Talks

I will review the analytic component of the geometric Langlands correspondence, developed recently in my joint work with E. Frenkel and D. Kazhdan (based on previous works by other authors, including A. Braverman, R. Langlands, J. Teschner, M. Kontsevich), with a special focus on archimedian local fields, especially R. This is based on our work with E. Frenkel and D. Kazhdan and insights shared by D. Gaiotto and E. Witten.

We identify infinitely many non-invertible generalized global symmetries in QED and QCD for the real world in the massless limit. In QED, while there is no conserved Noether current for the axial symmetry because of the ABJ anomaly, for every rational angle, we construct a conserved and gauge-invariant topological symmetry operator. Intuitively, it is a composition of the axial rotation and a fractional quantum Hall state coupled to the electromagnetic U(1) gauge field. These conserved symmetry operators do not obey a group multiplication law, but a non-invertible fusion algebra over TQFT coefficients. These non-invertible symmetries lead to selection rules, which are consistent with the scattering amplitudes in QED. We further generalize our construction to QCD, and show that the neutral pion decay can be understood from a matching condition of the non-invertible global symmetry.

I'll discuss a vertex algebra whose correlators are scattering amplitudes (and form factors) of self-dual Yang-Mills theory, for certain gauge groups and matter. The vertex algebra is a kind of vertex quantum group, and is a cousin of the affine Yangian. This is joint work with Natalie Paquette.

The past decade has witnessed tremendous advancements in the size, coherence and control accuracy of qubits across various material platforms. In the case of superconducting qubits fabricated from Josephson junctions, quantum systems with over 50 qubits and >99% gate fidelities can now be reliably fabricated. In this talk, I will introduce the basics of superconducting qubits, with a particular focus on the implementation and calibration of two-qubit gates. I will then describe an experiment demonstrating quantum computational advantage on a specific task, namely sampling from random quantum circuits comprising 53 qubits [1]. The success of this experiment hinges on the chaotic dynamics underlying the random circuits, which generates sufficiently large entanglement to challenge classical simulation within the coherence times of the qubits. To systematically study the physics of quantum chaos, we perform a second experiment which investigates the “fingerprints” of chaos on local quantum observables [2]. We demonstrate how the two fundamental mechanisms of quantum chaos, operator spreading and operator entanglement, may be diagnosed by reversing the flow of time and measuring the so-called out-of-time-order correlators (OTOCs). Additionally, we find that with proper error-mitigation strategies, even local quantum observables such as OTOCs may be measured up to accuracies requiring non-trivial classical computational resources to simulate. These works pave a critical path toward using quantum computers for scientific discovery in the NISQ era.

 

[1] Google Quantum AI, Nature 574, 505 (2019).

[2] X. Mi et al., Science 374, 1479 (2021).

Zoom Link: https://pitp.zoom.us/j/93446337538?pwd=UXpsUFZ4M0tDSDd6bnA0VFBsazNPQT09

"Motivated by applications to soft supersymmetry breaking, we revisit the Seiberg-Witten solution for N=2 super Yang-Mills theory in four dimensions with gauge group SU(N). We present a simple exact Taylor series expansion for the periods obtained at the origin of moduli space, thereby generalizing earlier results for SU(2) and SU(3). With the help of these analytic results and others, we analyze the global structure of the Kahler potential, presenting evidence for a conjecture that the unique global minimum is the curve at the origin of moduli space. Two applications of these results are considered. Firstly, we analyze candidate walls of marginal stability of BPS states on special slices for which the expansions of the periods simplify. Secondly, we consider soft supersymmetry breaking of the N=2 theory to non-supersymmetric four-dimensional SU(N) gauge theory with two massless adjoint Weyl fermions (""adjoint QCD""). The Seiberg-Witten Kahler potential and strong coupling spectrum play a crucial role in this analysis, which ultimately leads to an exploration of the adjoint QCD phase diagram."

This will be an introductory discussion of our joint work with Roman Bezrukavnikov. Given a symplectic resolution X, one may study its Gromov-Witten theory and the monodromy group of the curve-counting functions in the K\"ahler variables. There is also a large group of derived autoequivalences of X coming from its quantization in large prime characteristic, as studied by Bezrukavnikov and collaborators. Conjecturally, the action of the latter group on K(X) is identified with the former group, and we prove this for many $X$.

In this talk I will review some recent progress in the study of non-invertible symmetries in dimensions d>2. After introducing known constructions and describing how they lead to constraints on RG flows, I will discuss how non-invertible symmetries can also be used to obtain new RG flows. This involves the notion of ``non-invertible twisted compactification,” which can be used to construct e.g. novel 3d N=6 theories from 4d N=4 SYM. Finally, I will describe upcoming work in which we give a partial criterion for determining whether a given non-invertible symmetry is ``intrinsically non-invertible”, or whether it can be recast (in an appropriate sense) as a standard invertible symmetry with an anomaly.

 It is unknown how the Einstein Equivalence Principle (EEP) should be modified to account for quantum features. A possibility introduced in arXiv:2012.13754 is that the EEP holds in a generalized form for particles having an arbitrary quantum state. The core of this proposal is the ability to transform to a Quantum Reference Frame (QRF) associated to an arbitrary quantum state of a physical system, in which the metric is locally inertial. I will show that this extended EEP, initially formulated in terms of the local expression of the metric field in a QRF, can be verified in an interferometric setup via tests on the proper time of entangled clocks (arXiv:2112.03303). Moreover, the same setup can be analyzed with quantum sensing techniques (arXiv:2204.03006): I will talk about how gravitational time dilation may be used as a resource in quantum information theory, showing that it may enhance the precision in estimating the gravitational acceleration for long interferometric times.

 

Three dimensional conformal field theories(CFTs) describe important critical physics in the real world. In the past few years much progress has been made in 3D CFTs using the conformal bootstrap. In particular, using numerical bootstrap, the critical exponents of the 3D Ising, Super-Ising, O(2), O(3) CFTs have been determined precisely with rigorous error bars, while using analytic bootstrap, the information of the leading twist operators at large spins can be computed analytically. The two bootstrap approaches are sensitive to different regions of the spectrum and complement each other. In this talk, I will first give a general review of the numerical bootstrap and analytic bootstrap. Then I will discuss how to combine the numerical bootstrap with the analytic lightcone bootstrap, i.e. a hybrid bootstrap method. As a result, the bootstrap prediction for the actual CFT can be significantly improved.

Zoom Link: https://pitp.zoom.us/j/94186668943?pwd=ejRRb0M4VXNjeVVCWGdnTHQyaWRyQT09

The current theories of quantum physics and general relativity on their own do not allow us to study situations in which spacetime is in a quantum superposition. In this talk, I propose a general strategy to determine the dynamics of objects on an indefinite spacetime metric, using an extended notion of quantum reference frame transformations. First, we study the situation of the gravitational source mass being in a spatial superposition state and, using a generalized principle of covariance, show how to transform to a frame in which the standard theories of GR and QFT allow to determine the dynamics. In the second part, we consider superpositions of conformally equivalent metrics inhabited by a massive quantized Klein-Gordon field. By requiring invariance of the KG equation under quantum conformal transformations, we find that the superposition is transferred to the quantum field in the form of an effective, spacetime dependent mass term. Overall, the proposed strategy allows to construct the respective explicit quantum frame change operators, and to study physical phenomena such as time dilation and cosmological particle production in different quantum frames.

Zoom Link: https://pitp.zoom.us/j/96903859307?pwd=aEtLUy9tME5GL25nTjBVNXVmb2N3Zz09

There are two different standard ways of endowing a physical theory with a symplectic structure: the canonical and the covariant. The former is derived from the well-known symplectic structure of a certain cotangent bundle. The latter is based on the variational calculus. Including a boundary in the canonical formalism poses no problem, however, in the covariant formalism things break apart. In this talk, I will briefly introduce both formalisms without boundary and explain in detail a new framework that allows us to include boundaries in a straightforward way. To show it in action, time permitting, I will apply it to several theories of gravity. Finally, I will briefly show a new result where we proved that, actually, the canonical and covariant formalisms are equivalent in full generality.

Zoom Link: https://pitp.zoom.us/j/97641588140?pwd=dFl0SFdHOG5BYko2djNVWk11UkhSUT09