52nd North British Mathematical Physics Seminar

Abstract: The advent of the gauge/gravity correspondence has allowed us to tackle problems in strongly coupled field theories from a different perspective, in particular through the renormalisation group (RG). This gives a hope: that one might be able to address questions in strongly coupled condensed matter systems. A key feature of condensed matter is momentum dissipation, and I will briefly discuss how one can implement it using holography. After setting up the stage I will present a class of models for which the RG flow exhibits the peculiarity UV=IR. I will close showing how the scalings of the RG flow are transferred to the scalings of transport coefficients.

Abstract: The spectra of (strongly coupled) quantum systems can be studied by truncating the Fock space and numerically diagonalising the resulting finite-size Hamiltonian. This simple approach can be improved by approximately integrating out the states above the cut-off. I will outline this renormalisation process and discuss the allowed counterterms, given that the cut-off is intrinsically non-local.

Abstract: The sine-Gordon equation \phi_xx - \phi_tt = sin(\phi) is one of the earliest and most important examples of an integrable 2D eld theory solved in great detail via the IST. The quantum counterpart of the IST revealed that the classical soliton, antisoliton and breather solutions turn into solitonic fermions, antifermions and their bound states, with particle number preservation under scattering and factorized amplitudes gov- erned by the Yang-Baxter equations. In this talk we survey the relation between the relativistic sine-Gordon model and (a special case of) the hyperbolic relativistic integrable N-particle systems of Calogero-Moser type. More specically, we review the intimate link between the clas- sical version of the latter and the particle-like sine-Gordon solutions, and present compelling evidence that this soliton-particle correspon- dence turns into a physical equivalence on the quantum level, in the sense that the same scattering amplitudes and bound state energies arise in the quantum eld-theoretic and N-particle models.

Abstract: Ambi-twistor string models give a general framework for calculating tree-level field theory amplitudes. I will describe how this can be related to on-shell diagram techniques to give an expression for the four point one loop amplitude of N=8 supergravity, and I will discuss work in progress on how N=4 conformal supergravity amplitudes can be described in this framework.

Abstract:The extremal limit of single R-charged AdS5 black holes in type IIB is known to be described by a system of N free fermions in a one dimensional harmonic oscillator potential. Since the quantum mechanical problem is solvable and its phase space formulation appears in the gravity dual (LLM geometries), it allows us to explore the relation between entanglement, quantum correlation design and connectivity in space in this set-up, both in a single and a two boundary situation.