String Theory Group at YMSC

Holography, Black Holes, and Quantum Gravity

Faculty links: Chi-Ming Chang, Ling-Yan Hung, Wei Song.

A central direction is the use of protected sectors, deformed holography, and quantum-information-inspired constructions to probe the microscopic structure of gravity. Recent work studies BPS black-hole sectors, BMN matrix quantum mechanics, D1-D5 dynamics, flat and Carrollian holography, BMS field theories, $T\bar{T}$ and $J\bar{T}$ deformations, and the emergence of bulk geometry from BCFT ensembles and tensor-network RG.

• Words to describe a black holeChang, Lin, 2022
• Holographic covering and the fortuity of black holesChang, Lin, 2024
• 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

Faculty links: Babak Haghighat, Wenbin Yan, Junya Yagi, Chi-Ming Chang.

The group studies exact structures in supersymmetric quantum field theory and string theory, including BPS spectra, quantum curves, topological strings, class-$\mathcal{S}$ and 4d $\mathcal{N}=2$ SCFTs, instanton counting, mirror symmetry, chiral algebras, and M-theoretic constructions. This direction connects high-energy theory with algebraic geometry, representation theory, integrable systems, and enumerative geometry.

• SymTFTs and Duality Defects from 6d SCFTs on 4-manifoldsChen, Cui, Haghighat, Wang, 2023
• E-string Quantum CurveChen, Haghighat, Kim, Sperling, Wang, 2021
• Mirror symmetry for circle compactified 4d $\mathcal{N}=2$ SCFTsShan, Xie, Yan, 2023
• Tetrahedron instantonsPomoni, Yan, Zhang, 2021

Conformal Field Theory, Bootstrap, and Deformations

Faculty links: Ning Su, Wei Song, Babak Haghighat, Ling-Yan Hung.

Current CFT work ranges from numerical and analytic conformal bootstrap to deformed CFTs, Liouville theory, irregular conformal blocks, KZ equations, and exact operator-algebraic structures. The recent papers emphasize both computational methods for strongly coupled CFTs and exact structures that appear in holography, topological defects, and two-dimensional CFT.

• 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
• Correlation Functions in the TsT/$T{\bar T}$ CorrespondenceCui, Shu, Song, Wang, 2023

Generalized Symmetries, Topological Phases, and Quantum Information

Faculty links: Ling-Yan Hung, Babak Haghighat, Chi-Ming Chang.

Several projects connect high-energy theory with topological phases, generalized symmetries, tensor categories, and quantum information. Recent work develops SymTFT and SymQRG viewpoints, non-invertible defects, anyon condensation, fermionic systems, strange correlators, and tensor-network reconstructions of CFT and quantum spacetime.

• Topological Defect Lines in Two Dimensional Fermionic CFTsChang, Chen, Xu, 2022
• String Condensations in 3+1D and Lagrangian AlgebrasZhao, Lou, Zhang, Hung, Kong, Tian, 2022
• Para-fusion Category and Topological Defect Lines in $\mathbb Z_N$-parafermionic CFTsChen, Haghighat, Wang, 2023
• Non-Invertible Surface Defects in 2+1d QFTs from Half Spacetime GaugingCui, Haghighat, Ruggeri, 2024

Algebraic and Geometric Structures in QFT

Faculty links: Si Li, Junya Yagi, Wenbin Yan, Babak Haghighat.

Mathematical structures are not peripheral to the group's physics program: they provide concrete tools for quantization, chiral algebras, Chern-Simons matrix models, quantum cluster algebras, the tetrahedron equation, quantum flat connections, and integrable structures. This work links BV quantization, algebraic index theory, VOAs, Wilson lines, KZ equations, and higher-dimensional gauge theory.

• Q-operators are 't Hooft linesCostello, Gaiotto, Yagi, 2021
• Elliptic Trace Map on Chiral AlgebrasGui, Li, 2021
• Cluster transformations, the tetrahedron equation and three-dimensional gauge theoriesSun, Yagi, 2022
• Quantum Algebra of Chern-Simons Matrix Model and Large $N$ LimitHu, Li, Ye, Zhou, 2023

Faculty Map

• Chi-Ming Chang: supersymmetric sectors, black holes, BMN matrix models, celestial amplitudes, and fermionic/topological systems.
• Babak Haghighat: string theory, topological defects, KZ equations, Liouville theory, quantum curves, and SymTFT.
• Ling-Yan Hung: holography, tensor networks, generalized symmetries, topological phases, and quantum information.
• Si Li: algebraic and geometric aspects of QFT, BV quantization, chiral algebras, and Chern-Simons matrix models.
• Wei Song: quantum gravity, flat/BMS holography, warped/deformed CFT, and holographic entanglement.
• Ning Su: numerical and analytic conformal bootstrap, 3d CFTs, QED$_3$, and bootstrap algorithms.
• Junya Yagi: integrable systems, quantum field theory, tetrahedron equation, cluster algebras, and M-theory constructions.
• Wenbin Yan: supersymmetric field theory, 4d $\mathcal{N}=2$ SCFTs, mirror symmetry, instantons, and VOAs.