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Lorentzian quantum cosmology
Job Feldbrugge Perimeter Institute for Theoretical Physics
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Entanglement structure and UV regularization in cMERA
Adrian Franco Rubio University of Vienna
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Gravity degrees of freedom on a null surface
Florian Hopfmueller Nord Quantique
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Topological field theories and gapped phases of matter
Lakshya Bhardwaj Harvard University
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Quantum tunneling with a Lorentzian path integral
Laura Sberna University of Nottingham
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Topological Boundary Modes from Quantum Electronics to Classical Mechanics
Charles Kane University of Pennsylvania
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The holographic dual to general covariance
Vasudev Shyam Stealth Startup
One of the defining features of holography is the geometerization of the renormalization group scale. This means that when a quantum field theory is holographically dual to a bulk gravity theory, then the direction normal to the boundary in the bulk (the `radial' direction) is to be interpreted as the energy scale of the dual quantum field theory. So this direction can be seen to be `emergent', and the evolution of bulk fields along this direction is equated with the renormalization group flow of sources or couplings of boundary operators. Given that gravitational theories are generally covariant, this emergent direction must be treated on equal footing as those of the space on which the boundary field theory lives. I will describe the precise integrability condition the renormalization group flow need satisfy which encodes this peculiar response of the quantum field theory under coarse graining so as to respect this property of covariance. In other words, this condition is `dual' to general covariance itself. -
Lorentzian quantum cosmology
Job Feldbrugge Perimeter Institute for Theoretical Physics
Using Picard-Lefschetz theory we show that the Lorentzian path integral forms a good starting point for quantum cosmology which avoids the conformal factor problem present in Euclidean gravity. We study the Lorentzian path integral for a homogeneous and isotropic model with a positive cosmological constant. Applied to the “no-boundary” proposal, we show that this leads to the inverse of the result obtained by Hartle and Hawking. Including a inflation field, the Lorentzian path integral prefers to start at the 'top of the hill' leading to good initial conditions for slow roll inflation. However, when including gravitons the fluctuations seem to be unstable. -
Entanglement structure and UV regularization in cMERA
Adrian Franco Rubio University of Vienna
We give an introduction to cMERA, a continuous tensor networks ansatz for ground states of QFTs. We also explore a particular feature of it: an intrinsic length scale that acts as an ultraviolet cutoff. We provide evidence for the existence of this cutoff based on the entanglement structure of a particular family of cMERA states, namely Gaussian states optimized for free bosonic and fermionic CFTs. Our findings reflect that short distance entanglement is not fully present in the ansatz states, thus hinting at ultraviolet regularization. -
Gravity degrees of freedom on a null surface
Florian Hopfmueller Nord Quantique
A canonical analysis for general relativity is performed on a null surface without fixing the diffeomorphism gauge, and the canonical pairs of configuration and momentum variables are derived. Next to the well-known spin-2 pair, also spin-1 and spin-0 pairs are identified. The boundary action for a null boundary segment of spacetime is obtained, including terms on codimension two corners. FH, Laurent Freidel arXiv:1611.03096, Phys. Rev. D 95, 104006 (2017) -
Topological field theories and gapped phases of matter
Lakshya Bhardwaj Harvard University
I will introduce the idea that topological field theories describe the low-energy properties of gapped local quantum systems. This idea has proved fruitful in recent studies of gapped phases of matter. -
Rise of non-perturbative effects below the upper critical dimension
Extracting low energy universal data of quantum critical systems is a task whose difficulty increases with decreasing dimension. The increasing strength of quantum fluctuations can be tamed by using renormalization group (RG) schemes based on dimensional regularization close to the upper critical dimension of the system. By presenting a non-perturbative approach that allows the reliable extraction of the low energy universal data for the antiferromagnetic quantum critical metal in $2 \leq d < 3$-spatial dimensions, I will exemplify how an emergent non-commutativity between the low-energy limit and the dimensional limit preempts RG schemes based on dimensional regularization to access the correct low-energy universal data in integer dimensions. -
Quantum tunneling with a Lorentzian path integral
Laura Sberna University of Nottingham
We describe the tunneling of a quantum mechanical particle with a Lorentzian (realtime) path integral. The analysis is made concrete by application to the inverted harmonic oscillator potential, where the path integral is known exactly. We apply Picard-Lefschetz theory to the time integral of the Feynmann propagator at fixed energy, and show that the Euclidean integration contour is obtained as a Lefschetz thimble, or a sum of them, in a suitable limit. Picard-Lefschetz theory is used to make the integral manifestly convergent and is also essential for the saddle point or semiclassical approximation. The very simple example of the inverted harmonic oscillator presents many interesting mathematical features, such as the Stokes phenomenon and multiple relevant complex saddles. We also attempt to construct a more realistic picture of the tunneling process, by allowing for spreading in energy and duration. -
Quantum critical responses via holographic models and conformal perturbation theory
We investigate response functions near quantum critical points, allowing for finite temperature and a mild deformation by a relevant scalar. When the quantum critical point is described by a conformal field theory, we use conformal perturbation theory and holography to determine the two leading corrections to the scalar two-point function and to the conductivity. We build a bridge between the couplings fixed by conformal symmetry with the interaction couplings in the gravity theory. We construct a minimal holographic model that allows us to numerically obtain the response functions at all frequencies, independently confirming the corrections to the high-frequency response functions. In addition to probing the physics of the ultraviolet, the holographic model probes the physics of the infrared giving us qualitative insight into new physics scalings. -
Relative entropy with a twist
Matthew Beach Amazon.com
Quantum relative entropy is a measure of the indistinguishability of two quantum states in the same Hilbert space. I will discuss the relative entropy between a state with periodic boundary conditions and one with twisted boundary conditions for a free 1+1 CFT with c=1. I will also highlight the unresolved discrepancy between analytic and numeric results. -
Quasi-Conformal Quantum Error Correction Codes
Existing proposals for topological quantum computation have encountered
difficulties in recent years in the form of several ``obstructing'' results.
These are not actually no-go theorems but they do present some serious
obstacles. A further aggravation is the fact that the known topological
error correction codes only really work well in spatial dimensions higher
than three. In this talk I will present a method for modifying a higher
dimensional topological error correction code into one that can be embedded
into two (or three) dimensions. These projected codes retain at least some
of their higher-dimensional topological properties. The resulting subsystem
codes are not discrete analogs of TQFTs and as such they evade the usual
obstruction results. Instead they obey a discrete analog of a conformal
symmetry. Nevertheless, there are real systems which have these features,
and if time permits I'll discuss some of these. Many of them exhibit
strange low temperature behaviours that might even be helpful for
establishing finite temperature fault tolerance thresholds.
This research is still very much a work in progress... As such it has
numerous loose ends and open questions for further investigation. These
constructions could also be of interest to quantum condensed matter
theorists and may even be of interest to people who like weird-and-wonderful
spin models in general. -
Donaldson-Thomas transformations for moduli spaces of local systems on surfaces
Kontsevich and Soibelman defined Donaldson-Thomas invariants of a 3d Calabi-Yau category with a stability condition. Any cluster variety gives rise to a family of such categories. Their DT invariants are encapsulated in single formal automorphism of the cluster variety, called the DT-transformation. An oriented surface S with punctures, and a finite number of special points on the boundary give rise to a moduli space, closely related to the moduli space of PGL(m)-local systems on S, which carries a canonical cluster Poisson variety structure. We determine the DT-transformation of this space. This is a joint work with Alexander Goncharov.
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Topological Boundary Modes from Quantum Electronics to Classical Mechanics
Charles Kane University of Pennsylvania
Over the past several years, our understanding of topological electronic phases of matter has advanced dramatically. A paradigm that has emerged is that insulating electronic states with an energy gap fall into distinct topological classes. Interfaces between different topological phases exhibit gapless conducting states that are protected topologically and are impossible to get rid of. In this talk we will discuss the application of this idea to the quantum Hall effect, topological insulators, topological superconductors and the quest for Majorana fermions in condensed matter. We will then show that similar ideas arise in a completely different class of problems. Isostatic lattices are arrays of masses and springs that are at the verge of mechanical instability. They play an important role in our understanding of granular matter, glasses and other 'soft' systems. Depending on their geometry, they can exhibit zero-frequency 'floppy' modes localized on their boundaries that are insensitive to local perturbations. The mathematical relation between this classical system and quantum electronic systems reveals an unexpected connection between theories of hard and soft matter.