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The Fukaya category of a symplectic manifold is an excellent toy model for exploring the general structure of boundary conditions in two-dimensional topological field theories. In this talk I will explain an analogue for three dimensional theories. The natural playground for boundary conditions in d=3 is the 3d A-model into a hyperKahler target space. Here the fundamental BPS equation is the Fueter equation. I will explain how studying certain boundary value problems for the Fueter equation, one is lead to something resembling a higher categorical structure. I will then argue how a similar structure also seems to appear after performing a massive deformation by a hyperKahler moment map. 

Zoom link:  https://pitp.zoom.us/j/96574302292?pwd=dkpIVXN0UmFiRkdkenFzc2o2Nko0dz09

One central property of the S-matrix is its invariance under field redefinitions. I will discuss how the geometry of field space makes this invariance manifest. This geometric formulation also has practical consequences. Scattering amplitudes and the renormalization group equations for a theory of scalars and gauge bosons only depend on geometric quantities. Also, the scattering amplitudes satisfy a geometric soft theorem.

Zoom link:  https://pitp.zoom.us/j/98973018515?pwd=MFJFSGM4RS9KRHFOREFBc1gvWXYwQT09

I will speak about my recent work with Vladimir Kazakov where we study the SU(Nc) lattice Yang-Mills theory in the planar limit, at dimensions D=2,3,4, via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with the cut-off L on the maximal length of loops, and the positivity conditions on certain correlation matrices. Our algorithm is inspired by the pioneering paper of P. Anderson and M. Kruczenski but it is significantly more efficient, as it takes into account the symmetries of the lattice theory and uses the relaxation procedure in the line with our previous work on matrix bootstrap. We thus obtain the rigorous upper and lower bounds on the plaquette average at various couplings and dimensions. The results are quickly improving with the increase of cutoff L. For D=4 and L=16, the lower bound data appear to be close to the Monte Carlo data in the strong coupling phase and the upper bound data in the weak coupling phase reproduce well the 3-loop perturbation theory. We attempt to extract the information about the gluon condensate from this data. Our results suggest that this bootstrap approach can provide a tangible alternative to, so far uncontested, the Monte Carlo approach.

Zoom link:  https://pitp.zoom.us/j/96101268796?pwd=QkdJbm9GUzQ2YnIrM1NlcUt2Z3Nvdz09

It has long been known that the quantum ground state of a metal is characterized by an abstract manifold in the momentum space called the Fermi sea. Fermi sea can be distinguished topologically in much the same way that a ball can be distinguished from a donut by counting the number of holes. The associated topological invariant, i.e. the Euler characteristic (χ_F), serves to classify metals. Here I will survey two recent proposals relating χ_F  to experimental observables, namely: (i) equal-time density/number correlations, and (ii) Andreev state transport along a planar Josephson junction. Moreover, from the perspective of quantum information, I will explain how multipartite entanglement in real space probes the Fermi sea topology in momentum space. Our works not only suggest a new connection between topology and entanglement in gapless quantum matters, but also suggest accessible experimental platforms to extract the topology in metals. 

Zoom link:  https://pitp.zoom.us/j/98944473905?pwd=ak5nVmd4N0pSdXpjOFM0YnFJdnJ4dz09

A natural way to extend Einstein's General Relativity to the high-energy regime is to introduce quadratic curvature operators, which give rise to a renormalizable gravitational Lagrangian in four dimensions. However, this theory turns out to be pathological due to an additional massive spin-2 ghost that causes classical instabilities and breaks perturbative unitarity at the quantum level. In this talk, we investigate which principles of QFT are usually affected when higher-order derivative operators are present in a Lagrangian, and show that one possibility to avoid ghosts is giving up locality. In fact, the emergence of non-local physics at short distances and high energies is a common prediction for various quantum gravity approaches. We propose a model-independent approach to constrain the non-local Lagrangian in quantum gravity, thus providing a novel scenario in which different quantum gravity programs can be fruitfully contrasted in terms of foundational concepts and computational methods.

Zoom link:  https://pitp.zoom.us/j/96167652193?pwd=OWFDV1JXVGxLdE1qMHo4N3ZKcDByQT09

Charge (electric, magnetic, or any U(1) charge) is a parameter often neglected in simulations of black holes. As a result, little is known about the dynamics of charged binaries. In this talk, I will highlight the importance of understanding the non-linear interaction of charged black holes for astrophysics and fundamental physics. I will show results from fully self-consistent general-relativistic simulations of merging black holes, touching upon the challenges faced in performing such calculations and the improvements that enabled successful long-term evolution. I will discuss general features of quasi-circular inspirals, and present constraints on the charge of astrophysical black holes and deviation from general relativity obtained from the gravitational-wave event GW150914. Finally, I will highlight the relevance of this line of research in the context of the upcoming gravitational-wave detectors.

Zoom link:  https://pitp.zoom.us/j/93809443805?pwd=bmcvd3NZWjUraERBcGdtL2Y3WTl6QT09

In the new wave of quantum foundations activity with its indirect approach to problems of fundamental ontology, individual explicit positions of informational immaterialism are replaced by a shared "soft informatic realism" that governs research practice, encouraging conflation of theories of information processes and theories of physical processes, and disregard for the microphysical dynamics effecting a given information process.  This kind of abstraction, indispensable in the formulation of enlightening no-go theorems, can become problematic when imported to certain other projects, including recently popular investigations of quantum causal structure.  I shall provide examples, describe ramifications for the efficiency of knowledge production in quantum foundations, and consider when features of quantum information processing can legitimately be called informatic features of quantum physics.

Zoom link:  https://pitp.zoom.us/j/93415836509?pwd=MXJLZVVzMnZjcWFQSWM0dmg5czE3dz09

Symmetry-protected topological (SPT) phases are short-range entanglement (SRE) quantum states which cannot be adiabatically connected to trivial product states in the presence of symmetries. Recently, it is shown that symmetry-protected short-range entanglement can still prevail even if part of the protecting symmetry is broken by quenched disorder locally but restored upon disorder averaging, dubbed as the average symmetry-protected topological (ASPT) phases. In this talk, I will systematically construct the ASPT phases as a mixed ensemble or density matrix, which may not be realized in a clean system without any disorder. I will also design the strange correlator of the ASPT phases via a strange density matrix to detect the nontrivial ASPT state. Moreover, it is amazing that the strange correlator of ASPT can be precisely mapped to the loop correlation functions of some proper statistical loop models, with power-law behaviors.

Zoom link:  https://pitp.zoom.us/j/91672345456?pwd=N0dNQXNmVVoybnNxYXJuWnVRME8rUT09

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

In this talk, I will show that the action of soft graviton operators generates a w(1+infinity) symmetry in gravitational theories minimally coupled to massless and massive scalar matter in 4D asymptotically flat spacetimes.  I will discuss how the symmetry action follows from an infinite tower of soft graviton theorems in momentum space.  By generalizing the previous analyses of w(1+infinity) symmetry in massless amplitudes, these results clarify that the symmetry emerges in 4D asymptotically flat gravitational theories without any additional technical ingredients.  This talk is based on a forthcoming paper with Monica Pate. 

Zoom link:  https://pitp.zoom.us/j/91448920819?pwd=cFY0L1JPVFF2bDUwc3JiVlRlbE5ldz09