Scientific Series

I will discuss several issues related to the computation of Poisson brackets in field theories. I will show that by choosing appropriate functional spaces as configuration manifolds, it is possible to avoid the use of distributions. This is relevant, for instance, in the context of Loop Quantum Gravity, where the basic holonomy/flux variables play a central role. I will illustrate the main ideas by using simple examples based on Sobolev spaces.

Zoom link:  https://pitp.zoom.us/j/92794475242?pwd=T2Fjbk1lTXRCNnBxVDZabnJqWlAzUT09

Cluster structure on a quantum group allows one to work with its positive representations, a special class of modules similar in spirit to principal series representations but closed under tensor multiplication. On the other hand, cluster techniques proved inadequate for the study of finite-dimensional representation theory. I will discuss how one can reconcile positive and finite-dimensional representations into one theory by studying moduli spaces of local systems with non-generic monodromies.

Zoom link:  https://pitp.zoom.us/j/97677905324?pwd=Tkxlei9wN1llYVpncHA2cnpYKzlhUT09

The angular resolution of a stellar interferometer, as for a single telescope, becomes better at smaller wavelengths and larger baselines. The goal for ground detectors would then be optical interferometers with baselines as long as the Earth’s diameter. The latter goal has been achieved in radio, but it becomes prohibitive in the optical, as the electromagnetic field oscillates too rapidly to record and analyze directly over km-long baselines. Intensity interferometry relying on second-order correlations can make this possible: rather than the amplitude and phase of incoming light, we need only count photons. This technique has a long history and to date the best measurements of nearby stellar radii, dating back to the 1950s. Its main limitations are the need for very bright sources and its narrow field of view, restricting kilometer-long baselines to sources only a few μas away. In this talk, I will propose an optical-path modification of astronomical intensity interferometers, which introduces an effective time delay in the two-photon interference amplitude, splitting the main intensity correlation fringe into others at finite opening angles, allowing for differential astrometry of multiple compact sources such as stars or quasar images. Together with the exponential progress in the field of single photon detection, such a modification will immensely increase the scope of intensity interferometry beyond measurements of the optical emission region morphology. I will lay out the theory and technical requirements of time-delay intensity interferometry and, time permitting, I will talk about some promising applications, which include astrometric microlensing of stars and quasar images, binary-orbit characterization, exoplanet detection, Galactic acceleration measurements and calibration of the cosmic distance ladder, all at unprecedented relative astrometric precision.

Zoom Link: TBD

Chern-Simons theories can possess 't Hooft anomalies for time-reversal symmetry. In this talk, we will discuss abelian Chern-Simons theories with an interesting time-reversal symmetry algebra and compute the classification of the anomaly, which is captured by a bordism group. In order to get the classification correct I will explain the argument we used that utilized the Smith homomorphism for bordism groups. In order to compute the value of the anomaly we study the Atiyah-Hirzebruch spectral sequence and find a way to trivialize each layer of the anomaly. I will also discuss the generating manifold for the corresponding bordism group, and how it arises from the Smith homomorphism. The knowledge of this manifold allows one to compute the partition function by using the data that characterizes the Chern-Simons theory and the symmetry actions; this gives a robust check of our answer for the anomaly. This is based on work in progress with Arun Debray and Weicheng Ye. 

Zoom link:  TBA

Taking string theory off shell requires breaking Weyl invariance on the worldsheet, i.e. the worldsheet theory is now a QFT instead of a CFT. I will explain Tseytlin’s first-quantized approach to taking the worldsheet theory off-shell in a consistent manner, with a particular emphasis on the subtleties involved in calculating the sphere amplitude. This approach allows for the derivation of a classical string action which gives rise to the correct equations of motion and S-matrix, to all orders in perturbation theory. 

I'll also explain the underlying conceptual structure of the Susskind and Uglum black hole entropy argument. There I will show explicitly how the classical (tree-level) effective action and entropy S = A/4G_N may be calculated from the sphere diagrams. 

Time permitting, I will discuss ongoing efforts to derive the Ryu-Takayanagi formula in string theory.

Based on arXiv:2211.08607 and arXiv:2211.16448. 

Zoom link:  https://pitp.zoom.us/j/93668017324?pwd=K2pxZEhjalRTWkVVbVRESCtRVDFmUT09

After discussing the basics of Carrollian physics, we shall revisit the motion  of massless particles with anyonic spin in the black hole horizons. As recently shown, such particles can move within the horizon of the black hole due to the  coupling of charges associated with a 2-parametric central extension of the 2-dimensional Carroll group to the magnetic field around the black hole -- the so called "anyonic  spin-Hall effect". We shall study several examples of such motions. Of these, the most  interesting is the motion in misaligned (asymptotically uniform) magnetic field around Kerr,  which results in a time dependent motion of Carrollian particles that is reminiscent  of "monarch migration".

Zoom link:  https://pitp.zoom.us/j/97094479078?pwd=SHN6NEU5aE93OXVQYk9aWTVOdzRRUT09

 I will talk about new constructions to the parity-violating sector of gravity that can yield large observables, in particular those from inflation. Within this framework, I will demonstrate the potential for seeking gravitational parity-violation in  uncharted regions of parameter space and give hints to novel methods of probing baryogenesis. I will also comment on a few interesting theoretical aspects regarding inflationary  correlators.

Zoom link:  https://pitp.zoom.us/j/95924890817?pwd=MkRyWmV2a3g1dndPNFhoVlQvb3Ixdz09

Universal properties of two-dimensional conformal interfaces are encoded by the flux of energy transmitted and reflected during a scattering process.

In this talk, I will develop a method that allows me to extend previous results based on thin-brane holographic models to smooth domain-wall solutions of 3-dimensional gravity.

As an application, I will compute the transmission coefficient of a Janus interface in terms of its deformation parameter.

Zoom link:  https://pitp.zoom.us/j/98684574364?pwd=WGdrQXhRcHRJZUZMYmNObUVZT1ZCZz09

Dynamical fixed points are late-time attractors of interactive QFTs that differ from thermal equilibria by a constant entropy production rate. We use holographic framework to analyze such fixed points of strongly coupled gauge theories, driven by homogeneous and isotropic expansion of the background metric - equivalently, a late-time dynamics of a corresponding QFT in Friedmann-Lemaitre-Robertson-Walker Universe. As an application, we discuss gravitational reheating of quark-gluon plasma in the exit from the early-cosmology inflation.

Zoom link:  https://pitp.zoom.us/j/96385064629?pwd=NTZrdUdtbW0rZkxPdFZ3ZnZRUzhjZz09

I will describe a general categorical approach to constructing Hamiltonian actions on moduli spaces. In particular cases, this specializes to give a ``universal" Hitchin integrable system as well as the Calogero-Moser system.  Moreover, I will describe a generalization to higher dimensions of a classical result of Goldman which says that the Goldman Lie algebra of free loops on a surface acts by Hamiltonian vector fields on the character variety of the surface.  A key input is a description of deformations of Calabi-Yau structures, which is of independent interest. This is joint work with Chris Brav.

Zoom link:  https://pitp.zoom.us/j/92929253744?pwd=WGFNQmRJck5NdzFFdU8xcXRlN3RRQT09

We study the behavior of errors in the quantum simulation of  spin systems with long-range multibody interactions resulting from the  Trotter-Suzuki decomposition of the time evolution operator. We  identify a regime where the Floquet operator underlying the Trotter  decomposition undergoes sharp changes even for small variations in the  simulation step size. This results in a time evolution operator that  is very different from the dynamics generated by the targeted  Hamiltonian, which leads to a proliferation of errors in the quantum  simulation. These regions of sharp change in the Floquet operator,  referred to as structural instability regions, appear typically at  intermediate Trotter step sizes and in the weakly interacting regime,  and are thus complementary to recently revealed quantum chaotic  regimes of the Trotterized evolution [L. M. Sieberer et al. npj  Quantum Inf. 5, 78 (2019); M. Heyl, P. Hauke, and P. Zoller, Sci. Adv.  5, eaau8342 (2019)]. We characterize these structural instability  regimes in p-spin models, transverse-field Ising models with  all-to-all p-body interactions, and analytically predict their  occurrence based on unitary perturbation theory. We further show that  the effective Hamiltonian associated with the Trotter decomposition of  the unitary time-evolution operator, when the Trotter step size is  chosen to be in the structural instability region, is very different  from the target Hamiltonian, which explains the large errors that can  occur in the simulation in the regions of instability. These results  have implications for the reliability of near-term gate based quantum  simulators, and reveal an important interplay between errors and the  physical properties of the system being simulated.

Zoom link:  https://pitp.zoom.us/j/92045582127?pwd=WDUxcnlIeXdnVWM3WGJoSFVMNDE2dz09

There are numerous properties of quantum states that one might be interested in characterizing, including statistical moments of observables such as expectations or variances, or more generally purities, entropies, probabilities, eigenvalues, symmetries, marginals, etc. Given a fixed collection of properties, the realizability problem aims to determine which value-assignments to those properties are jointly exhibited by at least one quantum state. In addition to the decision problem of realizability, one might also be interested in quantifying what proportion of quantum states possesses those property values. 

Any property of a quantum state can always, at least in principle, be estimated empirically by suitably measuring an ensemble of many independently and identically prepared copies of that quantum state. The particular sequence of positive operator valued measures which estimates a given property is known as a property estimation scheme. The purpose of this talk is to discuss a strategy for tackling realizability problems by studying the large deviation behaviour of property estimation schemes.

The key idea of this approach is the following:
A given collection of properties is realized by a quantum state if and only if a random quantum state occasionally produces that collection of properties as estimates.
Under suitable conditions, this observation leads to a complete hierarchy of necessary conditions for realizability.

Zoom link:  https://pitp.zoom.us/j/91945653382?pwd=QTZqSnpjYjlxYndqaHZwN2lES1h1Zz09