Scientific Series

We present broadly applicable nonperturbative results on the behavior of eigenvalues and eigenvectors under the addition of self-adjoint operators and under the multiplication of unitary operators, in finite-dimensional Hilbert spaces. To this end, we decompose these operations into elementary 1-parameter processes in which the eigenvalues move similarly to the spheres in Newton's cradle. As special cases, we recover level repulsion and Cauchy interlacing. We discuss two examples of applications. Applied to adiabatic quantum computing, we obtain new tools to relate algorithmic complexity to computational slowdown through gap narrowing. Applied to information theory, we obtain a generalization of Shannon sampling theory, the theory that establishes the equivalence of continuous and discrete representations of information. The new generalization of Shannon sampling applies to signals of varying information density and finite length.

Zoom link: https://pitp.zoom.us/j/94120657832?pwd=SmpsWFhhVCtyeXM3a0pVQU9lMGFLdz09

Generalized noncontextuality is a well-studied notion of classicality that is applicable to a single system, as opposed to Bell locality. It relies on representing operationally indistinguishable procedures identically in an ontological model. However, operational indistinguishability depends on the set of operations that one may use to distinguish two procedures: we refer to this set as the reference of indistinguishability. Thus, whether or not a given experiment is noncontextual depends on the choice of reference. The choices of references appearing in the literature are seldom discussed, but typically relate to a notion of system underlying the experiment. This shift in perspective then begs the question: how should one define the extent of the system underlying an experiment? Our paper primarily aims at exposing this question rather than providing a definitive answer to it. We start by formulating a notion of relative noncontextuality for prepare-and-measure scenarios, which is simply noncontextuality with respect to an explicit reference of indistinguishability. We investigate how verdicts of relative noncontextuality depend on this choice of reference, and in the process introduce the concept of the noncontextuality graph of a prepare-and-measure scenario. We then discuss several proposals that one may appeal to in order to fix the reference to a specific choice, and relate these proposals to different conceptions of what a system really is.

arXiv link:  https://arxiv.org/abs/2209.04469

Zoom link:  https://pitp.zoom.us/j/97393198973?pwd=dWhCOUJQLytxeXVIVmEvOHRnRHc1QT09

In non-relativistic systems, the Lieb-Robinson Theorem imposes an emergent speed limit (independent of the relativistic limit set by c), establishing locality under unitary quantum dynamics and constraining the time needed to perform useful quantum tasks. We have extended the Lieb-Robinson Theorem to quantum dynamics with measurements. In contrast to the general expectation that measurements can arbitrarily violate spatial locality, we find at most an (M+1)-fold enhancement to the speed of quantum information, provided the outcomes of M local measurements are known; this holds even when classical communication is instantaneous. Our bound is asymptotically optimal, and saturated by existing measurement-based protocols (the "quantum repeater").  Our bound tightly constrain the resource requirements for quantum computation, error correction, teleportation, generating entangled resource states (Bell, GHZ, W, and spin-squeezed states), and preparing SPT states from short-range entangled states.

Zoom Link: https://pitp.zoom.us/j/95640053536?pwd=Z05oWlFRSEFTZWFRK2dwcHdsWlBBdz09

The supersymmetric index of N=4 SU(N) Super Yang-Mills is a well studied quantity. In 2104.13932, using the Bethe Ansatz approach, we analyzed some family of contributions to it. In the large N limit each term in this family has a holographic interpretation - it matches the contribution of a different Euclidean black hole to the partition function of the dual gravitational theory. By taking into account non-perturbative contributions (wrapped D3-branes, similar to Euclidean giant gravitons), we further showed a one to one match between the contributions of the gravitational saddles and this family of contributions to the index, both at the perturbative and non-perturbative levels. I'll end with newer results, concerning the form of these terms at finite N, new solutions to the Bethe Ansatz equations (i.e. additional contributions to the index beyond the ones described in that paper), and some ongoing effort to classify all the solutions to these equations.

Zoom Link: https://pitp.zoom.us/j/95037315617?pwd=ell4WExrSXJ4YUVyaXAzRGJjdjYxUT09

With no hints of dark matter in the "classical WIMP" region of parameter space, experimentalists have begun searching in earnest for low mass (MeV-GeV scale) dark matter. However, efforts to probe this region of parameter space have been hindered by an unexpected and mysterious source of background events, dubbed the "low energy excess." Recently, mechanical stress has been shown to create a "low energy excess"-like source of events, and a microphysical picture of how stress creates this background is emerging. In addition to providing a path forward for low mass dark matter searches, these results may address several outstanding problems limiting the performance of superconducting quantum computers.

Zoom Link:  https://pitp.zoom.us/j/92147233613?pwd=RW5PaUNUZlE3SUNnTlZHaVFrdnV3dz09

I'll explain work in progress, joint with Miroslav Rapcak, on geometric constructions of vertex algebras associated to divisors in toric Calabi-Yau threefolds, in terms of moduli stacks of objects in certain exotic abelian subcategories of complexes of coherent sheaves on the underlying threefold. These vertex algebras were originally proposed by Gaiotto-Rapcak, and constructed mathematically in the example of affine space by Rapcak-Soibelman-Yang-Zhao, building on Schiffmann-Vasserot's proof of the AGT conjecture. We give a geometric explanation and generalization of the quivers with potential that feature in the latter results, and outline the analogous construction of vertex algebras in this setting.

Zoom link:  https://pitp.zoom.us/j/93749710253?pwd=Y3NUTHBXZ3FPQUdPU0E0d0ttVzFFdz09

I discuss novel symmetries of perturbation theory around rotating and non-rotating black holes in general relativity, and discuss their origins and implications for gravitational-wave astronomy. This is motivated by two special aspects of black hole perturbations in four dimensions: isospectrality of quasinormal modes and the vanishing of tidal Love numbers. There turn out to be off-shell symmetries underlying each of these phenomena. One is a duality, which on shell reproduces the famous Chandrasekhar duality and therefore underlies isospectrality, and can be thought of as an extension of electric-magnetic duality to black hole backgrounds. The other is a set of "ladder symmetries" relating modes of different angular momentum or spin, which imply the vanishing of Love numbers. This has a geometric origin in the conformal symmetry of low-frequency modes.

Zoom link:  https://pitp.zoom.us/j/93633894223?pwd=cEFRYno5WSt5NUJlOWJLdVZHWjE1QT09

In this talk I will explore perspectives of quantum entanglement in (1+1)-d systems in presence of defects. The talk consists of two parts. In the first part, I will talk about the ground state entanglement entropy for 1d quantum spin chains with defects, using the transverse field Ising model and the three-state Potts model as examples. In the second part, I will describe the field theoretical replica trick approach to study entanglement entropy in such systems. This talk consists of some reviews about existing work, as well as work in progress with Linnea Grans-Samuelsson, Ananda Roy, Hubert Saleur, and Yifan Wang.

Zoom link: https://pitp.zoom.us/j/93049110080?pwd=QmpneGs2QlpZMlBROUlvU3VzaGtsZz09

Celestial holography posits a duality between a theory of quantum gravity in asymptotically flat spacetime and a "celestial" conformal field theory that lives on its co-dimension two boundary. By studying soft theorems of scattering amplitudes in the bulk it was shown that there exist infinite towers of corresponding soft currents in cCFT and their algebra was calculated. In this talk I will consider a bulk theory of Yang-Mills coupled to a massive scalar and show, via soft limits, that the corresponding boundary algebra admits a level proportional to the strength of the background. I will comment on some other aspects of this deformation as well as potentially important subtleties we have encountered with our method of computing celestial amplitudes.

Zoom link:  https://pitp.zoom.us/j/95423960414?pwd=RVoxc1FRRGRmL2RIMXJpbXFKZVBFdz09

The polarization measurements of particles produced in heavy-ion collisions allow us to study amazing phenomena such as, the collective rotation of the nuclear medium, quark spin-alignment with the global angular momenta, local vs global polarization effects and their evolution when there are drastic changes in the properties of the hot, dense and whirly medium. Recently, measurements by the STAR collaboration at RHIC and the HADES collaboration at GSI, show the rising of Lambda and anti-Lambda global polarization with decreasing collision energy and what seems to be a differentiated peak with a sharp decrease at a lower bound in collision energy. In this talk I will report on our recent work where we predict this differentiated peak behavior using a core-corona model, so that measuring the polarization of hyperons becomes a tool to learn about strangeness availability in the medium created in heavy-ion collisions for different initial conditions. I will also present a few new developments we have made to probe the strong magnetic field produced early after the collision with primordial photons and mention other relevant signals that we are working on in order to learn about the critical end-point in the QCD phase diagram.

Zoom link:  https://pitp.zoom.us/j/95896792626?pwd=QlovbE5EWEJBSDdOZjUyK2MxYktmQT09

In this talk, I will present a new tool to constrain low-energy Wilson coefficients in a scalar EFT (scalar for simplicity's sake but the range of applicability is much wider) based on the requirement that such theories should respect causality. Causality will be defined in the sense that no low-energy observer should be able to measure any resolvable time-advance resulting from a scattering event. I will show that these so-called causality bounds are in remarkable agreement with previously derived positivity bounds (where low energy constraints on the 4-point amplitude make use of physical assumptions of the UV completion of the EFT), while being considerably simpler and a better candidate to get cosmological and black hole gravitational bounds.

Zoom link: https://pitp.zoom.us/j/92424925160?pwd=bnRNWE81eEQ4NHY4a28rNGMwTitUdz09

Bang Nucleosynthesis (BBN) is one of the greatest outcome of the Standard Model of Particle Physics when put next to ΛCDM cosmology. In this talk, I will first review the key aspects of standard BBN and illustrate a new code -- PRyMordial -- to make state-of-the-art predictions of primordial light-element abundances within and beyond the Standard Model. I will then highlight the latest measurements regarding the primordial abundance of helium-4 and deuterium, and present evidence at the 2 sigma level for a nonzero lepton asymmetry from BBN data jointly with the Cosmic Microwave Background. I will leave some final comments on how a large total lepton asymmetry can be consistently realized in the Early Universe.

Zoom Link: https://pitp.zoom.us/j/95011247645?pwd=S0EwZG9nSHQvTjV0QjBxeHNUWWtmUT09