reinterpreting the exact renormalization group, to obtain a higher spin gravity theory of the general type which had been proposed and studied as a dual theory