Triangle Seminars
Tuesday, 8 Oct 2019
TBA
K Narayan
(Chennai Mathematical Institute)
The isolated Heisenberg magnet as a quantum time crystal
Marko Medenjak
(ENS)
Abstract:
Isolated systems consisting of many interacting particles are generally assumed to relax to a stationary equilibrium state whose macroscopic properties are described by the laws of thermodynamics and statistical physics. Time crystals, as first proposed by Wilczek, could defy some of these fundamental laws and for instance display persistent non-decaying oscillations. They can be engineered by external driving or contact with an environment, but are believed to be impossible to realize in isolated many-body systems. I will show that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not relax to stationarity and hence constitutes a genuine time crystal that does not rely on external driving or coupling to an environment. I will trace this phenomenon to the existence of periodic extensive quantities and find their frequency to be a no-where continuous (fractal) function of the anisotropy parameter of the chain.
Isolated systems consisting of many interacting particles are generally assumed to relax to a stationary equilibrium state whose macroscopic properties are described by the laws of thermodynamics and statistical physics. Time crystals, as first proposed by Wilczek, could defy some of these fundamental laws and for instance display persistent non-decaying oscillations. They can be engineered by external driving or contact with an environment, but are believed to be impossible to realize in isolated many-body systems. I will show that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not relax to stationarity and hence constitutes a genuine time crystal that does not rely on external driving or coupling to an environment. I will trace this phenomenon to the existence of periodic extensive quantities and find their frequency to be a no-where continuous (fractal) function of the anisotropy parameter of the chain.
Posted by: CityU2
Wednesday, 9 Oct 2019
't Hooft Anomalies and Holomorphy of Supersymmetric Partition Functions
📍 London
Heeyeon Kim
(Oxford)
Abstract:
I discuss the dependence of supersymmetric partition functions on continuous parameters for the flavour symmetry group. In the presence of the 't Hooft anomalies, the supersymmetric Ward identities imply that the partition function computed in the Wess-Zumino gauge has a non-holomorphic dependence on the flavour parameters. I show this explicitly for a large class of 4d N=1 partition functions on half-BPS four manifolds. I propose a new expression for the partition functions on M3 x S1, which differs from earlier holomorphic results by a non-holomorphic Casimir pre-factor.
I discuss the dependence of supersymmetric partition functions on continuous parameters for the flavour symmetry group. In the presence of the 't Hooft anomalies, the supersymmetric Ward identities imply that the partition function computed in the Wess-Zumino gauge has a non-holomorphic dependence on the flavour parameters. I show this explicitly for a large class of 4d N=1 partition functions on half-BPS four manifolds. I propose a new expression for the partition functions on M3 x S1, which differs from earlier holomorphic results by a non-holomorphic Casimir pre-factor.
Posted by: KCL
TTbar and TsT
Stijn van Tongeren
(Humboldt U)
Abstract:
The TTbar deformation of two dimensional QFTs has various attractive and interesting features, giving a simple CDD deformation of the S matrix, and for instance preserving integrability, if present. As a simple example, deforming massless free scalars gives a Nambu-Goto string in flat space in a uniform light-cone gauge. I will discuss what happens if we deform "twice", i.e. TTbar deform light-cone gauge fixed string sigma models. In this setting, TTbar deformations can be viewed as TsT transformations in a suitable T dual frame. This TsT picture also gives a natural interpretation of the TTbar CDD factor as a Drinfeld-Reshetikhin twist.
The TTbar deformation of two dimensional QFTs has various attractive and interesting features, giving a simple CDD deformation of the S matrix, and for instance preserving integrability, if present. As a simple example, deforming massless free scalars gives a Nambu-Goto string in flat space in a uniform light-cone gauge. I will discuss what happens if we deform "twice", i.e. TTbar deform light-cone gauge fixed string sigma models. In this setting, TTbar deformations can be viewed as TsT transformations in a suitable T dual frame. This TsT picture also gives a natural interpretation of the TTbar CDD factor as a Drinfeld-Reshetikhin twist.
Posted by: IC
Thursday, 10 Oct 2019
Non-relativistic gravity and strings
Niels Obers
(Nordita)
Abstract:
I will start by motivating the recent interest in non-relativistic gravity and strings, and introduce the basics of Newton-Cartan geometry.
Newton-Cartan (NC) geometry was introduced more than 90 years ago in order to find a geometric formulation of Newtonian gravity. This geometry (including recent novel generalisation
and extensions) has gained renewed interest as it appears in a variety of settings in modern theory involving gravity, string theory and holography. I will then talk about recent work on an action principle for non-relativistic gravity, including its Newtonian limit. This requires a new notion of NC geometry, which naturally arises in a covariant 1/c expansion of general relativity, with c being the speed of light. The corresponding non-relativistic truncation of general relativity goes beyond Newtonian gravity and is able to correctly describe gravitational time dilation. Finally, I will discuss the relevance and appearance of non-relativistic geometry in connection to non-relativistric string theory and holography.
I will start by motivating the recent interest in non-relativistic gravity and strings, and introduce the basics of Newton-Cartan geometry.
Newton-Cartan (NC) geometry was introduced more than 90 years ago in order to find a geometric formulation of Newtonian gravity. This geometry (including recent novel generalisation
and extensions) has gained renewed interest as it appears in a variety of settings in modern theory involving gravity, string theory and holography. I will then talk about recent work on an action principle for non-relativistic gravity, including its Newtonian limit. This requires a new notion of NC geometry, which naturally arises in a covariant 1/c expansion of general relativity, with c being the speed of light. The corresponding non-relativistic truncation of general relativity goes beyond Newtonian gravity and is able to correctly describe gravitational time dilation. Finally, I will discuss the relevance and appearance of non-relativistic geometry in connection to non-relativistric string theory and holography.
Posted by: QMW