Scientific Series

We study D dimensional pure Einstein gravity theory in a region of spacetime bounded by a generic null boundary. We show besides the graviton modes propagating in the bulk, the system is described by boundary degrees of freedom labeled by D surface charges associated with nontrivial diffeomorphisms at the boundary. We establish that the system admits a natural thermodynamical description. Using standard surface charge analysis and covariant phase space method, we formulate  laws of null surface thermodynamics which are local equations over an arbitrary null surface. This thermodynamical system is generally an open system and can be closed only when there is no flux of gravitons through the null surface. Our analysis  extends the usual black hole thermodynamics to a universal feature of any area element on a generic null surface in a generic diffeomorphism invariant theory of gravity. 

Zoom Link: https://pitp.zoom.us/j/91590041045?pwd=UXpWY3JEd0QwK2hXanBzSkdPRC94UT09

I will discuss the detailed process by which slow contraction smooths and flattens the universe using an improved numerical relativity code that accepts initial conditions with non-perturbative deviations from homogeneity and isotropy along two independent spatial directions. Contrary to common descriptions of the early universe, I will show that the geometry first rapidly converges to an inhomogeneous, spatially-curved, and anisotropic ultralocal state in which all spatial gradient contributions to the equations of motion decrease as an exponential in time to negligible values. This is followed by a second stage in which the geometry converges to a homogeneous, spatially flat, and isotropic spacetime. In particular, the decay appears to follow the same history whether the entire spacetime or only parts of it are smoothed by the end of slow contraction.

Zoom Link: https://pitp.zoom.us/j/95441238892?pwd=TUh4Mjh1MHJ6TDNCL0V1NUk5WWFZQT09

Euclidean wormholes are exotic types of gravitational solutions that we still don't understand completely. In the first part of the talk, I will analyze asymptotically AdS wormhole solutions from a gravitational point of view. By studying correlation functions of local and non-local operators, the universal properties that any putative holographic dual should exhibit, become manifest. In the second part, I will describe some concrete field theoretic models (both effective and microscopic) that share these properties.

Superradiant instabilities may create clouds of ultralight bosons around black holes, forming so-called “gravitational atoms.” It was recently shown that the presence of a binary companion can induce resonant transitions between a cloud's bound states. When these transitions backreact on the binary's orbit, they lead to qualitatively distinct signatures in the gravitational waveform that can dominate the overall behavior of the inspiral. In this talk, I will show that the interaction with the companion can also trigger transitions from bound to unbound states of the cloud---a process which I will refer to as ``ionization,'' in analogy with the photoelectric effect in atomic physics. Here, too, there is a type of resonance with a similarly distinct signature, which may ultimately be used to detect any dark ultralight bosons that exist in our universe.

Zoom Link: https://pitp.zoom.us/j/97300299361?pwd=azhmVTR5VmpPQ1hwbkVHTUsrOGlJZz09

The field of quantum information provides fundamental insight into central open questions in quantum thermodynamics and quantum many-body physics, such as the characterization of the influence of quantum effects on the flow of energy and information. These insights have inspired new methods for cooling physical systems at the quantum scale using tools from quantum information processing. These protocols not only provide an essentially different way to cool, but also go beyond conventional cooling techniques, bringing important applications for quantum technologies. In this talk, I will first review the basic ideas of algorithmic cooling and give analytical results for the achievable cooling limits for the conventional heat-bath version. Then, I will show how the limits can be circumvented by using quantum correlations. In one algorithm I take advantage of correlations that can be created during the rethermalization step with the heat-bath and in another I use correlations present in the initial state induced by the internal interactions of the system. Finally, I will present a recently fully characterized quantum property of quantum many-body systems, in which entanglement in low-energy eigenstates can obstruct local outgoing energy flows.

Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. In this talk, I will argue that MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. I will present some statistical mechanics and effective field theory approaches to such charge-sharpening transitions.

Zoom Link: https://pitp.zoom.us/meeting/register/tJcqc-ihqzMvHdW-YBm7mYd_XP9Amhypv5vO

Causality is fundamental to science, but it appears in several different forms. One is relativistic causality, which is tied to a space-time structure and forbids signalling outside the future. On the other hand, causality can be defined operationally using causal models by considering the flow of information within a network of physical systems and interventions on them. From both a foundational and practical viewpoint, it is useful to establish the class of causal models that can coexist with relativistic principles such as no superluminal signalling, noting that causation and signalling are not equivalent. We develop such a general framework that allows these different notions of causality to be independently defined and for connections between them to be established. The framework first provides an operational way to model causation in the presence of cyclic, fine-tuned and non-classical causal influences. We then consider how a causal model can be embedded in a space-time structure and propose a mathematical condition (compatibility) for ensuring that the embedded causal model does not allow signalling outside the space-time future. We identify several distinct classes of causal loops that can arise in our framework, showing that compatibility with a space-time can rule out only some of them. We then demonstrate the mathematical possibility of causal loops embedded in Minkowski space-time that can be operationally detected through interventions, without leading to superluminal signalling. Our framework provides conditions for preventing superluminal signalling within arbitrary (possibly cyclic) causal models and also allows us to model causation in post-quantum theories admitting jamming correlations. Applying our framework to such scenarios, we show that post-quantumjamming can indeed lead to superluminal  signalling contrary to previous claims. Finally, this work introduces a new causal modelling concept of ``higher-order affects relations'' and several related technical results, which have applications for causal discovery in fined-tuned causal models.

Deligne tensor categories are defined as an interpolation of the categories of representations of groups GL_n, O_n, Sp_{2n} or S_n to the complex values of the parameter n. One can extend many classical representation-theoretic notions and constructions to this context. These complex rank analogs of classical objects provide insights into their stable behavior patterns as n goes to infinity.
I will talk about some of my results on Harish-Chandra bimodules in Deligne categories. It is known that in the classical case simple Harish-Chandra bimodules admit a classification in terms of W-orbits of certain pairs of weights. However, the notion of weight is not well-defined in the setting of Deligne categories. I will explain how in complex rank the above-mentioned classification translates to a condition on the corresponding (left and right) central characters.
Another interesting phenomenon arising in complex rank is that there are two ways to define Harish-Chandra bimodules. That is, one can either require that the center acts locally finitely on a bimodule M or that M has a finite K-type. The two conditions are known to be equivalent for a semi-simple Lie algebra in the classical setting, however, in Deligne categories that is no longer the case. I will talk about a way to construct examples of Harish-Chandra bimodules of finite K-type using the ultraproduct realization of Deligne categories.

Zoom Link: https://pitp.zoom.us/j/93951304913?pwd=WVk1Uk54ODkyT3ZIT2ljdkwxc202Zz09

In this talk, I will consider quantum effects on some specific black hole solutions and take into account their gravitational backreaction. In particular, I will describe the holographic construction of the quantum BTZ black hole (quBTZ) from an exact four-dimensional bulk solution.  I will present some of the thermodynamic properties of these black holes, focus on the generalized first law and analyze the different complexity proposals for the quBTZ. Our results indicate that Action Complexity fails to account for the additional quantum contributions and does not lead to the correct classical limit. On the other hand, the Volume Complexity admits a consistent quantum expansion and agrees with known limits.

We develop a general approach to "interpret" what a network has learned by introducing strong inductive biases. In particular, we focus on Graph Neural Networks. 

The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical relations. The symbolic expressions extracted from the GNN using our technique also generalized to out-of-distribution data better than the GNN itself. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.

In particular, we will show examples of recovery of newton's law and masses of solar system bodies with real ephemeris data and recovery of navier-stokes equations with turbulence dataset.  We will speculate what one can do with this new tool.
 

We introduce a viewpoint that the Standard Model (SM) is a low-energy quantum vacuum arising from various neighbor Grand Unification (GUT) like vacua competition in an immense quantum phase diagram. In general, we find the SM arises near the gapless quantum critical regions between the competing neighbor vacua. Alternatively, we can also phrase this viewpoint in terms of the deformation class of quantum field theory (QFT), specified by its symmetry G and its anomaly (i.e., cobordism invariant). Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We show that GUT such as Georgi-Glashow su(5), Pati-Salam su(4)×su(2)×su(2), Barr’s flipped u(5), and familiar or modified so(n) models of Spin(n) gauge group, e.g., with n = 10, 18 can all reside in an appropriate SM deformation class, labeled by Z_{16} and Z_2 nonperturbative global anomaly index. We show that Ultra Unification, which replaces some of sterile neutrinos with new exotic gapped/gapless sectors (e.g., topological or conformal field theory) or gravitational sectors with topological origins via cobordism constraints, also resides in an SM deformation class. Neighbor quantum phases near SM or their phase transitions, and neighbor gauge enhanced gapless quantum criticality naturally exhibit beyond SM phenomena. We give a new proposal on the neutrino mass origin. The talk is mainly based on: arxiv 1910.14668, 2006.16996, 2008.06499, 2012.15860, 2106.16248, 2111.10369, 2112.14765. Some of these works are in collaboration with Zheyan Wan and Yi-Zhuang You. 

Zoom Link: https://pitp.zoom.us/j/94634619703?pwd=VWlWZHNIMm1sS2owWnlhSmhZTTNvUT09

There is an extremely rich history of interaction between physics and moduli spaces, for instance cohomological Hall algebras/algebras of BPS states, or vertex/chiral algebras. In this talk, I will explain a link between Joyce vertex algebras and one dimensional CoHAs, based on my paper 2110.14356, where quantum vertex algebras play a central role. The main technical tool is a ``bivariant" Euler class which makes torus localisation work in this context. I will also talk about ongoing work, in this area as well as in closely related projects.

Zoom Link: https://pitp.zoom.us/j/93045858347?pwd=N25FNVVjNEFFN09sdmFUV2M2YlZ5QT09