Scientific Series

In quantum field theory (QFT) the spin-statistics theorem says that in a unitary QFT, a particle has half-integer spin if and only if it is a fermion. I show how to phrase this statement in the language of functorial field theories. More precisely, I explain when a functorial field theory "has fermions" and "has spinors" and when they are "related". I will then restrict to topological field theories (TFTs) and define unitary TFTs. There are counterexamples of the spin-statistics theorem for non-unitary TFTs. I will prove that every unitary TFT satisfies the spin-statistics theorem.

I will discuss recent progress on the initial conditions for inflation and how this can potentially enhance gravitational wave non-Gaussianity (NG). In particular, there is a significant additional NG contribution in the flattened configuration, offering a straightforward way to boost parity-violating NG from Chern-Simons gravity, which typically suffers from graviton ghost-production. Furthermore, I will explore how this shape – at the level of the trispectrum – can enable direct measurement of NG in the stochastic gravitational wave background (SGWB) using pulsar timing arrays (PTA). This is particularly intriguing as it allows us to investigate NG at scales complementary to those observed in the CMB, which could help us distinguish between various early universe models and physical mechanisms.

We will explore the connection between Celestial and Euclidean Anti-de Sitter (EAdS) holography in the massive scalar case. Specifically, exploiting the so-called hyperbolic foliation of Minkowski space-time, we will show that each contribution to massive Celestial correlators can be reformulated as a linear combination of contributions to corresponding massive Witten correlators in EAdS. This result will be demonstrated explicitly both for contact diagrams and for the four-point particle exchange diagram, and it extends to all orders in perturbation theory by leveraging the bootstrapping properties of the Celestial CFT (CCFT).  Within this framework, the Kantorovic-Lebedev transform plays a central role, which will be introduced at the end of the talk. This transform will allow us to make broader considerations regarding non-perturbative properties of a CCFT. 

BPS line defects in 4d N=2 supersymmetric QFT are described by a monoidal category with a list of desired properties. For example, the Grothendieck group of this category is supposed to coincide with quantization of functions on Coulomb branch of the theory compactified on a circle. Based on an observation, that at a given vacuum the spectrum of PBS particles can be quipped with an algebra structure – cohomological Hall algebra of the corresponding BPS quiver – we propose a category generated by certain bimodules over this algebra that possesses expected properties of the category of lines. Based on a joint work with Davide Gaiotto and Wei Li. 

In this talk, I will present a published and an ongoing work in the direction of emergent gravity. The first is what I dubbed as the generalized Unruh effect, a mapping from arbitrary states in the Fock space of positive Minkowski (Kruskal) modes to Rindler (Schwarzschild) modes obtained by Bogoliubov transformation. The special case of vacuum state -- thermal bath mapping has been well known in the textbooks, the original Unruh effect. I will discuss the interesting physical implications of the generalized Unruh effect on the black hole information paradox. In the second part, I will give a novel conjecture of the dark energy when considering the spacetime as a 4d volume-conserved fluid. Einstein's equation with an always-positive metric term (Lambda, but not necessarily constant) can be interpreted as the differential version of this assumed conservation of 4d volume at linear order. The rich phenomenology of this theory will be discussed, including its solution to the anthropic problem of our currently dark-energy-dominated universe, and high-redshift over-evolved astrophysical objects that have been recently popping up in the JWST survey.

In this talk, I will provide an overview of neutron star (NS) mergers, highlighting the insights gained through numerical relativity simulations. I will mainly focus on the role of the cocoon shock breakout emission as a key early electromagnetic counterpart of NS mergers, with special relevance to events like GW170817. I will explore how the properties of the merger ejecta and the nature of the central engine influence the resulting emission. Additionally, I will present recent advancements in the development of our new general relativistic magnetohydrodynamics (GR-MHD) code GR-Athena++, and share ongoing research efforts on the evolution of magnetic fields in the post-merger remnant.

The Green-Schwarz anomaly cancellation condition says that the target space of heterotic string theory must come with a string structure for the theory to be consistent. In this talk we discuss a new tangential structure called string^h, first introduced by Devalapurkar, as a spin^c analogue of string. We will show that the spectrum of string^h has the notable property that it orients tmf_1(n), just like how the spectrum of string orients tmf, by the work of Ando-Hopkins-Rezk. Finally we will show that the anomaly of the partition function of type IIA, studied by Diaconescu-Moore-Witten induces a string^h structure on the target space of type IIA, in parallel to the Green-Schwarz anomaly for heterotic string theory, and discuss applications for anomaly cancellation. This is joint work in progress with Arun Debray.

In this talk, I shall recall the nonlocality transitivity problem, which concerns the possibility of inferring the Bell-nonlocality of certain marginals in a multipartite scenario based on other given marginals. Then, I explain how considering this problem has led to a more general class of problems known as resource marginal problems (RMPs). More precisely, RMPs concern the possibility of having a resource-free target subsystem compatible with a given collection of marginal density matrices. We briefly discuss how a resource theory for a collection of marginal density matrices naturally arises from any given RMP and present some general features of such a theory. After that, we focus on a special case of RMPs known as the entanglement transitivity problems and explain how our progress on this problem has led to progress in the original nonlocality transitivity problem.

Abstract:  In relativity, the geometry of the light cones determines the causal structure of spacetime. Under the influence of gravity, the light cones bend and curve. A previously expanding light cone can fall back into itself. In this way, the causal structure becomes a dynamical aspect of spacetime. How do we understand this link between gravity, geometry and causality at the quantum level? Is there a quantum light cone geometry? In my talk, I will argue that the answer to this problem is crucial for making progress in quantum gravity. It is, in fact, a problem that is shared among different approaches, from holography, to celestial amplitudes and loop quantum gravity. In my presentation, I report on three new results on this frontier. First, I provide a non-perturbative characterization of impulsive gravitational null initial data for tetradic gravity on a light cone. Second, the description is taken to the quantum level. Third, an immediate physical implication is found: in the model, the Planck luminosity separates the eigenvalues of the radiated power. Below the Planck power, the spectrum of the radiated power is discrete. Above the Planck power, the spectrum is continuous and the resulting physical states contain caustics that can spoil the semi-classical limit.  The talk is based on arXiv:2402.12578, arXiv:2401.17491, arXiv:2104.05803.

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Generic unital quantum channels, for example, have the maximally mixed state with no entanglement as their unique steady state. However, we find that for a unital quantum channel that is `strongly symmetric', i.e. it preserves a global on-site symmetry, the maximally mixed steady state in certain symmetry sectors can be highly entangled. For a given symmetry, we analyze the entanglement and correlations of the maximally mixed state in the invariant sector (MMIS), and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For all Abelian symmetries, the MMIS is separable, and for all non-Abelian symmetries, the MMIS is entangled. Remarkably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g. SU(2)), the bipartite entanglement of formation for the MMIS scales logarithmically ∼logN with the number of qudits N.

I discuss how quantum mechanical effects prevent violations of causality in low energy processes, even when faster-than-light propagation is possible. At the classical level, faster-than-light propagation can be used to build "time-machine" configurations that violate causality. However, low-energy quantum excitations propagating on these backgrounds lead to divergent backreaction through loop effects. These divergences fully probe the UV dynamics of the system, making it impossible to prepare and describe causality violating configurations in the regime of validity of effective field theory. In light of these results, I conclude that effective field theories with negative Wilson coefficients or Galileon-symmetric interactions are not in tension with causality, despite leading to faster-than-light propagation.