AdS(Algeometry, duality and Strings) seminar
Student No.:40
Time:13:30-15:00, 2018.1.11/ 10:00-11:00, 2018.1.12
Instructor:Song Wei, Lin Hai, Yan Wenbin, Babak Haghighat, Rak-Kyeong Seong, Wen Qiang, Xu Jianfei  
Place:Conference room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-8-24
Ending Date:2018-1-12

This is a weekly seminar of the string theory group at YMSC


Date: 2018-1-11


Speaker: Chi-Ming Chang [U.C.Davis]

Time: 13:30-15:00, 2017-1-11

Place: Conf. room 3, Floor 2, Jin Chun Yuan West Bldg.

Title: Topological Defect Lines and Renormalization
Group Flows in Two Dimensions

Abstract: In conformal field theory, besides local point-like operators, there are extended objects, or "defects", such as boundary conditions and interfaces, that can be characterized purely in terms of the response of local operators in the presence of the defect. A basic example is given by considering a global symmetry element g, which by definition is a linear transformation on the local operators that preserve their OPEs. The action of g on a local operator may be viewed as the contraction of a closed codimension-one topological defect on the local operator. Interestingly, there are topological defect lines (TDLs) that do not correspond to any global symmetry, and are ubiquitous in two-dimensional CFTs. The fusion and crossing relations of general TDLs are captured by a mathematical structure known as fusion category.
I will discuss the constraints from TDLs on renormalization group (RG) flows and on the infrared topological quantum field theories (TQFTs). In particular, I will derive a generalization of the 't Hooft anomaly matching condition: when certain TDLs are preserved along an RG flow, these TDLs will survive in the infrared, maintaining the same fusion and crossing relations that put interesting constraints on the infrared CFT or TQFT. In fact, the TDLs of the TQFT inherited from the ultraviolet CFT allow us to completely determine many interesting TQFTs.




Date: 2018-1-12


Speaker: Cyril Cloeest [Cern]

Time: 10:00-11:00, 2018-1-12 

Place: Conf. room 1, Jin Chun Yuan West Bldg.

Title: Supersymmetric gauge theories on Seifert manifolds

Abstract: I will present some new results about supersymmetric partition functions of 3d N=2 supersymmetric gauge theories on Seifert manifolds. These partition functions can be understood as expectation values of certain geometry-changing half-BPS line operators, or equivalently as local defect operators in an auxiliary 2d TFT.





Date: 2018-1-4


Speaker: Mauricio Romo

Time: 13:30-15:00, 2017-1-4

Place: Conf. room 3, Floor 2, Jin Chun Yuan West Bldg.

Title: All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory

Abstract: I'll review some general aspects of complex Chern-Simons theory on hyperbolic 3-manifolds, focusing on the case of gauge group G=SL(2,C). After a brief introduction to the Volume Conjecture (VC), for knot complements and, a very recent mathematical proposal, for closed hyperbolic 3-manifolds, I'll show how complex Chern-Simons theory is related with them and how this connection leads to a novel generalization of the most recently proposed VC for closed 3-manifolds.




Date: 2017-12-28


Speaker: Hui Zhai [IAS THU]

Time: 2017-12-28, 13:30-15:00

Place: Conf. room 3, Floor 2, Jin Chun Yuan West Bldg. THU

Title: Exact Quantum Dynamics for Symmetry, Topology and Entropy

Abstract: In this talk I will discuss several examples of interesting universal dynamics that can reveal the information about symmetry, topological number or entropy spreading in a quantum system. In the first example, I will discuss an expansion dynamics of scale invariant quantum gases in a time-dependent harmonic trap, that displays a discrete temporal scaling symmetry, and we term it as “ the Efimovian expansion”. This dynamics reveals the emergent scaling symmetry of strongly interacting quantum system. In the second example, I will discuss quench dynamics from a topological trivial Chern insulator to a topological nontrivial one, and we show how to extract a quantized value from the quench dynamics, that exactly equals to the topological Chern number of the final Hamiltonian after the quench. In the third example, I will prove a theorem that relates the entropy growth after a quench to the out-of-time-ordered correlation that recently discussed in the content of quantum chaos and holographic duality. These three examples reveal the interplay between quantum dynamics with symmetry, topology and entropy, respectively.


[1] Shujin Deng, Zhe-Yu Shi, Pengpeng Diao, Qianli Yu, Hui Zhai, Ran Qi and Haibin Wu, Science, 353, 371 (2016)
[2] Ce Wang, Pengfei Zhang, Xin Chen, Jinlong Yu and Hui Zhai, arXiv: 1611.03304, Phys. Rev. Lett. 118, 185701 (2017)
[3] Ruihua Fan, Pengfei Zhang, Huitao Shen and Hui Zhai, Science Bulletin, 62, 707 (2017)
[4] Jun Li, Ruihua Fan, Hengyan Wang, Bingtian Ye, Bei Zeng, Hui Zhai, Xinhua Peng, Jiangfeng Du, Phys. Rev. X, 7, 031011 (2017)



Date: 2017-12-21


Speaker: Jia-ju Zhang [University of Milano-Bicocca & INFN]

Time: 2017-12-21, 13:30-15:00 (Thu)

Place: Conf. room 3, Jin Chun Yuan West Bldg.

Title: Eigenstate thermalization hypothesis in two-dimensional large central charge CFT

Abstract: By the eigenstate thermalization hypothesis (ETH), a highly excited energy eigenstate behaves like a thermal state. It is about how various statistical ensembles emerge in our quantum world. I will talk about ETH in two-dimensional large central charge CFT and compare the excited state of a primary operator with the thermal state. To define ETH precisely, one needs to know how similar, or equivalently dissimilar, the excited state and thermal state are. I will talk about short interval expansions of the entanglement entropy, relative entropy, Jensen-Shannon divergence. For the canonical ensemble, the excited state and thermal state are the same at the leading order of large central charge and are different at the next-to-leading order. I will also discuss briefly ETH for generalized Gibbs ensemble, and ETH for the descendant excited states.




Date: 2017-12-15


Speaker: Wang Huajia [University of Illinois, Urbana]

Time: 2017-12-15, 13:30-15:00 (Fri)

Place: Conf. room 1, Jin Chun Yuan West Bldg.

Title: Entanglement, causality and energy conditions in QFTs

Abstract: It has become increasingly clear that the key to understanding many fundamental questions in quantum field theories (QFTs) is encoded in the underlying structure of entanglement and causality. In this talk, I will discuss a particular direction along such a line: tracing the quantum information and causality origins of energy conditions in QFTs. In particular, I will discuss two approaches to prove the averaged null energy condition (ANEC), one from entanglement constraint and the other from causality constraint. Furthermore, I will discuss how, by combining both elements and consider causality probed by the entanglement data, one can prove the stronger quantum null energy condition (QNEC).




Date: 2017-12-7


Speaker: Cynthia Keeler [Bohr Inst.]

Time: 2017-12-7, 13:30-15:00

Place: Conf. room 3, Floor 2, Jin Chun Yuan West B., THU

Title: Non-relativistic Coset Constructions

We first review the proposed duals to non-relativistic field theories known as "Lifshitz spacetimes", focusing on features which limit the reconstructability of bulk spacetime information from boundary data. With this motivation in hand, we study the use of coset constructions of boundary symmetries to produce bulk dual candidates (such as AdS and Lifshitz spacetimes), generalizing the usual coset manifold construction to allow for degenerate two-forms.  In particular we examine cosets of non-relativistic algebras such as Bargmann, viewed as a contraction from the relativistic algebra. These new cosets have a metric complex that can be interpreted as a Newton-Cartan structure.




Date: 2017-11-30


Speaker: Arjun Bagchi [Indian Test. Tech.,Kanpur]

Time: 2017-11-30, 13:30-15:00

Place: Conf. room 3, Floor 2, Jin Chun Yuan West B., THU

Title: Constructing the BMS Bootstrap

We elaborate on aspects of the recently introduced BMS bootstrap programme. We consider 2d field theories with BMS3 symmetry and extensively use highest weight representations to uncover the BMS version of crossing symmetry in 4-point functions that are constrained by symmetry. The BMS bootstrap equation is formulated and then analytic expressions for BMS blocks are constructed by looking at the limit of large central charges. These results are also applicable to 2d Galilean Conformal Field Theories through the isomorphism between the BMS3 and 2d Galilean Conformal Algebras. We recover our previously obtained results in the non-relativistic limit of the corresponding ones in 2d relativistic CFTs. This provides a comprehensive check of our previous analysis.




Date: 2017-11-23


Speaker: Peter Koroteev [U.C. Davis]

Time: 2017-11-23, 13:30-15:00

Place: Conf. room 3, Floor 2, Jin Chun Yuan West B., THU

Title: Quantum Geometry, Quiver W-algebras and Gauge Origami    

We discuss instanton counting in quiver gauge theories in connection with representation theory and integrable systems. In particular we find intriguing relations between quantum geometry (K-theory) of the moduli space of instantons, spectrum of elliptic Ruijsenaars-Schneider model and quiver W-algebras by Kimura and Pestun. Some of these dualities can be naturally realized in the gauge origami framework proposed by Nekrasov.



Date: 2017-11-9


Speaker: Song He [ITP, CAS]  

Time: 2017-11-9, 13:30-15:00


Place: Conf. room 3, Floor 2, Jin Chun Yuan West B., THU

Title: Scattering forms, geometries and the worldsheet (+ color as kinematics)

I will first introduce the general idea of viewing scattering amplitudes as differential forms on the space of physical kinematic data. As the simplest example of the Amplituhedron, I will show that ``scattering form” for tree-level phi^3 amplitudes turns out to be the canonical form of an associahedron in the space of Mandlestam variables. Moreover, the form can be obtained as pushforward of the canonical form on the worldsheet associahedron, where the scattering equations provide a map between the two associahedra. If time permits, I will also discuss the idea that color is kinematics for scattering forms and how all the above apply to e.g. Yang-Mills theory and the non-linear sigma model. (Based on ongoing work with N. Arkani-Hamed, Y. Bai, G. Yan.)



Date: 2017-11-2


Speaker: Seok Kim [Seoul Natl. U.]  

Time: 2017-11-2, 13:30-15:00


Place: Conf. room 3, Floor 2, Jin Chun Yuan West B., THU

Title: 6d strings and exceptional instantons
We propose new ADHM-like methods of studying the instanton partition functions in the Coulomb branch, with certain exceptional gauge groups or matters. We study G_2 theories with matters in 7, and SO(7) theories with matters in the spinor representation 8. The results are applied to study self-dual instanton strings in 6d SCFTs.



Date: 2017-10-26


Speaker: Wei Li [ITP]  

Time: 2017-10-26, 13:30-15:00


Place: Conf. room 3, Floor 2, Jin Chun Yuan West B., THU

Title: A holographic dual of string in AdS_3 x S^3 x S^3 x S^1
The CFT dual of string in AdS_3 x S^3 x S^3 x S^1 is more difficult to find than the T^4 or K3 case due to the additional D5 fluxes in the D1D5 system. I will first explain the recent computation of its BPS spectrum from the gravity side, which gives much fewer BPS states than previously conjectured. I then discuss an old candidate for the case when the number of D5 fluxes is divisible by the number of D5 branes — the symmetric orbifold of S_kappa theory, and show that its BPS spectrum matches that of the gravity side.



Date: 2017-10-19


Speaker: Jian Shaokai [IASTHU]    

Time: 2017-10-19, 13:30-15:00  


Place: Conf. room 3, Floor 2, Jin Chun Yuan West B., THU

Title: Quantum criticality and duality in the SYK/AdS2 chain

We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or antiferromagnetic) phases in the SYK chain has a gravitational description corresponding to the double-trace deformation in an AdS2 chain. Specifically, by studying a double-trace deformation of a Z2 scalar in an AdS2 chain where the Z2 scalar is dual to the order parameter in the SYK chain, we find that the susceptibility and renormalization group equation describing the QCP in the SYK chain can be exactly reproduced in the holographic model. Our results suggest that the infrared geometry in the gravity theory dual to the diffusive metal of the SYK chain is also an AdS2 chain. Moreover, such correspondence can be readily generalized to SYK models in two and higher dimensions.



Date: 2017-10-12


Speaker: Yang Gang [ITP]    

Time: 2017-10-12, 13:30-15:00  


Place: Conf. room 3, Floor 2, Jin Chun Yuan West B., THU

Title: A mysterious and powerful duality between spacetime and gauge symmetry
In gauge theories, while momentum variables are related to the spacetime, color factors are associated to the internal gauge symmetry. Recent studies of scattering amplitudes show that there is a remarkable duality between the momentum and color factors. This duality also suggests an intriguing relation between gauge and gravity theories, via the so-called double copy description. It has been successfully used to construct many highly non-trivial multi-loop amplitudes in gauge and gravity theories.  However, a fundamental principle of this duality is still not known. In this talk, I will give an introduction to this duality and explain its first five-loop realization (arXiv:1610.02394). More recently, the four-loop (yet the leading order!) non-planar cusp anomalous dimension in N=4 SYM was finally obtained (arXiv:1705.03444) which was also based on this duality.




Date: 2017-09-28


Speaker: Wan Yidun [Fudan University]    

Time: 2017-09-28, 13:30-15:00  


Place: Conf. room 3, Floor 2, Jin Chun Yuan West B., THU

Title: Boundary Hamiltonian theory of 2D topological orders
Abs: I shall present our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. We construct the creation and hopping operators of boundary quasi-particles. We find that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.  


Date: 2017-09-07      



Speaker: Du Pei (Caltech)    


Time: 2017-09-07, 13:30-15:00  



Place: Conf. room 3, Floor 2, Jin Chun Yuan West B., THU



Title: Can one hear the shape of a drum?



Abstract: Much like harmonics of musical instruments, spectra of quantum systems contain wealth of useful information. In this talk, I will discuss how to obtain new invariants of three- and four-manifolds from BPS spectra of quantum field theories. While most of them are completely novel, some of the new invariants categorify well-known old invariants such as the WRT invariant of 3-manifolds and the Donaldson invariant of 4-manifolds. This talk is based on arXiv:1701.06567 and ongoing work with Sergei Gukov, Pavel Putrov and Cumrun Vafa.




Date: 2017-08-24     


Speaker: Kaiwen Sun (USTC)    

Time: 2017-08-24, 13:30-15:00  

Place: Conf. room 3, Floor 2, Jin Chun Yuan West B., THU


Title: Blowup Equations for Refined Topological String


Abstract: We propose the functional equations for the partition function of refined topological string theory on arbitrary local Calabi-Yau threefolds, called the blowup equations. They are inspired from the Gottsche-Nakajima-Yoshioka's K-theoretic blowup equations which characterize the Nekrasov partition function of five dimensional N=1 supersymmetric gauge theories compactified on a circle. Evidences show that these blowup equations can be used to determine the full refined BPS invariants of local Calabi-Yau threefolds. This serves an independent and sometimes more powerful way to compute the partition function other than the refined topological vertex in A-model and the refined holomorphic anomaly equations in B-model. Part of the equations called the vanishing blowup equations are also responsible for the previously mysterious compatibility formulae between the exact Nekrasov-Shatashivili quantization of the mirror curves and the Grassi-Hatsuda-Marino conjecture on Topological String/Spectral Theory correspondence. This talk is based on a to-appear paper with Min-xin Huang and Xin Wang.