北京雁栖湖应用数学研究院

We prove that the supersymmetric deformed $\mathbb{CP}^1$ sigma model admits an equivalent description as a generalized Gross-Neveu model. Remarkably we find new Nahm-type conditions, which guarantee renormalizability and supersymmetric invariance. Moreover it provides formalism, which is useful for the study of renormalization properties and particularly for calculation of such observables as $\beta$ and correlation functions. We study the RG flow of the new class and find special UV conformal points from both sides of the new Chiral/Sigma model correspondence. We further explore novel relations of our construction through mirror symmetry and dimensional reductions. We demonstrate its emergence from the four-dimensional TQFT with defects, investigate surface observables and provide the associated spin chain system.

A central challenge in holography is understanding how spacetime emerges from the boundary conformal field theory (CFT). Entanglement provides a geometric perspective through kinematic space—the space of CFT point pairs or bulk minimal cuts—where spacetime geometry is encoded in an integral formula with quantum information meaning: the Crofton formula, a cornerstone of integral geometry. In this talk, I will present recent advances revealing a novel two-sided Crofton formula, which reconstructs wormhole geometries by resolving quantum puzzles. This reveals a deeper organizational principle, leading to the discovery of new topological kinematic spaces with rich topological structure that underlies spacetime emergence.

In this talk, we show that the length of a shortest closed geodesic on Riemannian manifolds of dimension 4 with diameter D, volume v, and $|Ric|<3$ can be bounded by a function of v and D. In particular, this function can be explicitly computed if the manifold is Einstein. The proof of this result depends on a structural theorem proven by J. Cheeger and A. Naber. This is joint work with N. Wu.

We bootstrap the first-order correction in the curvature expansion of the Virasoro-Shapiro amplitude in AdS spacetime, for arbitrary Kaluza-Klein charges of external operators. By constructing a universal ansatz based on single-valued multiple polylogarithms as well as an AdSxS formalism, and matching it with the low-lying result, we derive a unified formula in terms of world-sheet integrals. Our result predicts an infinite number of Wilson coefficients that were not available in previous literature. I will also report some ongoing progress on the second-order correction.

In this talk I will describe a surprising interplay between representation theory and gravitational consistency, introducing a first-principles framework for deriving sharp and universal constraints on UV completions of gravity. Using the S-matrix bootstrap—where Lorentz invariance, analyticity, unitarity, and causality restrict interactions, I will show that the graviton pole, once seen as an obstruction, becomes a powerful tool. Gravitational consistency enforces the presence of specific irreps of the symmetry group, ruling out spectra that appear viable without gravity. This mechanism provides direct support for the Completeness Hypothesis of the Swampland Program, marking a concrete step toward a rigorous proof of a Swampland conjecture.

Recent studies have shown that the concept of entanglement can be extended to causally connected subregions. Starting from correlation functions, one can naturally define a “density matrix” for such regions, which we call the spacetime density matrix. In this talk, I will briefly introduce how to construct the spacetime density matrix and represent it using the Schwinger–Keldysh path integral. We find that by introducing a super-operator, the spacetime density matrix can be expressed more systematically, and on this basis we also derive the corresponding Liouville–von Neumann equation. The super-operator further allows us to introduce two natural generalizations. Finally, I will give examples illustrating entropy-related quantities defined from the spacetime density matrix and its generalizations, as well as their computations in quantum mechanics and quantum field theory.

The Newman-Janis transformation allows for the simple mapping of the Schwarzschild solution to the Kerr solution. Such procedures can be applied to analyze the interaction of spinning objects. First, I present a simplified model that considers the electromagnetic (Maxwell) interaction of two Kerr-Newman solutions (zero gravity limit). The interaction potential can be computed in specific configurations to all orders in spin. Then I adress a similar issue involving two interacting Kerr solutions in a weak (linearized) field approximation.

Higher-spin gravity in 4D is a set of theories that contain infinitely many interacting higher-spin gauge fields. When we try to construct solutions to such theories, activating the fields of one particular spin very often leads to the activation of (infinitely) many other spins. However, there do exist special solutions that activate only a small number of spins. In my talk I will present two examples of such solutions with only spin-0 and spin-1 activated. I will briefly introduce higher-spin gravity theories before presenting the solutions.

We propose the gravity dual of conformal field theory defined in networks (AdS/NCFT), which is the multi-branch generalization of AdS/BCFT and a natural realization of parallel universes. We prove that the multi-junction condition on the Net-brane results in the conservation of energy flux at the network node. We find that the spectrum of gravitational Kaluza-Klein modes on the Net-brane is a mixture of that of AdS/BCFT with Neumann boundary condition and Dirichlet boundary condition, corresponding to the isolated and transparent modes, respectively. We propose that the Ryu-Takayanagi surfaces intersect at the same point on the Net-brane for connected subsystems within the network and verify this with the monotonicity of entanglement entropy. We establish that the network entropy, defined as the difference in entanglement between NCFT and BCFT, is always non-negative and effectively illustrates the network's complexity.

In this work, we investigate possible supersymmetric extensions of the Carrollian algebra and the Carrollian conformal algebra in both $d=4$ and $d=3$. For the super-Carrollian algebra in $d=4$, we identify multiple admissible structures, depending on the representations of the supercharges with respect to the Carrollian rotation. Some of these structures can be derived by taking the speed of light $c\to 0$ limit from super-Poincar\'e algebra, but others are completely novel. In the conformal case, we derive nontrivial Carrollian superconformal algebras in dimensions $d=4$ and $d=3$. Among these, the superconformal algebra in $d=4$ and one of the algebras in $d=3$ exhibit isomorphisms to the super-Poincar\'e algebras in $d=5$ and $d=4$, respectively. Additionally, we identify a novel, nontrivial superconformal algebra in $d=3$ that is not isomorphic to any super-Poincar\'e algebra. Remarkably, neither of these constructions requires R-symmetry to ensure the algebraic closure. Given that BMS$_4$ algebra constitutes the infinite-dimensional extension of the $d=3$ Carrollian conformal algebra, their supersymmetric extension gives rise to nontrivial superconformal Carrollian algebras. Specifically, we demonstrate the existence of a singlet super-BMS$_4$ algebra emerging from the extension of the $d=3$ Carrollian superconformal algebra, as well as a multiplet super-BMS$_4$ algebra that does not admit this methodology, as its finite-dimensional subalgebra incorporates supercharges with conformal dimension $\Delta=\pm\frac{3}{2}$.

In this work, we quantize the Proca field in the global AdS3 spacetime with the covariant phase space formalism. Holding the quantization, we compute the correlation function and the thermal partition function, which are the same as the ones from other methods.

Weyl spin 1/2 fermions, when minimally coupled to Einstein's gravity, cannot be produced purely gravitationally in an expanding universe at tree level. However, this picture changes at the gravitational 1-loop level in the presence of cosmic perturbations, leading to a new and unavoidable mechanism for gravitational particle production. In this talk, I will explore the theory and phenomenological implications of this new effect.

We investigate asymptotically locally anti-de Sitter spacetimes exhibiting radiative behavior, using null gauges that admit well-defined flat limits. The radiative content in the bulk is captured by the super-Poynting vector, which we reinterpret holographically in terms of fluid variables in the dual boundary theory. For algebraically special solutions, we uncover a close connection between bulk radiation and dissipative corrections in the boundary stress tensor, demonstrating a direct link between radiation and entropy production in the boundary fluid. This reveals a rich interplay between radiative dynamics in the bulk and out-of-equilibrium conformal physics at the boundary. We then investigate the flat limit of this correspondence in the context of flat-space holography. In this setting, we obtain the Carrollian analogue of the super-Poynting vector and introduce Celestial observables, such as energy detectors, which emerge naturally from the bulk's radiative structure. Our analysis shows that bulk radiation sources the Carrollian viscous stress tensor and heat current, which encodes the Bondi news in this framework. We illustrate our results with explicit examples, including Robinson-Trautman spacetimes and accelerating black holes.

Investigations of non-hermitian quantum systems recently has drawn much interest in the field of holography and the AdS/CFT correspondence. In this talk, I will focus on non-hermiticity of the PT symmetric type and, after a short introduction into the subject, present several results for PT symmetric systems of interest in holography: In the first part of the talk, I will discuss our recent [1] investigation of the phase structure and the interaction induced quantum critical conductivity in a PT symmetric non-hermitian holographic metal. In particular the conductivity shows interesting new features in the different phases, which are qualitatively reproduced in a PT symmetrically deformed version of Landau-Ginzburg theory. In the second part of the talk, I will present analytic and numerical work [2] on the operator size growth in Lindbladian SYK models. I will in particular present a new timescale, the plateau time, after which the operator size growth reaches a plateau. Finally, I will present recent work [3] on the entanglement structure in these Lindbladian SYK models, and a new entanglement measure with better properties for non-hermitian systems. [1] Z.Y. Xian, D. Rodriguez-Fernandez, Z.H. Chen, Y. Liu, R. Meyer, SciPost Physics 16 (2024) [2] J.S. Liu, R. Meyer, Z.Y. Xian, JHEP 08 (2024) [3] Z.H. Chen, R. Meyer, Z.Y. Xian, arXiv:2508.09261