Scientific Series

Neural networks offer a novel approach to represent wave functions for solving quantum many-body problems. But what kinds of quantum states are efficiently represented by neural networks? In this talk, we will discuss entanglement properties of an ensemble of neural network states represented by random restricted Boltzmann machines. Phases with distinct entanglement features are identified and characterized. In particular, for certain parameters, we will show that these neural network states can look typical in their entanglement profile while still being distinguishable from a typical state by their fractal dimensions. The obtained phase diagrams may help inform the initialization of neural network ansatzes for future computational tasks.

Zoom link:  https://pitp.zoom.us/j/94316902357?pwd=RGxWYm9EWGtGYzBvUzM5ZWdwVTB5dz09

The Deligne-Mumford moduli space of genus 0 curves plays many roles in representation theory.  For example, the fundamental group of its real locus is the cactus group which acts on tensor products of crystals.

I will discuss a variant on this space which parametrizes "cactus flower curves".  The fundamental group of the real locus of this space is the virtual cactus group.  This moduli space of cactus flower curves is also the parameter space for inhomogeneous Gaudin algebras.

Zoom link:  https://pitp.zoom.us/j/96658223425?pwd=NUxRN2FsdWJ1SWtHMlRDcTdHMGNPQT09

In this talk, I will describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced by Fortin and Skiba (DOI:10.1007/JHEP06(2020)028). To begin with, I will give some background on the formalism. In particular, I will map out how to build two-, three-, and four-point functions within this framework. I will then lay out how to construct tensorial generalizations of the well-known scalar four-point blocks for symmetric traceless exchange. As I will discuss, these generalized objects satisfy a number of contiguous relations. Together, these empower us to fully contract the four-point tensorial blocks, ultimately yielding finite spin-independent linear combinations of four-point scalar blocks potentially acted upon by first-order differential operators. I will next proceed to describe how to set up the conformal bootstrap equations directly in the embedding space. I will begin by mapping out a general strategy for counting the number of independent tensor structures, which leads to a simple path to generating the bootstrap equations. I will then examine how to implement this method to construct the two-point, three-point, and ultimately four-point conformal bootstrap equations. Lastly, I will illustrate this method in the context of a simple example.

Zoom link:  https://pitp.zoom.us/j/98920533892?pwd=cDQvOExJWnBsUWNpZml5S1cxb0FJQT09

Many topological phases of lattice systems display quantized responses to lattice defects. Notably, 2D insulators with C_n lattice rotation symmetry hosts a response where disclination defects bind fractional charge. In this talk, I will show that the underlying physics of the disclination-charge response can be understood via a theory of continuum fermions with an enlarged SO(2) rotation symmetry. This interpretation maps the response of lattice fermions to disclinations onto the response of continuum fermions to spatial curvature. Additionally, in 3D, the response of continuum fermions to spatial curvature predicts a new type of lattice response where disclination lines host a quantized polarization. This disclination-polarization response defines a new class of topological crystalline insulator that can be realized in lattice models. In total, these results show that continuum theories with spatial curvature provide novel insights into the universal features of topological lattice systems. In total, these results show that theories with spatial curvature provide novel insights into the universal features of topological lattice systems.

Zoom link:  https://pitp.zoom.us/j/97325013281?pwd=MU5tdFYzTFljMGdaelZtNjJqbmRPZz09

As was realized by Bondi, Metzner, van der Burg, and Sachs (BMS), the symmetry group of asymptotic infinity is not the Poincaré group, but an infinite-dimensional group called the BMS group. Because of this, understanding the BMS frame of the gravitational waves produced by numerical relativity is crucial for ensuring that analyses on such waveforms and comparisons with other waveform models are performed properly. Up until now, however, the BMS frame of numerical waveforms has not been thoroughly examined, largely because the necessary tools have not existed. In this talk, I will highlight new methods that have led to improved numerical waveforms; specifically, I will explain what the gravitational memory effect is and how it has recently been resolved in numerical relativity. Following this, I will then illustrate how we fix the BMS frame of numerical waveforms to perform much more accurate comparisons with either quasi-normal mode or post-Newtonian models. Last, I will briefly highlight  some exciting results that this work has enabled, such as building memory-containing surrogate models and finding nonlinearities in black hole ringdowns.

Zoom Link:  https://pitp.zoom.us/j/96739417230?pwd=Tm00eHhxNzRaOEQvaGNzTE85Z1ZJdz09

The usual quantum mechanical description of measurements, unitary kicks, and other local operations has the potential to produce pathological causality violations in the relativistic setting of quantum field theory (QFT). While there are some operations that do not violate causality, those that do cannot be physically realisable. For local observables in QFT it is an open question whether the projection postulate, or more specifically the associated ideal measurement operation, is consistent with causality, and hence whether it is physically realisable in principle.

In this talk I will recap a criteria that distinguishes causal and acausal operations in real scalar QFT. I will then focus on operations constructed from smeared field operators - the basic local observables of the theory. For this simple class of operations we can write down a more practical causality criteria. With this we find that, under certain assumptions - such as there being a continuum spacetime - ideal measurements of smeared fields are acausal, despite prior heuristic arguments to the contrary. For a discrete spacetime (e.g. a causal set), however, one can evade this result in a ‘natural’ way, and thus uphold causality while retaining the projection postulate.

Zoom link:  https://pitp.zoom.us/j/94464896161?pwd=UkhPQnJONmlxYy9pQXJINThpY3l4QT09

We give a new definition of self-testing for correlations in terms of states on C*-algebras. We show that this definition is equivalent to the standard definition for any class of finite-dimensional quantum models which is closed under submodels and direct sums, provided that the correlation is extremal and has a full-rank model in the class. This last condition automatically holds for the class of POVM quantum models, but does not necessarily hold for the class of projective models by a result of Mancinska and Kaniewski. For extremal binary correlations and for extremal synchronous correlations, we show that any self-test for projective models is a self-test for POVM models. The question of whether there is a self-test for projective models which is not a self-test for POVM models remains open. An advantage of our new definition is that it extends naturally to commuting operator models. We show that an extremal correlation is a self-test for finite-dimensional quantum models if and only if it is a self-test for finite-dimensional commuting operator models, and also observe that many known finite-dimensional self-tests are in fact self-tests for infinite-dimensional commuting operator models.

Zoom link: https://pitp.zoom.us/j/95783943431?pwd=SDFyQVVZR1d4WlVNSDZ4OENzSmJQUT09

In my talk I will discuss the Euclidean gravitational path integral of N=2 (timelike) Liouville theory on a two-sphere.  We view N= 2 Liouville as a gauge fixed form of a 2d supergravity theory coupled to an N=2 superconformal field theory. N=2 super Liouville admits a positive cosmological constant. I will discuss and contrast the results of supersymmetric localization and the explicit higher-loop evaluation of the path integral around it's dS_2 saddle.

Zoom Link: https://pitp.zoom.us/j/91448729065?pwd=TmJSOGg4dkNxMVJsTWxRRHBYZnVoZz09

Rare meson decays are among the most sensitive probes of both heavy and light new physics. Among them, new physics searches using kaons and pions benefit from their small total decay widths and the availability of very large datasets. In this talk, we first give an overview of new opportunities to search for axion-like particles (ALPs) in light meson decays. Second, we revisit the theory and constraints on ALPs interacting with leptons, pointing out the relevance of charged current meson and W decays to ALPs. This is particularly prominent in models where the ALP couples in an isospin-violating way. Finally, we highlight the role of the future PIONEER experiment in probing these new charged current pion decays to ALPs.

Zoom Link:  https://pitp.zoom.us/j/98376159809?pwd=eDNHd1NhTUlVTmV4Y1RONjllNTNPdz09

A brief introduction to Celestial Holography

We introduce the origins of holography and illustrate in broad strokes the theory of celestial holography. We discuss the development of asymptotic symmetries from soft theorems and how these symmetries point to a codimension 2 boundary on which would live the dual CFT. We show the connection between predicted asymptotic symmetries and observable memory effects, completing the famous infrared triangle. We conclude with some applications and current problems we are thinking about, in particular with respect to bulk reconstruction.

It is well known that quantum information can be strictly localized in quantum field theory. Similarly, one can also localize information in classical gravity up to quantities like the ADM mass which are fixed by the constraints of general relativity. On the other hand, the holographic nature of quantum gravity suggests that information can never be localized deep inside some spacetime region, and is always accessible from the boundary. This is meant to hold as a non-perturbative statement and it remains to be understood whether quantum information can be localized within G_N perturbation theory. In this talk, I will address this problem from the point of view of the AdS/CFT correspondence. I will construct candidate local operators that can be used to localize information deep inside the bulk. They have the following two properties: they act just like standard HKLL operators to leading order at large N, but commute with the CFT Hamiltonian to all orders in 1/N. These operators can only be constructed in a particular class of states which have a large energy variance, for example coherent states corresponding to semi-classical geometries. The interpretation of these operators is that they are dressed with respect to a feature of the state, rather than to the boundary. I will comment on connections with black holes and computations of the Page curve.

Zoom link: https://pitp.zoom.us/j/94678968773?pwd=NUJhOEJmRWxLa3pCVUtVVi9DdkE3QT09

In the early 1980s, axions and WIMPs were identified as promising dark matter candidates. The last forty years have seen a spectacularly successful experimental program attempting to discover the WIMPs, with sensitivity that has by now improved by many orders of magnitude compared to the earliest results. The parallel program to search for axions has made less progress and has reached the necessary sensitivity only over a very limited mass range. However, progress has recently accelerated, with the invention of many new axion detection techniques that may eventually provide a definitive answer to the question of whether the dark matter is made of axions. I will review some of these new developments with emphasis on Fermilab’s program, including ADMX- Extended Frequency Range and Broadband Reflector Experiment for Axion Detection (BREAD).

Zoom link:  https://pitp.zoom.us/j/97234421735?pwd=UGNJRWxYMkErRmdWSnJiWTdoOFNaZz09