Titles and abstracts will be posted here as they are received.
Xenia de la Ossa: On the Moduli Space of Heterotic Strings Compactifications
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Menika Sharma: Extensions of W-Algebras
W-algebras are generalizations of the Virasoro algebra and are the symmetry algebras of "minimal-model" coset conformal field theories. They are also the asymptotic symmetry algebras of higher-spin theories in three-dimensional AdS spacetime. In recent times, it has become evident that W-algebras can be embedded in larger algebras. I will talk of two such enlargements of W-algebras: The first is associated with a symmetric product orbifold CFT and the second comes from a coset CFT. I will also discuss the relation of these enlarged algebras with the symmetry algebra of string theory.
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Tom Frith: Time Dependence in non-Hermitian Quantum Systems
It is known that non-Hermitian quantum systems with PT-symmetry exhibit real eigenvalues and have unitary time evolutions. When this symmetry is spontaneously broken, the eigenvalues become complex and we would ordinarily dismiss the system as meaningless. However, we demonstrate that non-Hermitian Hamiltonians with broken PT-symmetry and can be made meaningful
when introducing some explicit time dependence into their parameters. We show that explicitly time dependent non-Hermitian Hamiltonians lose their dual nature, that is simultaneously satisfying the Schrodinger equation and acting as the energy operator. Instead the Hamiltonian becomes unobservable and we must define a new energy operator. We use three separate methods used to solve such systems; namely the Dyson equation, the quasi-Hermiticity equation and the Lewis Riesenfeld Invariant method. Each method is analysed for its relative merits using two examples: A two level matrix model and a two dimensional model with infinite Hilbert space, both with exact analytical solutions. The key auxiliary equation to be solved in both models is the nonlinear Ermakov-Pinney equation with time-dependent coefficients.
References
[1] A. Fring and T. Frith, Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians, Physical Review A 95, 010102(R) (2017)
[2] A. Fring and T. Frith, Mending the broken PT-regime via an explicit time-dependent Dyson map, Physics Letters A 381 (2017) 2318-2323
[3] A. Fring and T. Frith, Metric versus observable operator representation, higher spin models. The European Physical Journal Plus, 133(2):57, Feb 2018.
[4] A. Fring and T. Frith, Solvable two dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime, JPhysA-109733.R2 (2018)
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Jason Myers: Energy Transport in non-Equilibrium Integrable Systems
I will discuss a recently developed formalism called generalised hydrodynamics which can be used to determine the time scaled cumulants of energy flow in non-equilibrium integrable systems in 1+1 D. For this talk I will use the toy model of a gas made up of hard rods that collide elastically. Although the hard rods gas is a classical model, the formalism used is general enough to be applied to interesting non-equilibrium quantum systems such as the Lieb-Liniger gas.
________________________________________________________________________________________
Anne Taormina: The Conway Moonshine Module is a reflected K3 theory
Abstract: In a suitable class of superconformal field theories (SCFTs), which will be characterised in this talk, it is possible to
transform all fields into holomorphic ones through a procedure devised in collaboration with Katrin Wendland and called `reflection’. Our interest in reflection is rooted in the fact that it bridges the gap between `full-fledged' SCFTs and super vertex operator algebras of CFT type. In particular, the relation between a very symmetric K3 theory and the Conway Moonshine Module constructed by John Duncan will be sketched with the help of lattices and the free fermion description of both theories.
________________________________________________________________________________________
Yuri Van Nieuwkerk: Realizing Integrable Field Theories with Cold Atomic Gases
I will discuss how matter interferometry can be used to probe integrable field theories out of equilibrium. In particular, I will focus on a proposed realization of the sine-Gordon model as the low-energy description of a pair of one-dimensional bose gases, connected by a tunnel coupling. After reviewing the low-energy projection using Luttinger Liquid theory, I will show how individual measurements of the gas density can be used to rigorously construct full distribution functions of a vertex operator in the field theory. In the absence of tunnel-coupling, such distribution functions show a remarkable match between theory and experiment. For the tunnel-coupled case, I will highlight some puzzling open questions, related to unknown properties of the sine-Gordon model out of equilibrium.
Xenia de la Ossa: On the Moduli Space of Heterotic Strings Compactifications
________________________________________________________________________________________
Menika Sharma: Extensions of W-Algebras
W-algebras are generalizations of the Virasoro algebra and are the symmetry algebras of "minimal-model" coset conformal field theories. They are also the asymptotic symmetry algebras of higher-spin theories in three-dimensional AdS spacetime. In recent times, it has become evident that W-algebras can be embedded in larger algebras. I will talk of two such enlargements of W-algebras: The first is associated with a symmetric product orbifold CFT and the second comes from a coset CFT. I will also discuss the relation of these enlarged algebras with the symmetry algebra of string theory.
________________________________________________________________________________________
Tom Frith: Time Dependence in non-Hermitian Quantum Systems
It is known that non-Hermitian quantum systems with PT-symmetry exhibit real eigenvalues and have unitary time evolutions. When this symmetry is spontaneously broken, the eigenvalues become complex and we would ordinarily dismiss the system as meaningless. However, we demonstrate that non-Hermitian Hamiltonians with broken PT-symmetry and can be made meaningful
when introducing some explicit time dependence into their parameters. We show that explicitly time dependent non-Hermitian Hamiltonians lose their dual nature, that is simultaneously satisfying the Schrodinger equation and acting as the energy operator. Instead the Hamiltonian becomes unobservable and we must define a new energy operator. We use three separate methods used to solve such systems; namely the Dyson equation, the quasi-Hermiticity equation and the Lewis Riesenfeld Invariant method. Each method is analysed for its relative merits using two examples: A two level matrix model and a two dimensional model with infinite Hilbert space, both with exact analytical solutions. The key auxiliary equation to be solved in both models is the nonlinear Ermakov-Pinney equation with time-dependent coefficients.
References
[1] A. Fring and T. Frith, Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians, Physical Review A 95, 010102(R) (2017)
[2] A. Fring and T. Frith, Mending the broken PT-regime via an explicit time-dependent Dyson map, Physics Letters A 381 (2017) 2318-2323
[3] A. Fring and T. Frith, Metric versus observable operator representation, higher spin models. The European Physical Journal Plus, 133(2):57, Feb 2018.
[4] A. Fring and T. Frith, Solvable two dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime, JPhysA-109733.R2 (2018)
________________________________________________________________________________________
Jason Myers: Energy Transport in non-Equilibrium Integrable Systems
I will discuss a recently developed formalism called generalised hydrodynamics which can be used to determine the time scaled cumulants of energy flow in non-equilibrium integrable systems in 1+1 D. For this talk I will use the toy model of a gas made up of hard rods that collide elastically. Although the hard rods gas is a classical model, the formalism used is general enough to be applied to interesting non-equilibrium quantum systems such as the Lieb-Liniger gas.
________________________________________________________________________________________
Anne Taormina: The Conway Moonshine Module is a reflected K3 theory
Abstract: In a suitable class of superconformal field theories (SCFTs), which will be characterised in this talk, it is possible to
transform all fields into holomorphic ones through a procedure devised in collaboration with Katrin Wendland and called `reflection’. Our interest in reflection is rooted in the fact that it bridges the gap between `full-fledged' SCFTs and super vertex operator algebras of CFT type. In particular, the relation between a very symmetric K3 theory and the Conway Moonshine Module constructed by John Duncan will be sketched with the help of lattices and the free fermion description of both theories.
________________________________________________________________________________________
Yuri Van Nieuwkerk: Realizing Integrable Field Theories with Cold Atomic Gases
I will discuss how matter interferometry can be used to probe integrable field theories out of equilibrium. In particular, I will focus on a proposed realization of the sine-Gordon model as the low-energy description of a pair of one-dimensional bose gases, connected by a tunnel coupling. After reviewing the low-energy projection using Luttinger Liquid theory, I will show how individual measurements of the gas density can be used to rigorously construct full distribution functions of a vertex operator in the field theory. In the absence of tunnel-coupling, such distribution functions show a remarkable match between theory and experiment. For the tunnel-coupled case, I will highlight some puzzling open questions, related to unknown properties of the sine-Gordon model out of equilibrium.