The annual Graduate Students’ Conference showcases the diverse research directions at Perimeter Institute, both organized and presented by the students. Our graduate students are invited to share their best work with their fellow PhD students, PSI students and other PI residents interested in hearing about physics research and discussing it in a lively atmosphere full of questions.
PSI students are welcome to join as audience members on Friday, Sept 13 and to present a Lightning Talk if they wish to do so.
What types of differences among causal structures with latent variables are impossible to distinguish by statistical data obtained by probing each visible variable? If the probing scheme is simply passive observation, then it is well-known that many different causal structures can realize the same joint probability distributions. Even for the simplest case of two visible variables, for instance, one cannot distinguish between causal influence of one variable on the other and the two variables sharing a latent common cause. However, it is possible to distinguish between these two causal structures if we have recourse to more powerful probing schemes, such as the possibility of intervening on one of the variables and observing the other. Herein, we address the question of which causal structures remain indistinguishable even given the most informative types of probing schemes on the visible variables. We find that two causal structures remain indistinguishable if and only if they are both associated with the same mDAG structure (as defined by Evans (2016)). We also consider the question of when one causal structure dominates another in the sense that it can realize all of the joint probability distributions that can be realized by the other using a given probing scheme. (Equivalence of causal structures is the special case of mutual dominance.) Finally, we investigate to what extent one can weaken the probing schemes implemented on the visible variables and still have the same discrimination power as a maximally informative probing scheme.
Violations of Bell’s inequality have been studied for spin-1/2 systems in much detail. Turns out that one can show Bell violation for systems that are expressed in terms of continuous variables such as position and momentum. The most ubiquitous examples of such systems are Gaussian states, notably the two-mode squeezed vacuum state. I will talk about how one can quantify violations of local realism in such states. I will discuss the dependence of Bell violation on temperature as well as the result that entanglement is not a monotonic function of Bell's inequality.
We reveal that the information exchange between particle detectors and their ability to harvest correlations from a quantum field can interfere constructively and destructively. This allows for scenarios where the presence of entanglement in the quantum field is actually detrimental to the process of getting the two detectors entangled.
We present a study of the relationship between energy and entanglement in finite regions of possibly arbitrary shape in QFT. We show how one can quantify the entanglement avoiding divergences by using techniques inspired by the formalism of particle detectors in relativistic quantum information. We also show how the energy cost of entanglement extraction varies with the shape and size of the regions, as well as analyze the energy density of the quantum field after this entanglement has been extracted.
The AdS/CFT correspondence proposes that observables in the bulk side must have boundary duals. Within this framework, one can select initial and final spacetime regions on the boundary and consider a scattering process either on the boundary itself or through the bulk. Remarkably, for certain setups, local scattering may be possible in the bulk but not on the boundary, a phenomenon called holographic scattering. Its dual boundary description relies on entanglement between subregions of the spacetime. In this talk I will give an introduction to holographic scattering and present some preliminary results of holographic scattering in a rotating conical defect spacetime.
Entanglement of massive systems mediated by the gravitational field has been suggested as a possible signature of quantum gravity in the so-called gravity-induced entanglement (GIE) tabletop experiments. In contrast, in recent works it has been suggested that the classical propagation of the field source’s quantum degrees of freedom (through quantum-controlled classical fields) can also explain the entanglement of the masses in GIE experiments in their currently proposed regimes. We will analyze how demanding causal behaviour of the experiment can help us constraint the regimes in which GIE experiments cannot be explained via quantum controlled classical fields, opening the possibility of probing the existence of genuinely quantum degrees of freedom in the gravitational field.
The dynamics of closed quantum systems undergoing unitary processes has been well studied, leading to notions of measures for the expressive power of parameterized quantum circuits, relative to the unique, maximally expressive, average behaviour of ensembles of unitaries. Such unitary expressivity measures have further been linked to concentration phenomena known as barren plateaus. However, existing quantum hardware are not isolated from their noisy environment, and such non-unitary dynamics must therefore be described by more general trace-preserving operations. To account for hardware noise, we propose several, non-unique measures of expressivity for quantum channels and study their properties, highlighting how average non-unitary channels differ from average unitary channels. In the limit of large composite system and environments, average noisy quantum channels are shown to be maximally globally depolarizing, with next-leading-order non-unital perturbative behaviour. Furthermore, we rigorously prove that highly-expressive parameterized quantum channels will suffer from barren plateaus, thus generalizing explanations of noise-induced phenomena. This work is based on forthcoming work with Diego Martin, Zoe Holmes, and Marco Cerezo, in affiliation with Los Alamos National Laboratory.
In this paper, we demonstrate that relativistic corrections to gravitational perturbations in amplitudes and fluxes
are essential for accurately studying Extreme Mass Ratio Inspirals (EMRIs) in both vacuum and non-vacuum
environments. We extend the Fast EMRI Waveforms (FEW) framework to the Kerr background for circular
equatorial orbits, providing fully relativistic waveforms in the adiabatic approximation. For beyond-vacuum
scenarios, we investigate the impact of accretion disks using power-law torque models and axionic superradiant
scalar clouds in a relativistic context. Our results highlight the significance of these corrections for improving the
precision and reliability of waveform predictions, parameter estimation, and model selection, which are crucial for the analysis and interpretation of EMRI data in gravitational wave detection
and astrophysical research.
The accurate computation of 3x2pt statistics plays a crucial role in understanding the large-scale structures in the universe using cosmological surveys. While the Limber approximation has traditionally provided a simple and efficient method for this computation, its limitations become apparent in the context of recent and future surveys, demanding more precise and efficient techniques. In this work, we propose a novel, computationally fast, approach to compute 3x2pt statistics without relying on the Limber approximation, ensuring both efficiency and precision.
Our method addresses the challenge of dealing with a 3D integral with Bessel functions by employing a combination of techniques, effectively handling the oscillatory nature of the Bessel functions.
An important aspect of our approach is its compatibility with automatic differentiation techniques, facilitating likelihood exploration and maximization even in high-dimensional parameter space. This feature enhances the usability of our method in cosmological parameter estimation tasks.
Overall, our proposed method offers a promising solution for accurately computing 3x2pt statistics in upcoming cosmological surveys, addressing the shortcomings of the Limber approximation and providing a valuable tool for extracting information from large-scale structure. In particular, the tool provided will be of critical importance for the Euclid survey, enabling the core scientific analyses to be performed using modern statistical inference techniques.
The Gaia catalogue, providing positions and proper motions of stars as faint as 21 mags, has been revolutionary in Galactic astronomy and other subfields. Using the DESI Legacy Imaging Survey, our goal is to extend our data to stars as faint as 27 mags. To do so, we have been working on correcting for systematic errors in the Legacy data, including tree rings, differential chromatic refraction, and lateral color.
Surface operators are nonlocal probes of gauge theories capable of distinguishing phases that are not discernible by the classic Wilson-'t Hooft criterion. I will prove that the correlation function of a surface operator with a chiral primary operator in N=4 super Yang-Mills is a finite polynomial in the Yang-Mills coupling constant. Surprisingly, in spite of these observables receiving nontrivial quantum corrections, we find that these correlation functions are exactly captured in the 't Hooft limit by supergravity in asymptotically AdS5×S5! I will explain how to compute these correlation functions and other surface operator's observables using supersymmetric localization. I will also review how by perturbatively quantizing N=4 SYM around the surface operator singularity and identifying the Feynman diagrams one can reproduce the exact result obtained by localization. This talk is based on 2406.08541, with Changha Choi and Jaume Gomis.
I will review a recently discovered connection (Nima Arkani-Hamed, et al) between tree-level amplitudes of massless Pions and that of a massless scalar in the adjoint of $U(N)$. The scattering of massless Pions can be described by a $U(N)$ Non-Linear Sigma Model Lagrangian. Using the Feynamn rules derived from this Lagrangian, I will outline the salient features of Pion amplitudes such as their vanishing under soft limits. I will then give a brief overview of amplitudes in the adjoint scalar theory. I will conclude by explaining a kinematic deformation that allows one to obtain Pion amplitudes from that of the adjoint scalar.
This talk will be based on SciPost Phys. 17, 021 (2024). Defects are common in physical systems with boundaries, impurities or extensive measurements. The interaction between bulk and defect can lead to rich physical phenomena. Defects in gapless phases of matter with conformal symmetry usually flow to a defect conformal field theory (dCFT). Understanding the universal properties of dCFTs is a challenging task. In this talk, we propose a computational strategy applicable to a line defect in arbitrary dimensions. Our main assumption is that the defect has a UV description in terms of a local modification of the Hamiltonian so that we can compute the overlap between low-energy eigenstates of a system with or without the defect insertion. We argue that these overlaps contain a wealth of conformal data, including the $g$-function, which is an RG monotonic quantity that distinguishes different dCFTs, the scaling dimensions of defect creation operators $\Delta^{+0}_\alpha$ and changing operators $\Delta^{+-}_\alpha$ that live on the intersection of different types of line defects, and various OPE coefficients. We apply this method to the fuzzy sphere regularization of 3D CFTs and study the magnetic line defect of the 3D Ising CFT. Using exact diagonalization and DMRG, we report the non-perturbative results $g=0.602(2),\Delta^{+0}_0=0.108(5)$ and $\Delta^{+-}_0=0.84(5)$ for the first time. We also obtain other OPE coefficients and scaling dimensions. Our results have significant physical implications. For example, they constrain the possible occurrence of spontaneous symmetry breaking at line defects of the 3D Ising CFT. Our method can be potentially applied to various other dCFTs, such as plane defects and Wilson lines in gauge theories.
We extend Noether’s first theorem to symmetries which are not symplectomorphisms but instead transform the symplectic form in a characteristic way. To do so, we use the framework of the covariant phase space method, and focus on the symmetries of the Euler-Lagrange equations which generalize the typical Lagrangian symmetries. We then show how under appropriate assumptions we can construct a dynamically conserved current and scalar charge from these general symmetries. Poisson-Lie symmetries (the semi-classical picture of quantum groups), provide a natural example of such generalized symmetries. We illustrate our framework with the generalized and deformed spinning top, the Klimcık-Severa non-linear σ-model, and 3D gravity as a BF theory, which all are shown to possess such Poisson-Lie type symmetries.
The mathematical object that describes 1/2-BPS line defects in 4d N=2 Supersymmetric QFT is naturally a monoidal category with some extra structure. I'll try to explain why and how leveraging the algebra structure on the BPS spectrum one can try to reconstruct this category.
Based on the work 2406.07134 with Davide Gaiotto and Wei Li.
Most of the research on topological phases of matter has primarily focused on pure states. However, in the real world, systems are often disordered and affected by various forms of imperfections. Consequently, developing notions for mixed-state topological phases has recently attracted significant interest. Among these developments, the notion of symmetry-protected topological (SPT) phases has been extended to include average (or weak) symmetries, leading to the introduction of Average Symmetry-Protected Topological (ASPT) phases, which are found to be relevant in cases of disordered, decohered, and intrinsic average SPT phases. However, finding topological invariants (or simply phase identifiers) to characterize such mixed-state topological phases remains an open problem. In this talk, I will address this problem by introducing a practically computable real-space topological invariant for a two-dimensional disordered ASPT system protected by the average time-reversal symmetry. I'll conclude the talk by discussing our conjectures on interpreting the behavior of this topological invariant as a function of disorder strength, aiming to formalize a notion of phase transition for disordered ensembles of ASPT states.
In this work (arXiv:2405.09450), we study the low-energy effective field theory of the full Fermi surface at the Ising-nematic quantum critical point using the recently developed field-theoretic functional renormalization group (RG). Given that the theory is strongly coupled in two spatial dimensions, we employ dimensional regularization to systematically access the theory in a controlled manner, beginning at d = 5/2. Our analysis reveals that the Fermi momentum, when measured in units of the low-energy scale, continuously grows under RG. Consequently, the space of IR fixed points can only be described projectively. We illustrate the non-trivial implications of this projective nature through two key examples. First, it leads to a discrepancy between the scaling dimension and the relevance of coupling functions. Second, there is no single dynamical critical exponent that universally governs the scaling between energy and momentum across all low-energy observables. Moreover, we identify another critical dimension, dsc, below which superconducting instabilities emerge in the true low-energy limit. Above this dimension, the projective fixed point remains stable and we establish that two marginal coupling functions—the Fermi surface shape function and the Fermi velocity—determine all the coupling functions that define the space of projective fixed points.
In this work, we propose a systematic method to obtain the effective field theory of the quantum dissipative systems which nonlinearly realize symmetries. We focus on the high temperature or Brownian limit, in which the effective action of the dissipative dynamics is localized in time. We first introduce a microscopic model at the linear response level, which shows how the dissipative dynamics on Lie group emerges effectively through the reduced dynamics of a system interacting with a thermal bath. The model gives a systematic method to give the Langevin equation which is covariant with respect to the symmetries of the system. In addition, the model shows a systematic way to go beyond the Gaussian white noise and the interaction between the noise and dissipation. Then, using the dynamical KMS symmetry, without any reference to the microscopic structure of the bath, we obtain the most general effective action of the nonlinearly realized dissipative dynamics at high temperature. The universal dissipative coefficients are larger than the case of the linear response approximation. Then, we focus on the case of Ohmic friction where the corresponding dissipative coefficients are more restricted; we suggest an alternative model, the bulk model, to describe any Ohmic dissipative system at high temperature. The Bulk model provides a geometrical picture for the noise in the case of Ohmic friction.
There are now multiple direct probes of the region near black hole horizons, including direct imaging with the Event Horizon Telescope (EHT). As a result, it is now of considerable interest to identify what aspects of the underlying spacetime are constrained by these observations. For this purpose, we present a new formulation of an existing broad class of integrable, axisymmetric, stationary spinning black hole spacetimes, specified by four free radial functions, that makes manifest which functions are responsible for setting the location and morphology of the event horizon and ergosphere. We explore the size of the black hole shadow and high-order photon rings for polar observers, approximately appropriate for the EHT observations of M87*, finding analogous expressions to those for general spherical spacetimes. Of particular interest, we find that these are independent of the properties of the ergosphere, but does directly probe on the free function that defines the event horizon. Based on these, we extend the nonperturbative, nonparametric characterization of the gravitational implications of various near-horizon measurements to spinning spacetimes. Finally, we demonstrate this characterization for a handful of explicit alternative spacetimes.
It is well known that alternative theories to the Standard Model allow
fundamental constants, such as the fine structure constant, to vary in
spacetime. One way to investigate these variations is to utilize the Mass-
Radius relation of compact objects, which is inherently affected by α
variations. As such, we initially construct the model of a polytropic
white dwarf, which we perturb by adding the α variations for various
GUT models. We continue our analysis with neutron stars, investigating
both polytropic and more realistic equations of state. We outline how
future observations might distinguish between extensions of the Standard
Model.
Violations of Bell’s inequality have been studied for spin-1/2 systems in much detail. Turns out that one can show Bell violation for systems that are expressed in terms of continuous variables such as position and momentum. The most ubiquitous examples of such systems are Gaussian states, notably the two-mode squeezed vacuum state. I will talk about how one can quantify violations of local realism in such states. I will also discuss the dependence of Bell violation on temperature as well as the result that entanglement is not a monotonic function of Bell's inequality.
We discuss the concept of spontaneous symmetry breaking and illustrate it with a general example. We consider Wigner-Weyl and Nambu-Goldstone realisations of symmetry in the quantum theory. Next, we state Goldstone’s theorem and sketch its proof. We discuss why quantum chromodynamics is not realised in the Wigner-Weyl mode.
The theory $S = \int\text{d}^{4-\epsilon}x\left(\frac{1}{2}|\partial\phi|^2 - \frac{m^2}{2}|\phi|^2-\frac{g}{16}|\phi|^4\right)$ exhibits a global $U(1)$ symmetry, and the operators $\phi^n$ ($\bar\phi^n$) have charge $n$ ($-n$) with respect to this symmetry. By rescaling the fields and the coupling constant, it is possible to work in a double limit $n\to\infty$, $g\to 0$ with $\lambda = gn$ kept constant. In this way, it is possible to compute 2-point functions of the form $\langle \phi^n(x) \bar\phi^n(0) \rangle$ in the large $n$ limit, either diagrammatically by a resummation of the leading contribution at all orders in $g$, or using semiclassical methods through the saddle point approximation. This second approach is particularly powerful because it can also be applied to the theory on a curved background. This allows obtaining the form of the 2-point function for an arbitrary metric, and by functionally differentiating with respect to it, it is also possible to obtain, in the flat theory, the 3-point function $\langle T^{ij}(z) \phi^n(x) \bar \phi^n(0) \rangle$ in which an energy-momentum tensor has been inserted. This allows for a non-trivial check of the conformal symmetry of this sector of the theory by verifying the Ward identities that this 3-point function should satisfy.
Almost all spiral galaxies have been observed to have a flattening rotation curve, the new Milky Way Gaia DR3 data challenges these observations. The Gaia DR3 data presents a Keplerian declining rotation curve, starting at $\sim19$ kpc and ending at $\sim26.5$ kpc from the galactic centre. This data reduces the total Milky Way mass by an order of magnitude, $M = 2.06\times10^{11} M_\odot$, compared to the previously required dark matter halo mass $M ∼ (2 − 5)\times10^{12} M_\odot$. Newtonian and modified gravity (MOG) fits are applied to the Milky Way Gaia DR3 rotation curve. The fit obtained using MOG has a total required mass of $M = 1.59\times10^{11} M_\odot$. This is in excess of the estimated visible baryon mass of the Milky Way $M_b ∼ 0.65\times10^{11} M_\odot$. The excess mass can be attributed to either dark matter or a circumula galactic hot gas.
It may be the case that a spacetime exhibits no asymptotia where gauge invariant observables can be defined in a natural way. On such occasions the introduction of a timeline boundary may be helpful. We therefore discuss the initial boundary value problem in the context of General Relativity.
The black hole information paradox is a fundamental conflict between the quantum-mechanical and thermodynamic descriptions of black holes, specifically of their particle-emission process known as the Hawking radiation. The paradox concerns whether the radiation of a black hole is a unitary time evolution or a thermal process that erases most information about the initial state of the black hole. Multiple black hole models (e.g. [1,2]) were shown to exhibit the Page curve behavior, suggesting the unitarity of the Hawking radiation. However, without a verified theory of quantum gravity, the exact structure of black holes remains undetermined, and we need a model-independent way to test black hole unitarity. My project thus aims to develop a general framework for testing black hole unitarity by searching for its physical signatures. In particular, we employ the "hybrid" RST model [3], which possesses a Page-curve behavior, and study whether the unitarity is manifested in the transition rate of the Unruh-DeWitt particle detector.
[1] Hong Zhe Chen, Robert C. Myers, Dominik Neuenfeld, Ignacio A. Reyes, Joshua Sandor. Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane".
https://doi.org/10.48550/arXiv.2010.00018.
[2] Yohan Potaux, Sergey N. Solodukhin, and Debajyoti Sarkar. "Spacetime Structure, Asymptotic Radiation, and Information Recovery for a Quantum Hybrid State.” Physical Review Letters 130, no. 26 (June 30, 2023): 261501. https://doi.org/10.1103/PhysRevLett.130.261501.
[3] Yohan Potaux, Debajyoti Sarkar, and Sergey N. Solodukhin. "Quantum States and Their Back-Reacted Geometries in 2D Dilaton Gravity.” Physical Review D 105, no. 2 (January 12, 2022): 025015. https://doi.org/10.1103/PhysRevD.105.025015.
The Selberg zeta function and trace formula are powerful tools used to calculate kinetic operator spectra and quasinormal modes on hyperbolic quotient spacetimes. In this article, we extend this formalism to non-hyperbolic quotients by constructing a Selberg zeta function for warped AdS3 black holes. We also consider the so-called self-dual solutions, which are of interest in connection to near-horizon extremal Kerr. We establish a map between the zeta function zeroes and the quasinormal modes on warped AdS3 black hole backgrounds. In the process, we use a method involving conformal coordinates and the symmetry structure of the scalar Laplacian to construct a warped version of the hyperbolic half-space metric, which to our knowledge is new and may have interesting applications of its own, which we describe. We end by discussing several future directions for this work, such as computing 1-loop determinants (which govern quantum corrections) on the quotient spacetimes we consider, as well as adapting the formalism presented here to more generic orbifolds.
Surface operators are nonlocal probes of gauge theories capable of distinguishing phases that are not discernible by the classic Wilson-'t Hooft criterion. I will prove that the correlation function of a surface operator with a chiral primary operator in N=4 super Yang-Mills is a finite polynomial in the Yang-Mills coupling constant. Surprisingly, in spite of these observables receiving nontrivial quantum corrections, we find that these correlation functions are exactly captured in the 't Hooft limit by supergravity in asymptotically AdS5×S5! I will explain how we added this entry to the holographic dictionary. This talk is based on 2406.08541, with Changha Choi and Jaume Gomis.
This work investigates the ferroelectric properties of γ − In₂Se₃, a material that uniquely retains its spontaneous polarization at the nano-scale, making it resistant to depolarizing fields. With a direct band gap of 1.8 eV and the ability to switch between insulating and semiconducting phases at room temperature, γ − In₂Se₃ holds promise for next-gen memory devices, where its stable ferroelectricity could revolutionize data storage and processing.