Research
Holography, Black Holes, and Quantum Gravity
The group studies holography as a way to turn questions about quantum gravity into precise field-theoretic and information-theoretic problems. One strand uses supersymmetric indices, cohomological sectors, and protected operator algebras to probe black-hole microstates, BPS spectra, and the finite-$N$ structure of matrix quantum mechanics and D1-D5 systems; recent BMN work asks which $Q$-cohomology data remain invariant under mass flows and therefore capture robust information about protected sectors. Another strand studies non-Lorentzian and deformed holography, including BMS and Carrollian field theories, flat limits, $T\bar{T}$, $J\bar{T}$, and TsT deformations. These projects are linked by a common question: which reduced or protected sectors of a boundary theory still retain enough information to reconstruct bulk geometry, black-hole states, or gravitational dynamics? Tensor-network, BCFT-ensemble, and SymQRG constructions add a complementary viewpoint in which spacetime emergence is treated as a renormalization problem controlled by symmetry and entanglement.
- Mass-Flow Invariance of $Q$-Cohomology in BMN Matrix Quantum MechanicsChang, Du, Duary, Liu, Tao, 2026
- Holographic covering and the fortuity of black holesChang, Lin, 2024
- It from ETH: Multi-interval Entanglement and Replica Wormholes from Large-$c$ BCFT EnsembleGeng, Hung, Jiang, 2025
- Modular Hamiltonian and entanglement entropy in the BMS free fermion theoryHao, Lai, Song, Xiao, 2025
- A BMS-invariant free scalar modelHao, Song, Xie, Zhong, 2021
- CFT$_D$ from TQFT$_{D+1}$ via Holographic Tensor Network, and Precision Discretisation of CFT$_2$Chen, Ji, Zhang, Shen, Wang, Zeng, Hung, 2022
Supersymmetric Field Theory, Strings, and Geometry
Supersymmetric field theory provides a shared language for the group's work on strings, geometry, integrability, and protected sectors. Recent work uses compactifications of 6d SCFTs, SymTFT, Vafa-Witten theory, class-$\mathcal{S}$ constructions, four-dimensional $\mathcal{N}=2$ SCFTs, mirror symmetry, IIB engineering, boundary brane systems, and M-theoretic lattice models to extract exact algebraic and geometric data from strongly coupled theories. Rather than treating BPS spectra, quantum curves, instantons, chiral algebras, Higgs and Coulomb branch geometry, and defect operators as separate topics, the group studies them as different probes of the same protected structure. This direction connects string theory to representation theory, algebraic geometry, quantum topology, and the exact study of supersymmetric defects.
- Quantum Flat Connections, KZ equations, and IntegrabilityBanerjee, Haghighat, Latifi, 2026
- Higgs Branch and VOA of 4d $\mathcal{N}=2$ SCFTs from IIBWang, Yan, Yang, 2026
- Solving the tetrahedron equation by Teichmüller TQFTShim, Sun, Wang, Yagi, 2026
- A class of half-BPS boundary conditions for $A_{K-1}$ circular quiversBason, Valandro, 2026
- Finite-$N$ BMN index across all vacuum sectorsChang, Duary, Liu, 2026
- Mirror symmetry for 4d $A_1$ class-$\mathcal{S}$ theories: modularity, defects and Coulomb branchPan, Yan, 2024
Conformal Field Theory, Bootstrap, and Deformations
CFT appears here both as a target of nonperturbative bootstrap methods and as an exact language for holography, defects, and deformations. The bootstrap program develops numerical and analytic tools that can isolate strongly coupled fixed points, constrain operator spectra, and map CFT landscapes such as the 3d Ising and super-Ising models, Potts and cubic fixed points, non-Abelian current systems, and deconfined criticality. In parallel, work on Liouville theory, KZ and irregular KZ connections, W-algebras, VOAs, and $T\bar{T}$/$J\bar{T}$-deformed theories studies CFTs with additional algebraic or geometric structure. The common aim is to understand which data of a CFT are rigid enough to survive deformations, boundary conditions, or topological and holographic reorganizations.
- New Developments in the Numerical Conformal BootstrapRychkov, Su, 2023
- Navigator Function for the Conformal BootstrapReehorst, Rychkov, Simmons-Duffin, Sirois, Su, van Rees, 2021
- Precision Bootstrap for the $\mathcal{N}=1$ Super-Ising ModelAtanasov, Hillman, Poland, Rong, Su, 2022
- Liouville CFT, Matrix Models and constrained WZWHaghighat, 2025
- Precision reconstruction of rational CFT from exact fixed point tensor networkCheng, Chen, Gu, Hung, 2023
- Correlation Functions in the TsT/$T{\bar T}$ CorrespondenceCui, Shu, Song, Wang, 2023
Generalized Symmetries, Topological Phases, and Quantum Information
Generalized symmetry is one of the bridges between the group's high-energy, condensed-matter, and mathematical-physics directions. Recent work studies non-invertible defects, half-spacetime gauging, higher and subsystem anomalies, parafermionic defect categories, fermionic systems, SymTFT and SymQRG, anyon condensation, strange correlators, and tensor-network reconstruction as ways to organize phases and interfaces beyond ordinary group symmetry. These projects are not just classifications of defects or phases; they ask how topological data control RG flows, critical lattice models, deconfined quantum criticality, holographic tensor networks, and protected sectors of quantum field theory. This perspective also connects to quantum information through entanglement, reconstruction, and the use of categorical data as a diagnostic of hidden long-range structure.
- $E_\infty^{1,2}$-type Lieb-Schultz-Mattis anomalies, deconfined quantum critical points, and non-invertible symmetry breakingZhang, Lin, Yang, Wang, 2026
- Classification of 2D Fermionic Systems with a $\mathbb Z_2$ Flavor SymmetryChang, Chen, Xu, 2026
- Para-fusion Category and Topological Defect Lines in $\mathbb Z_N$-parafermionic CFTsChen, Haghighat, Wang, 2023
- Half-Spacetime Gauging of 2-Group Symmetry in 3dBason, Cui, Ruggeri, 2026
- A 2D-CFT Factory: Critical Lattice Models from Competing Anyon Condensation Processes in SymTO/SymTFTHung, Ji, Shen, Wan, Zhao, 2025
- Systematic Constructions of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological PhasesLoo, Wang, 2024
Algebraic and Geometric Structures in QFT
Many of the group's research directions depend on algebraic and geometric structures that make quantum field theory computable. Recent work develops chiral algebras, elliptic trace maps, quadratic duality, contact-term algebras, Chern-Simons matrix models, quantum flat connections, cluster transformations, the tetrahedron equation, state-integral models, and quantum-integrable lattice models. These tools connect formal aspects of QFT, such as BV quantization and algebraic index theory, with concrete constructions from supersymmetric gauge theory, string/M-theory, and representation theory. The emphasis is on using algebra not as notation, but as a mechanism that explains exact solvability, duality, and the persistence of protected information.
- Quantum Flat Connections, KZ equations, and IntegrabilityBanerjee, Haghighat, Latifi, 2026
- Quantization and Algebraic IndexLi, 2025
- Elliptic Trace Map on Chiral AlgebrasGui, Li, 2021
- Chiral algebra, Wilson lines, and mixed Hodge structure of Coulomb branchLi, Pan, Yan, 2025
- Solving the tetrahedron equation by Teichmüller TQFTShim, Sun, Wang, Yagi, 2026
- Quantum Algebra of Chern-Simons Matrix Model and Large $N$ LimitHu, Li, Ye, Zhou, 2023
Faculty Map
- Chi-Ming Chang: protected sectors in supersymmetric field theory, black-hole microstate counting, BMN and D1-D5 systems, celestial holography, and fermionic/topological systems.
- Babak Haghighat: string theory and supersymmetric geometry, SymTFT, non-invertible defects, Liouville/KZ structures, quantum flat connections, and topological field theory.
- Ling-Yan Hung: holography, BCFT ensembles, tensor-network RG, generalized symmetries, topological phases, and quantum information.
- Si Li: algebraic and geometric QFT, BV quantization, chiral algebras, algebraic index theory, and Chern-Simons matrix models.
- Wei Song: quantum gravity, flat and BMS holography, warped/deformed CFT, $T\bar{T}$/$J\bar{T}$ deformations, and holographic entanglement.
- Ning Su: numerical and analytic conformal bootstrap, 3d CFTs, super-Ising and Potts/cubic fixed points, QED$_3$, and bootstrap algorithms.
- Junya Yagi: integrable systems from quantum field theory, tetrahedron equations, quantum cluster algebras, state-integral models, and M-theory constructions.
- Wenbin Yan: supersymmetric field theory, 4d $\mathcal{N}=2$ SCFTs, Higgs and Coulomb branches, mirror symmetry, instantons, and VOAs.