As part of the program on Quantum Matter in Mathematics and Physics, the CMSA will be hosting two weekly seminars. The Quantum Matter/Quantum Field Theory seminar will take place on Wednesdays from 10:30 – 12:00pm in CMSA G10. The Condensed Matter/Math Seminar will take place on Thursdays from 11:501:00pm in CMSA, G10. The schedules for both seminars will be updated below as speakers are confirmed:
Date  Speaker  Title/Abstract 

9/05/2019 
Juven Wang (Harvard CMSA) 
Title: Quantum Matter Basics for Mathematicians 
9/18/2019 
Poshen Hsin (Caltech) 
Title: Lorentz symmetry fractionalization and duality in (2+1)d Abstract: I will introduce a discrete transformation in bosonic QFTs with Z2 oneform symmetry using the concept of symmetry fractionalization in condensed matter physics. I will then discuss some applications including boson/fermion dualities in (2+1)d. 
9/19/2019 
Poshen Hsin (Caltech) 
Title: “3d duality” 
9/20/2019 Members’ Seminar 
Ryohei Kobayashi (U of Tokyo) 
Title: Fermionic phases of matter on unoriented spacetime 
9/25/2019 
Juven Wang (CMSA) 
Title: HigherRank Tensor Field Theory of NonAbelian Fracton and Embeddon Abstract: We introduce a new class of tensor field theories in any dimension that has an interesting mixing between symmetrictensor gauge theory and antisymmetric tensor topological field theory. The “gauge structure” can be compact, continuous, abelian or nonabelian. Our theory may be a new gem sitting in the virgin territory outside the familiar gauge theories — outside the paradigm of Maxwell theory in 1865 and YangMills theory in 1954. We discuss its relation to the nonabelian generalization of Fracton in condensed matter, and Embeddon that we will introduce. This is based on https://arxiv.org/abs/1909.13879, jointly with Kai Xu (Harvard). 
9/26/2019 
ShuHeng Shao (IAS) 
Title: Anomalies and Charged Operators Abstract: We study the implications of ‘t Hooft anomaly for conformal field theory. Using the modular bootstrap, universal bounds on (1+1)dimensional bosonic conformal field theories with an internal Z2 global symmetry are derived. We find that there is a universal upper bound on the lightest Z2 odd operator if the symmetry is anomalous, but there is no bound if the symmetry is nonanomalous. We further discuss the implications for the Weak Gravity Conjecture in AdS3/CFT2. Finally we present a conjecture on more general anomalies that cannot be matched by TQFTs, a notion known as the “symmetryprotected gaplessness” in condensed matter physics. 
10/2/2019

Zhen Bi (MIT) 
Title: Novel quantum criticality beyond LandauGinzburgWilsonFisher paradigm Abstract: The infrared behavior of 3 + 1D nonabelian gauge fields with massless matter fields is an extremely important and intensively studied topic in particle physics. In this talk, we asking the following question from a condensed matter perspective: given some deconfined gauge theory in 3 + 1D, what phase transition can this theory describe? It turns out to be a fruitful way to think about these gauge theories and provides many explicit examples for several novel quantum critical phenomena. 1. We present several examples of Deconfined Quantum Critical Points (DQCP) between Symmetry Protected Topological phases in 3 + 1D for both bosonic and fermionic systems. 2. We find situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. 3. We exhibit the possibility – which we dub “unnecessary quantum critical points” – of stable generic continuous phase transitions within the same phase. 4. We present examples of interaction driven bandtheory forbidden continuous phase transitions between two distinct band insulators. 5. We find an example for a Landauallowed quantum phase transition, however, with a critical theory that is beyond Landau description. 
10/3/2019 
Ryan Thorngren (CMSA) 
Title: Domain Walls and the CPT Theorem Abstract: I will describe how in a relativistic quantum field theory, symmetrybroken domain walls enjoy a curious remnant of the broken symmetry obtained by a combination with the unbreakable CPT symmetry. There is an anomalymatching condition relating the symmetrypreserving bulk phase to the anomaly on the wall. This condition is related to an interesting property of manifold cobordisms called the Smith isomorphism. I will prove some generalizations of the Smith isomorphism theorem and discuss some physics applications to superfluids and gauge theories. This is joint work with Itamar Hason and Zohar Komargodski. 
10/4/2019 
Liang Kong (Shenzhen Institute of Quantum Sciences and Engineering, Southern University of Science and Technology) 
Title: A unified mathematical theory of both gapped and gapless boundaries of 2+1D topological orders Abstract: It was well known that a gapless boundary of a 2+1D topological order is different from and significantly richer than a gapped boundary. In this talk, however, we will propose a unified mathematical theory of both gapped and gapless boundaries of 2+1D topological orders. In particular, we will show that observables on the 1+1D world sheet of a chiral gapless boundary in the long wave length limit form an enriched fusion category, the Drinfeld center of which is precisely the unitary modular tensor category associated to the bulk. If time permits, we will also briefly discuss some consequences of this result, including a theory of nonchiral gapless boundaries, applications to boundary topological phase transitions, 0+1D defects between different gapless boundaries and a generalized boundarybulk relation. This is joint work with Hao Zheng. 
10/9/2019 
Peter Koroteev (Berkeley) 
Title: On Quiver Walgebras and Defects from Gauge Origami Abstract: Using Nekrasov’s gauge origami framework, we study two different versions of the BPS/CFT correspondence – first, the standard AGT duality and, second, the quiver W algebra construction which has been developed recently by Kimura and Pestun. The gauge origami enables us to work with both dualities simultaneously and find exact matchings between the parameters. In our main example of an Atype quiver gauge theory, we show that the corresponding quiver qWalgebra and its representations are closely related to a largen limit of spherical gl(n) double affine Hecke algebra whose modules are described by instanton partition functions of a defect quiver theory. 
10/10/2019 
Julio Parra Martinez (UCLA) 
Title: GSO projections and Dbrane classification via SPT phases Abstract: I will explain how a choice of fermionic SPT phases on the string worldsheet gives rise to the different GSO projections. This point of view not only easily explains why there are essentially two type II and 0 theories, but also predicts an eightfold classification of unoriented Pin type 0 theories. A similar analysis for unoriented Type II strings requires introducing Double Pin (DPin) structures, and confirms that there is an essentially unique choice of the type I worldsheet theory. By considering the implications of the bulk SPTs on the boundary of opens strings we provide an alternative route to the Ktheoretic classification of Dbranes, and clarify some of their properties. As an example, I will describe the classification of Dbranes in the unoriented Pin type 0 theories, in which all higher real Kgroups play a role. 
10/16/2019 G02 
Kantaro Ohmori (SUNY SCGP) 
Title: Anomaly Obstructions to Symmetry Preserving Gapped Phases: Discrete symmetry case
Abstract: Anomalies are renormalization group invariants and constrain the dynamics of quantum field theories. In this talk we show that certain anomalies for discrete global generalized symmetries imply that the underlying theory either spontaneously breaks its global symmetry or is gapless. This is done by observing that a symmetry preserving unitary TQFT is not compatible with the anomaly whose inflow action evaluates nontrivially on a certain manifold. 
10/17/2019 
No Seminar 

10/23/2019 
Chong Wang (Perimeter) 

10/24/2019 
Andrew Turner (MIT) 
Title: General Ftheory models with SU(3) x SU(2) x U(1) / Z_6 symmetry Abstract: We construct a general form for an Ftheory Weierstrass model over any base giving a 6D or 4D supergravity theory with gauge group SU(3) x SU(2) x U(1) / Z_6 and associated generic matter. The concept of ‘generic matter’ can be rigorously defined in 6D supergravity and generalizes naturally to four dimensions for Ftheory models. We describe general Ftheory models with this gauge group and the associated generic matter content, which fit into two distinct classes, and present an explicit Weierstrass model that realizes these models as two distinct branches. We also discuss, as a special case, the class of models recently studied by Cvetic, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an SU(5) unHiggsing. 
10/30/2019 G02 
Chong Wang (Perimeter) 

10/31/2019 
Patrick Lee (MIT) 
Title: Gapless spin liquid and emergent gauge theory Abstract: I shall review the emergence of gauge theory as a description of quantum spin liquid, particularly the gapless variety. The matter field plays a key role in stabilizing the deconfined phase. I shall also discuss the current experimental status of gapless spin liquid candidates, including the recently “rediscovered” example of TaS2. 
11/6/2019 
Dan Freed (UT Austin) 
Title: Mtheory is timereversal invariant Abstract: In joint work with Mike Hopkins we prove that there is no parity anomaly in Mtheory in the lowenergy field theory approximation. There are two sources of anomalies: the RaritaSchwinger field and the cubic form for the Cfield. I will explain the general principles behind these anomalies, since they apply in many problems. Then I’ll turn to the specific computations we did to verify this anomaly cancellation. They include topologial and geometric methods for computing etainvariants as well as homotopytheoretic techniques for computing bordism groups. 
11/7/2019 
Mathias Scheurer (Harvard) 
Title: Gauge theories for the cuprates:thermal Hall effect and optimal doping Abstract: Recent experiments [1] have revealed an enhanced thermal Hall effect in the pseudogap phase of several different cuprate compounds. The large signal even persists in the undoped system and, thus, challenges our understanding of the squarelattice antiferromagnet fundamentally. In the first part of the talk, I will analyze possible mechanisms that can give rise to a thermal Hall effect in the antiferromagnet [2,3]. In particular, I will discuss the possibility [3] that the magnetic field can drive the Néel state close to a transition to a phase where Néel order coexists with a chiral spin liquid. A spinon lattice model for this transition is shown to give rise to a large thermal Hall conductivity that also features a magneticfield and temperature dependence similar to experiment. We will derive the lowenergy continuum field theory for the transition, which is characterized by an emergent global SO(3) symmetry and has four different formulations that are all related by dualities. If time permits, I will present, in the second part of the talk, a nonAbelian gauge theory that we propose [4] as an effective field theory for the cuprates near optimal doping. In this theory, spindensitywave order is fractionalized into Higgs fields while all lowenergy fermionic excitations are electronlike and gauge neutral. The conventional Fermiliquid state corresponds to the confining phase of the theory at large doping and there is a quantum phase transition to a Higgs phase, describing the pseudogap, at low doping. It will be shown that the topological order of the Higgs phase is very naturally intertwined with chargedensitywave, Isingnematic, and scalar spinchirality order. We will also discuss the quantum critical point of the model. 
11/13/2019 G02 
Michael Pretko (U Colorado) 
Title: Introduction to Fractons Abstract: A fracton is an exotic new type of emergent quasiparticle with restricted mobility. While a single fracton is strictly immobile in isolation, they can often come together to form certain mobile bound states. In this talk, I will give a bird’seye overview on the current state of the field of fractons. I will begin with the theoretical formalism for fractons in terms of symmetric tensor gauge theories, which possess unusual higher moment conservation laws. I will then outline some physical realizations of fractons, such as spin models and topological crystalline defects, the latter of which arises through a novel field theory duality. Finally, I will discuss some of the most interesting phenomenology of fracton systems, such as their nonergodic and gravitational behavior. 
11/14/2019 G02 
Michael Pretko (U Colorado) 
Title: Advances in Fracton Physics: Dualities, Field Theories, and Classification Abstract: In this talk, I will give short informal explanations of three topics in the field of fractons with some interesting mathematical structure. I will begin with a detailed discussion of fractonelasticity duality, relating the properties of tensor gauge theories to the elastic description of twodimensional crystals. I will emphasize the role of symmetries in this duality, and also discuss how the duality extends to three dimensions, giving rise to “higherform” analogues of fracton conservation laws. Next, I will discuss recent advances on the field theory description of fractons, showing how fractons can be obtained by gauging field theories with a “vector” global symmetry. Finally, I will describe recent work towards classifying fracton phases in terms of their fusion theory, which can be described as a module over the group ring of translations. 
11/20/2019 
Subir Sachdev (Harvard) 
Title: Models of optimal doping criticality in the cuprate superconductors Abstract: There is now much experimental evidence for a significant change in the electronic structure of cuprate superconductors near a hole doping p=p_c optimal for superconductivity. Only for p > p_c do the electronic properties agree with the predictions of band theory. We argue that the data supports the existence of a quantum critical point (QCP) at p=p_c, and for p < p_c we have a novel state characterized by emergent gauge fields, possibly coexisting with conventional symmetry breaking orders. We present evidence that such a QCP is present in the Hubbard model with random, and alltoall, hopping and exchange. We also discuss a SU(2) gauge theory for the QCP in model of fluctuating incommensurate spin density waves in the absence of disorder. 
11/21/2019 
Natalie Paquette (Caltech) 

11/25/2019 
YuAn Chen (Caltech)  Title: Exact bosonization in higher dimensions and the duality between supercohomology fermionic SPT and highergroup bosonic SPT phases
Abstract: The first part of this talk will introduce generalized Jordan–Wigner transformation on arbitrary triangulation of any simply connected manifold in 2d, 3d and general dimensions. This gives a duality between all fermionic systems and a new class of lattice gauge theories. This map preserves the locality and has an explicit dependence on the second Stiefel–Whitney class and a choice of spin structure on the manifold. In the Euclidean picture, this mapping is exactly equivalent to introducing topological terms (ChernSimon term in 2d or the Steenrod square term in general) to the Euclidean action. We can increase the code distance of this mapping, such that this mapping can correct all 1qubit and 2qubits errors and is useful for the simulation of fermions on the quantum computer. The second part of my talk is about SPT phases. By the bosonfermion duality, we are able to show the equivalent between any supercohomology fermionic SPT and some highergroup bosonic SPT phases. Particularly in (3+1)D, we have constructed a unitary quantum circuit for any supercohomology fermionic SPT state with gapped boundary construction. This fermionic SPT state is derived by gauging higherform symmetry in the highergroup bosonic SPT and ungauging the fermion parity. The bulkboundary correspondence in (3+1)D fermion SPT phases will also be briefly discussed. 
11/27/2019 
Meng Cheng (Yale) 
TBA 
12/4/2019 


12/5/2019 
Yizhi You (Princeton) 
TBA 
12/11/2019 
Yuya Tanizaki (NCSU) 
TBA 
12/12/2019 
TBA 
