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 10:30 – 12:00pm in CMSA, G10. The schedules for both seminars will be updated below as speakers are confirmed:
Date  Speaker  Title/Abstract 

2/5/2020  YaHui Zhang (Harvard)  Title: A new theory for pseudogap metal in hole doped cuprates
Abstract: We provide a new parton theory for hole doped cuprates. We will describe both a pseudogap metal with small Fermi surfaces and the conventional Fermi liquid with large Fermi surfaces within mean field level of the same framework. For the pseudogap metal, “Fermi arc” observed in ARPES can be naturally reproduced. We also provide a theory for a critical point across which the carrier density jumps from x to 1+x. We will also discuss the generalization of the theory to Kondo breaking down transition in heavy fermion systems and generic SU(N) Hubbard model. 
2/6/2020  Yuan Cao (MIT)  Title: Twistronics in Graphene Superlattices: Correlation and Superconductivity 
2/12/2020  XueYang Song (Harvard)  Title: Monopoles in QED3 Dirac Spin Liquids 
2/13/2020  Grigory Tarnopolskiy (Harvard)  Title: Spontaneous symmetry breaking in SYK models 
2/19/2020  Zhehao Dai (MIT)  Title: Modeling the pseudogap state in cuprates: quantum disordered pair density wave
Abstract: I will briefly review the pseudogap phenomenology in high Tc cuprate superconductors, especially recent experiments related to charge density waves and pair density waves, and propose a simple theory of the pseudogap. By quantum disordering a pair density wave, we found a state composed of insulating antinodal pairs and a nodal electron pocket. We compare the theoretical predictions with ARPES results, optical conductivity, quantum oscillation and other experiments. 
2/20/2020  Lokman Tsui (MIT)  Title: Lattice models that realize $Z_n$ 1symmetryprotected topological states for even $n$
Abstract: Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high energy scales while other topological excitations have low energies. The low energy properties of topological orders in this limit, with the emergent higher symmetries, may be described by higher symmetry protected topological order. This motivates us, as a simplest example, to study a lattice model of $Z_n$1symmetry protected topological (1SPT) states in 3+1D for even $n$. We write down an exactly solvable lattice model and study its boundary transformation. On the boundary, we show the existence of anyons with nontrivial selfstatistics. For the $n=2$ case, where the bulk classification is given by an integer $m$ mod 4, we show that the boundary can be gapped with double semion topological order for $m=1$ and toric code for $m=2$. The bulk ground state wavefunction amplitude is given in terms of the linking numbers of loops in the dual lattice. Our construction can be generalized to arbitrary 1SPT protected by finite unitary symmetry. 
2/26/2020  Nat Tantivasadakarn
(Harvard) 
Abstract: Inspired by recent constructions of JordanWigner transformations in higher dimensions by Kapustin et. al., I will present a framework for an exact bosonization, which locally maps a translationinvariant model of spinless fermions to gauge theory of Pauli spins. I will show that the duality exists for an arbitrary number of (possibly manybody) “hopping” operators in any dimension and provide an explicit construction. The duality can be concisely stated in terms of an algebraic formalism of translationinvariant Hamiltonians proposed by Haah.
I will then present two interesting applications. First, bosonizing Majorana stabilizer codes, such as the Majorana color code or the checkerboard model, into Pauli stabilizer codes. Second, bosonizing fermionic systems where fermion parity is conserved on submanifolds such as higherform, line, planar or fractal symmetry. In 3+1D, the latter two can give rise to fracton models where emergent particles are immobile, but yet can be “fermionic”. This may give rise to new nonrelativistic ‘t Hooft anomalies.

3/3/2020
Tuesday 
Robert Gompf (UT Austin)  
3/5/2020
G02 

3/11/2020  
3/12/2020  
3/18/2020  
3/19/2020
G02 

3/25/2020
G02 

3/26/2020  
4/1/2020  
4/2/2020  
4/8/2020
G02 

4/9/2020
G02 

4/15/2020  
4/16/2020  
4/22/2020  
4/23/2020  
4/29/2020
G02 

4/30/2020
G02 

5/6/2020  Quantum Matter Workshop  
5/7/2020  
5/13/2020
G02 

5/14/2020
G02 
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)  Title: Unquantized quantum anomalies: electric polarization, Luttinger theorem and correlated Weyl semimetals 
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)  Title: A theory of deconfined pseudocriticality 
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)  Title: Koszul duality in field theory & holography 
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)  Title: Gapped boundary of symmetric topological phases and relative anomalies in (1+1)d CFTs
Abstract: Many (2+1)d topological phases admit gapped boundaries. In the presence of global symmetry, the classification of symmetric boundary conditions is further enriched. I will discuss recent work on classifying such boundary conditions for a doubled topological phase, and a general construction of such boundaries in symmetryenriched stringnet models using module categories. I will also describe how the results can be used to compute relative ’t Hooft anomalies in (1+1)d CFTs algebraically. 
12/3/2019  Quantum Matter workshop  
12/5/2019  Yizhi You (Princeton)  Title: Emergent fractons and algebraic quantum liquid from plaquette melting transitions
Abstract: Paramagnetic spin systems with spontaneously broken spatial symmetries, such as valence bond solid (VBS) phases, can host topological defects carrying nontrivial quantum numbers, which enables the paradigm of deconfined quantum criticality. In this talk, I will show that the defects of the valence plaquette solid(VPS) order parameter, in addition to possessing nontrivial quantum numbers, have fracton mobility constraints in the VPS phase. The spinon inside a single vortex cannot move freely in any direction, while a dipolar pair of vortices with spinon pairs can only move perpendicular to its dipole moment. These mobility constraints, while they persist near QCP, can potentially inhibit the condensation of spinons and preclude a continuous transition from the VPS to the Néel antiferromagnet. Instead, the VPS melting transition can be driven by the proliferation of spinon dipoles. In particular, we argue that a 2d VPS can melt into a stable gapless phase in the form of an algebraic bond liquid with algebraic correlations and longrange entanglement. Such a bond liquid phase yields a concrete example of the elusive 2d Bose metal with symmetry fractionalization. 
12/6/2019
1:00pm CMSA G02 
Nick G. Jones (University of Bristol)  Title: Toeplitz determinants and correlations in topological quantum chains
Abstract: Topological phases protected by symmetry can occur in both gapped and critical systems. I will discuss recent work on such phases for noninteracting fermions in one dimension with spinless timereversal symmetry. I will show how the phases are classified by a topological invariant and a central charge, explaining also the connection to edge modes. The bulk order parameters of these phases are correlators of fermionic string operators. I will explain how to derive exact asymptotics of these correlation functions using Toeplitz determinant theory, giving insight into the interplay between topology and criticality. This is largely based on the papers: Asymptotic correlations in gapped and critical topological phases of 1D quantum systems, N. G. Jones and R. Verresen, J. Stat. Phys. 175 (2019) Topology and edge modes in quantum critical chains, R. Verresen, N. G. Jones and F. Pollmann, Phys. Rev. Lett. 120 (2018) 
12/11/2019  Yuya Tanizaki (NCSU)  Title: Constraints on possible dynamics of QCD by symmetry and anomaly
Abstract: Lowenergy dynamics of Quantum Chromodynamics (QCD) is an important subject for nuclear and hadron physics, but it is a strongly coupled system and difficult to solve. In this situation, symmetry and also anomaly give us an important guide to make a solid conclusion onpossible behaviors of QCD. We find a new discrete anomaly in massless QCD, which says that the baryon number current is anomalously broken under the background gauge field for vectorlike flavor symmetry and discrete axial symmetry. To match this anomaly in the chiralsymmetry broken phase, the existence of baryons as Skyrmions is mandatory, and Skyrmion current must show the same anomaly. This is satisfied in the ordinary scenario of chiral symmetry breaking, but not satisfied in an exotic scenario of chiral symmetry breaking proposed by Stern about two decades ago. Since the anomaly matching is applicable even with the sign problem, Stern phase is excluded even for the finitedensity QCD at zero temperatures.

12/12/2019  Yuya Tanizaki (NCSU)  Title: Modifying instanton sums in QCD
Abstract: In the path integral formulation, we need to sum up all possible field configurations to define a QFT. If the configuration space is disconnected, we must specify how they should be summed by giving extra data to specify the QFT. In this talk, we try to restrict the possible number of instantons in SU(N) gauge theories, YangMills theory and QCD, and we find out the vacuum structures of them. For consistency with locality, we have to introduce an extra topological degrees of freedom, and the theory acquires the 3form symmetry. The existence of this 3form symmetry leads to extra vacua, and moreover it turns out to give an interesting selection rule for the domainwall excitation/vacuum decay. 
12/18/2019
12:00pm 
Artan Sheshmani (Harvard CMSA)  Title: Higher rank flag sheaves and VafaWitten invariants
Abstract: We study moduli space of holomorphic triples $f: E_{1} \rightarrow E_{2}$, composed of (possibly rank $>1$) torsionfree sheaves $(E_{1}, E_{2})$ and a holomorphic map between them, over a smooth complex projective surface $S$. The triples are equipped with a Schmitt stability condition. We prove that when the Schmitt stability parameter becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute obstruction theory in some cases (depending on Chern character of $E_{1}$). We further generalize our construction to higherlength flags of higher rank sheaves by gluing triple moduli spaces, and extend earlier work, with Gholampur and Yau, where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of flags $E_{1}\rightarrow E_{2}\rightarrow \cdots \rightarrow E_{n}$, where the maps are injective (by stability). There is a connection, by wallcrossing in the master space, developed by Mochizuki, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of any threefold given by a line bundle over the surface, $X :={\rm Tot}(L \rightarrow S)$. The latter DT invariants, when L is the canonical bundle of S, contribute to VafaWitten invariants. Joint work with ShingTung Yau, arXiv:1911.00124. 