Scientific Series

Fermi liquids are gapless quantum many-body states of fermions, which describes electrons in the normal state of most metals at low temperature. Despite its long history of study, there has been renewed interest in understanding the stability of Fermi liquid from the perspectives of emergent symmetry and quantum anomaly. In this talk, I will introduce the concept of Fermi surface anomaly and propose a possible scheme to classify it. The classification scheme is based on viewing the Fermi surface as the boundary of a Chern insulator in the phase space, with an unusual dimension counting arising from the non-commutative phase space geometry. This enables us to extend the notion of Fermi surface anomaly to the non-perturbative cases and discuss symmetric mass generation on the Fermi surface when the anomaly is canceled. I will provide examples of lattice models that demonstrate Fermi surface symmetric mass generation and make connections to the recent progress in understanding the pseudo-gap transition in cuprate materials.

Zoom link: https://pitp.zoom.us/j/97223165997?pwd=SkhJZEt1ejhQRm0yK2tKS3NhM2o2Zz09

We construct two-dimensional quantum states associated to four-dimensional linearized rotating self-dual black holes in (2,2) signature Klein space. The states are comprised of global conformal primaries circulating on the celestial torus, the Kleinian analog of the celestial sphere. By introducing a generalized tower of Goldstone operators we identify the states as coherent exponentiations carrying an infinite tower of w1+inf charges or soft hair. We relate our results to recent approaches to black hole scattering, including a connection to Wilson lines, S-matrix results, and celestial holography in curved backgrounds.

Zoom link:  https://pitp.zoom.us/j/94163164577?pwd=RHFVZU5XUEN0T3c3Zm1VR3VhZnNsZz09

Fast Radio Bursts (FRBs) are extremely energetic, millisecond-duration radio bursts coming outside our galaxy. The burst arrival time at different frequencies implies the number of electrons it has encountered in the foreground. Therefore, FRB is considered a promising new cosmology probe. The uncertainty of the circum-burst environment is one of the biggest concerns regarding its potential as a probe. In this talk, I will review the current understanding of the FRB progenitor and the recent study of the circum-burst environment. I will also discuss the many remaining mysteries, including the seemingly diverse nature of the sources, the magneto-environment, and the 16-day periodicity I found with one source. With the current and upcoming instruments, there will be more FRBs with orders of magnitude better spatial resolution detected in the next few years. The result will be an explosion of opportunity for understanding the burst origin and probing cosmic matter distribution at various spatial scales.

Zoom link: https://pitp.zoom.us/j/92030175800?pwd=dWlGVjV0Qnh5bGhLMk1pd01yRmNKQT09

Generative modeling via diffusion processes is already a vast field of literature. In this introduction, I will give an entry point to this field by going over the main concepts and deriving the essential results of the area. Thus, by the end of the talk, we would have a minimal pipeline for implementing the generative model. Furthermore, I will outline several alternative ways for learning such models that the community has developed in recent years. These directions bring novel perspectives and new capabilities of generative modeling.

Zoom link:  https://pitp.zoom.us/j/98786491081?pwd=U1cvZzBQT2VUZDl5Ykd0c1lqY29aZz09

For n≥3, we demonstrate the existence of quantum codes which are local in dimension n with V qubits, distance V^{(n−1)/n}, and dimension V^{(n−2)/n}, up to a polylog(V) factor. The distance is optimal up to the polylog factor. The dimension is also optimal for this distance up to the polylog factor. The proof combines the existence of asymptotically good quantum codes, a procedure to build a manifold from a code by Freedman-Hastings, and a quantitative embedding theorem by Gromov-Guth.

Zoom link:  https://pitp.zoom.us/j/96227350980?pwd=TEFtamRmTXg3dnBMNEhKUkpHbmVoZz09

Trace map on deformation quantized algebra leads to the algebraic index theorem. We investigate a two-dimensional chiral analogue of the algebraic index theorem via the theory of chiral algebras developed by Beilinson and Drinfeld. We construct a trace map on the elliptic chiral homology of the free beta gamma-bc system using the BV quantization framework. As an example, we compute the trace evaluated on the unit constant chiral chain and obtain the formal Witten genus in the Lie algebra cohomology. This talk is based on joint work with Si Li.

Zoom link:  https://pitp.zoom.us/j/91920988875?pwd=dUE1WDI5Q21KWTUxTGNsM21nblh5Zz09

Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law, with a constant correction term known as the topological entanglement entropy (TEE). In many models, the TEE takes a universal value that characterizes the underlying topological phase. However, the TEE is not truly universal: it can differ even for two states related by constant-depth circuits, which are necessarily in the same phase. The difference between the TEE and the value predicted by the anyon theory is often called the spurious topological entanglement entropy. We show this spurious contribution is always nonnegative, thus the value predicted by the anyon theory provides a universal lower bound. This observation also leads to a definition of TEE which is invariant under constant-depth quantum circuits.

Based on a joint work with Daniel Ranard (MIT), Michael Levin (U Chicago), Ting-Chun Lin (UCSD), and Bowen Shi (UCSD)

Zoom link:  https://pitp.zoom.us/j/93809342984?pwd=QXJkK0ZYR3QzdjlUUWlkMEFXMWRnQT09

In holography, the quantum extremal surface formula relates the entropy of a boundary state to the sum of two terms: the area term and the entropy of bulk fields inside the entanglement wedge. As the bulk effective field theory suffers from UV divergences, the second term must be regularized. It has been conjectured since the work of Susskind and Uglum that the renormalization of Newton’s constant in the area term exactly cancels the difference between different choices of regularization for bulk entropy. In this talk, I will explain how the recent developments on von Neumann algebras appearing in the large N limit of holography allow to prove this claim within the framework of holographic quantum error correction, and to reinterpret it as an instance of the ER=EPR paradigm. This talk is based on the paper arXiv:2302.01938.

Zoom link:  https://pitp.zoom.us/j/97435154387?pwd=OHYrRW9uSW5VeHRFUld1dmtVbmJiZz09

In any approach to quantum gravity, the quantum representation theory of the "algebra" of Cauchy hypersurface deformations plays a crucial role. Its faithful implementation is a key step towards constructing a valid theory of quantum gravity as it ensures quantum spacetime diffeomorphism covariance. Bergmann and Komar were the first to consider the possibilty of a corresponding quantum "group". Its construction is mathematically challenging in more than 1+1 spacetime dimensions because one leaves the realm of Lie algebras and Lie groups. After an introduction to these concepts, we show that the Bergmann Komar "group" can indeed be faithfully implemented in a weakly self-interacting truncation of 3+1 quantum gravity with two propagating polarisations. We then discuss possible implications for the actual, untruncated theory.

Zoom link:  https://pitp.zoom.us/j/91488383205?pwd=bkxGS0huMGNEYXc3Y2FJSGZHQ0pqQT09

On smooth schemes, every coherent sheaf admits a finite resolution by vector bundles, but on singular schemes, this is no longer true. The Arinkin-Gaitsgory singular support of coherent sheaves is an invariant of coherent sheaves on certain singular spaces that measures how far a particular coherent sheaf is from having such a resolution. In this talk, I will explain how the Arinkin-Gaitsgory theory of singular support decategorifies to a notion of singular support for chains on the associated complex analytic space of our scheme, measuring the difference between cohomology and Borel-Moore homology on singular spaces. In order to do so, we take advantage of the relationship between coherent sheaves and certain categories of matrix factorizations, also know as D-branes in Landau-Ginzburg models.

Zoom link: https://pitp.zoom.us/j/95698955865?pwd=Rm9ld3FUK3hiWGUzenBuZnQyTTRYZz09

I will use the S-matrix Bootstrap to carve out the space of unitary, crossing symmetric, and supersymmetric graviton scattering amplitudes in nine, ten, and eleven dimensions. I will introduce a novel extension of positivity for massless particles beyond the forward limit called “positivity in the sky” that significantly improves the convergence of the bootstrap algorithm.

I will show the bounds on the first leading correction to maximal supergravity, study the physics of the extremal amplitudes and compare them with the available nonperturbative String and M-theory results.

Zoom link:  https://pitp.zoom.us/j/99182927406?pwd=bWxIazFvUzhVQkpBdWluZURIM21wUT09

Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT.  This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity.  Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes.  These edge modes transform under a quantum group, which defines the data associated to an extended topological quantum field theory  Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.  Finally, we give a proposal for obtaining the Ryu Takayanagi formula using the same quantum group edge mode

Zoom link:  https://pitp.zoom.us/j/98275430953?pwd=TzdTUXIvVWU4Ym1jcWRWbkgxZnhMdz09