Scientific Series

Factorization algebras are local-to-global objects, much like sheaves, and it is natural to ask what kind of topology, geometry, and physics they are sensitive to. We will examine this question with a focus on less-perturbative phenomena, touching on topics like moduli of vacua for 4-dimensional gauge theories and Dijkgraaf-Witten-type TFTs. Apologies hereby issued in advance to the (hopefully) friendly audience (and to my collaborators!) for speaking before achieving complete clarity.

Zoom link:  https://pitp.zoom.us/j/94417858154?pwd=ak54UFpPb3hFbnBwcUlnMnhCdG1odz09

Phase transitions in everyday systems are often catalysed by the presence of impurities, but in cosmology we typically assume the initial state is a homogeneous vacuum. In this talk I will discuss how topological defects can seed first order phase transitions in the early universe, causing them to proceed much more rapidly than in the usual case. The field profiles describing the decay do not have the typically assumed O(3)/O(4) symmetry, requiring an extension of the usual decay rate calculation. To numerically determine the saddle point solutions which describe the decay we use a new algorithm based on the mountain pass theorem. I will present results showing the significance of this effect for catalysis by magnetic monopoles in a simplified model, then discuss the same effect for domain walls catalysing the electroweak phase transition. The presence of domain walls can significantly modify the predictions for gravitational wave signal which may be observed with LISA.

Zoom link:  https://pitp.zoom.us/j/96182819088?pwd=cXhnVjFlT0tkc1VsRld0Yk43bFROUT09

Inspired by the emergence of bulk diffeomorphism invariance in holography, I will give an explicit description how entanglement between quantum subsystems can lead to emergent gauge symmetry in a classical limit. Along the way, I will provide a precise characterisation of when it is consistent to treat a quantum subsystem classically in such a limit, and show that this gives strong constraints on the entanglement structure of classical states. I will explain how this generically leads to emergent fundamentally non-local classical degrees of freedom, which may nevertheless be accounted for in a kinematically local way if one employs an appropriately redundant description. The mechanism I describe is general and elementary, but for concreteness I will exhibit a toy example involving three entangled spins at high angular momentum, and I will also describe a significant generalisation of this toy example based on coadjoint orbits. If there is time, I will discuss evidence for the role this phenomenon plays in gravity. This talk is based on arXiv:2209.03979.

Zoom link:  https://pitp.zoom.us/j/92066956880?pwd=OTRySTlOVGgvM3RCRmkzWHFVSUF3Zz09

Gravitational waves emitted by compact binaries enable unprecedented tests of gravity at highly non-linear regimes, as well as the underlying cosmological model. Going beyond the current null tests of gravity requires accurate theoretical modelling of the waveforms in viable extensions of General Relativity. In the first part of this talk, I will present the recent results and physical insights from analytical modelling of the gravitational waves in the so-called Einstein-scalar-Gauss-Bonnet gravity. Being a sub-class of both Horndeski and quadratic gravity, this theory introduces non-linear curvature corrections to strong-field regime of gravity, allows for hairy-black hole solutions, and scalar-induced tidal deformations. I will present the gravitational-wave signatures of theory’s curvature corrections and the prospects of testing the features of this theory through gravitational wave observations. In the second part of the talk, I will discuss the prospects of using compact mergers for cosmological tests by solely relying on their gravitational wave signals. Using recent constraints on the equation-of-state of neutron stars from multi-messenger observations of NICER and LIGO/Virgo, I show possible bounds on the Hubble constant (H0) found from (single and multiple) neutron star-black hole standard sirens in the next-generation gravitational wave detector era. I show that such systems could enable unbiased 13% - 4% precision measurement of H0 (68% credible interval) within an observation time-frame of hours to a day.

Zoom link:  https://pitp.zoom.us/j/93964588227?pwd=cGsxcEZHRlNjd3R5eHg5dzdtT2lndz09

Central to many of the paradoxes arising in quantum theory is that the act of measurement cannot be understood as merely revealing the pre-existing values of some hidden variables, a phenomenon known as contextuality. In the past few years quantum contextuality has been formalized in a variety of ways; operation-theoretic, sheaf-theoretic, (hyper)graph-theoretic, and cohomological. In this seminar we will discuss the simplicial approach to contextuality introduced in arXiv:2204.06648, which builds off the earlier sheaf-theoretic approach of Abramsky-Brandenberger (arXiv:1102.0264) and the cohomological approach of Okay, et al. (arXiv:1701.01888). In the simplicial approach measurement scenarios and their statistics can be modeled topologically as simplicies using the theory of simplicial sets. The connection to topology provides an additional analytical handle, allowing for a rigorous study of both state-dependent and state-independent contextuality. Using this formalism we present a novel topological proof of Fine's theorem for characterizing noncontextuality in Bell scenarios.

Zoom link:  https://pitp.zoom.us/j/93748699892?pwd=SVhVaTdoRmlwaGdCZVdIWVlKTktjQT09

In this talk I will describe a topological response theory that predicts the physical manifestation of a class of topological invariants in systems with crystalline symmetry. I focus on two such invariants, the 'discrete shift' and a quantized charge polarization. Guided by theory, I discuss how these invariants can be extracted from lattice models by measuring the fractional charge at lattice disclinations and dislocations, as well as from the angular and linear momentum of magnetic flux. These methods are illustrated using the Hofstadter model of spinless fermions in a background magnetic field; they give new topological invariants in this model for the first time since the quantized Hall conductance was computed by TKNN in 1982.

Zoom link:  https://pitp.zoom.us/j/93633131128?pwd=d2h4U1l0ZVU5aE1ORURkdFNSanB4dz09

A quantum computer is a new type of computer based on quantum physics. When it comes to certain computational objectives, the computational ability of quantum computers is much stronger than that of the familiar digital computers, and their construction will enable us to factor large integers and to break most of the current cryptosystems.

The question of whether quantum computation is possible is one of the fascinating clear-cut open scientific questions of our time. In my lecture I will explain theoretical discoveries from the 1990s that suggested that quantum computation is possible and present my theory as to why quantum computation is nevertheless impossible.

At the crux of the matter is the study of noisy intermediate scale quantum (NISQ) computers. Based on the mathematical notions of "noise sensitivity vs noise stability" (Benjamini, Kalai, and Schramm 1999, Kalai and Kindler 2014), we identify the inherent noise sensitivity of probability distributions arising from NISQ computers. This leads to a very low complexity class of probability distributions that can be robustly described by such quantum computers; consequently, NISQ computers will not allow good-quality quantum error-correction which are the necessary building blocks for larger quantum computers.

The lecture will be self-contained and will start with a gentle explanation of some basic notions about computation, and quantum computers.

Zoom link:  https://pitp.zoom.us/j/93847236670?pwd=T2Z2emZ5ZExaZTVYcTNCdU1FNkxOdz09

We consider four-point correlators in an arbitrary excited state of a quantum field theory.  We show that when the theory and state are holographic, such correlators can produce high-quality movies of point-like bulk particles, revealing the geometry in which they move. In some situations, Einstein’s equations amount to a local differential equation on the correlator data. In theories or states that are not holographic, images are too blurry to extract a bulk geometry. Calculations are performed by adapting formulas from conformal Regge theory, to excited states and out-of-time-order correlators.

Zoom link: https://pitp.zoom.us/j/94153545930?pwd=YUFsUW44S1Z5Ri83a2xQdEN0Vk9XZz09

Direct detection experiments search for dark matter through its potential interactions with the SM particles. However, light dark matter models with particle masses below the GeV scale are still largely unconstrained. As we will see in this talk, sensitivity to such small momentum transfer can benefit from quantum sensors, which employ fundamental quantum mechanical phenomena to notice energy depositions otherwise unreachable. Quantum sensors can considerably extend the range in dark matter mass of traditional WIMP experiments and be complementary to other direct detection methods. In the first part of the talk, I will examine a proposal to use atom interferometers to detect a light dark matter subcomponent at sub-GeV masses. DM scattering off of one “arm” of the atom interferometer can cause trackable decoherence and phase shifts. Two key factors render atom interferometers highly competitive experiments for very low masses: they are sensitive to extremely low momentum deposition and their coherent atoms give them a boost in sensitivity. On the second part of the talk, I will present a new proposal to search for axions with optomechanical cavities.  As we will see, the Bose-enhancement of a final state coherent population of photons or phonons can help overcoming the strong suppression from the axion to photon coupling. A unique advantage of this novel search, axioptomechanics, is that the cavity size need no longer be matched to the axion mass, which allows to probe a wide window of axion masses.

Zoom Link:  https://pitp.zoom.us/j/92645586400?pwd=bm1VUEVqUzNOOXV2VnhEUkJtdWZrZz09

The tension between measurements of the Hubble constant obtained at different redshifts may provide a hint of new physics active in the relatively early universe, around the epoch of matter- radiation equality. A leading paradigm to resolve the tension is a period of early dark energy, in which a scalar field contributes a subdominant part of the energy budget of the universe at this time. This scenario faces significant fine-tuning problems which can be ameliorated by a non- trivial coupling of the scalar to the standard model neutrinos. These become non-relativistic close to the time of matter-radiation equality, resulting in an energy injection into the scalar that kick- starts the early dark energy phase, explaining its coincidence with this seemingly unrelated epoch. We present a minimal version of this neutrino-assisted early dark energy model, and perform a detailed analysis of its predictions and theoretical constraints. We consider both particle physics constraints — that the model constitute a well-behaved effective field theory for which the quantum corrections are under control, so that the relevant predictions are within its regime of validity — and the constraints provided by requiring a consistent cosmological evolution from early through to late times. Our work paves the way for testing this scenario using cosmological data sets. 

Zoom link:  https://pitp.zoom.us/j/95613703701?pwd=amlmNUdXdXFuQitFVk8xTnNwcDlMUT09

A large class of Λ < 0 cosmologies have big-bang / big crunch spacetimes with time-symmetric backgrounds and asymptotically AdS Euclidean continuations suggesting a possible holographic realization. We argue that these models generically have time-dependent scalar fields, and these can lead to realistic cosmologies at the level of the homogeneous background geometry, with an accelerating phase prior to the turnaround and crunch. We first demonstrate via explicit effective field theory examples that models with an asymptotically AdS Euclidean continuation can also exhibit a period of accelerated expansion without fine tuning. We then show that certain significantly more tuned examples can give predictions arbitrarily close to a ΛCDM model. Finally, we demonstrate via an explicit construction that the potentials of interest can arise from a superpotential, thus suggesting that these solutions may be compatible with an underlying supersymmetric theory.

This talk is based on 2212.00050.

Zoom link:  https://pitp.zoom.us/j/93499736007?pwd=Qmw5cmZERUN3UmtwTzdKcEdXejJ5UT09

Periodic driving is a ubiquitous tool for controlling experimental quantum systems. When the drive fields are of comparable, incommensurate frequencies, new theoretical tools are required to treat the resulting quasiperiodic time dependence. Similarly, new and surprising phenomena of topological origin may emerge in this regime, including the quantized pumping of energy from one drive field to another. I will describe how to exploit this energy pumping to coherently translate––or boost––quantum states of a cavity in the Fock basis. This protocol enables the preparation of highly excited Fock states for use in quantum metrology––one need only boost low occupation Fock states. Energy pumping, and hence boosting, may be achieved nonadiabatically as a robust edge effect associated to a topological phase. I will present a simple coupled-layer model for the phase, and briefly describe the topological classification which characterizes its robust properties.

Zoom link:  https://pitp.zoom.us/j/94040881668?pwd=THh1WlIxZmZnYlp6QVRKRDhMWnk1UT09