Triangle Seminars

Abstract:
The hydrodynamic approximation is an extremely powerful tool to describe the behavior of many-body systems such as gases. At the Euler scale (that is, when variations of densities and currents occur only on large space-time scales), the approximation is based on the idea of local thermodynamic equilibrium: locally, within fluid cells, the system is in a Galilean or relativistic boost of a Gibbs equilibrium state. This is expected to arise in conventional gases thanks to ergodicity and Gibbs thermalization, which in the quantum case is embodied by the eigenstate thermalization hypothesis. However, integrable systems are well known not to thermalize in the standard fashion. The presence of infinitely-many conservation laws preclude Gibbs thermalization, and instead generalized Gibbs ensembles emerge. In this talk I will introduce the associated theory of generalized hydrodynamics (GHD), which applies the hydrodynamic ideas to systems with infinitely-many conservation laws. It describes the dynamics from inhomogeneous states and in inhomogeneous force fields, and is valid both for quantum systems such as experimentally realized one-dimensional interacting Bose gases and quantum Heisenberg chains, and classical ones such as soliton gases and classical field theory. I will give an overview of what GHD is, how its main equations are derived and its relation to quantum and classical integrable systems. If time permits I will touch on the geometry that lies at its core, how it reproduces the effects seen in the famous quantum Newton cradle experiment, and how it leads to exact results in transport problems such as Drude weights and non-equilibrium currents.

This is based on various collaborations with Alvise Bastianello, Olalla Castro Alvaredo, Jean-Sébastien Caux, Jérôme Dubail, Robert Konik, Herbert Spohn, Gerard Watts and my student Takato Yoshimura, and strongly inspired by previous collaborations with Denis Bernard, M. Joe Bhaseen, Andrew Lucas and Koenraad Schalm.

Abstract:
Anti-de-Sitter solutions play an important role in the
gauge-theory/gravity correspondence, and understanding
their properties has provided important insights into
the dual field theories. We consider ADS solutions
which are highly supersymmetric, in the sense that they
preserve more than 16 supersymmetries, and show how
how modified versions of the homogeneity theorems of
Figureoa-O'Farrill, combined with aspects of the global
properties of the geometries, can be used to classify
these solutions.

Abstract:
A powerful approach to compute multi-loop Feynman integrals is to reduce the integrals to a basis of integrals and set up a first-order linear system of partial differential equations for the basis integrals. In this talk I will discuss the differential equations that arise when the loop integrals are parametrized in Baikov representation. In particular, I give a proof that dimension shifts (which are undesirable) can always be avoided. I will moreover show that in a large class of two- and three-loop diagrams it is possible to avoid integrals with squared propagators in the intermediate stages of setting up the differential equations. This is interesting because it implies that the differential equations can be set up using a smaller set of reductions.

Abstract:
Exceptional geometry is an attempt to combine the geometric diffeomorphisms and matter gauge transformations in gravity-matter theories into a single geometric structure. I will review recent results associated with a 2+9 split of maximal supergravity where the affine symmetry group E9 plays a central role. The results also provide a general formula that is applicable to many other cases.