arXiv subjects

Juven Wang

Publications and source records attributed to Juven Wang.

At least 37 records · Page 2Linked to original sources

arXiv2022

Fermi Surface Symmetric Mass Generation

Symmetric mass generation is a novel mechanism to give gapless fermions a mass gap by non-perturbative interactions without generating any fermion bilinear condensation. The previous studies of symmetric mass generation have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this work, we generalize the concept of symmetric mass generation to Fermi liquid with a finite Fermi volume and discuss how to gap out the Fermi surfaces by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of Fermi surface symmetric mass generation in both (1+1)D and (2+1)D Fermi liquid systems when several Fermi surfaces together cancel the Fermi surface anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a non-perturbative interaction mechanism is the only way to gap out the Fermi surfaces. This symmetric Fermi surface reconstruction is in contrast to the conventional symmetry-breaking mechanism to gap the Fermi surfaces. As a side product, our model provides a pristine 1D lattice regularization for the (1+1)D U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction.

cond-mat.str-el↗

arXiv2022

Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory

We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at $θ=π$ (SU(2)$_{θ=π}$ YM), by turning on background fields for both the time-reversal (i.e., on unorientable manifolds) and 1-form center global symmetry. We find four classes of time-reversal and Lorentz symmetry-enriched SU(2)$_{θ=π}$ YM, labeled by $(K_1, K_2)$: $K_1=0,1$ specifies Kramers singlet/doublet Wilson line and new mixed higher 't Hooft anomalies; $K_2=0,1$ specifies boson/fermionic Wilson line and a new Wess-Zumino-Witten-like counterterm. Higher anomalies indicate that to realize all higher $n$-global symmetries locally on $n$-simplices, the 4d theory becomes a boundary of a 5d higher-symmetry-protected topological state (SPTs, as an invertible topological quantum field theory (TQFT) or a cobordism invariant in math, or as a 5d higher-symmetric interacting topological superconductor in condensed matter). By dynamically gauging the 1-form symmetry, we transform a 5d bulk SRE SPTs into an LRE symmetry-enriched topologically ordered state (SETs); thus we obtain the 4d SO(3)$_{θ=π}$ YM-5d LRE-higher-SETs coupled system with higher-form gauge fields. We further derive new exotic anyonic statistics of extended objects such as 2-worldsheet of strings and 3-worldvolume of branes, physically characterizing the 5d SETs. We discover triple and quadruple link invariants associated with the 5d higher-gauge TQFTs, hinting at a relation between non-supersymmetric 4d pure YM and topological links in 5d. We provide 4d-5d lattice simplicial complex regularizations and bridge to 4d quantum spin liquids. We constrain gauge dynamics by higher anomalies and a higher symmetry-extension method.

hep-th↗

arXiv2022

C-P-T Fractionalization

Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as $\mathbb{Z}_2$-involutions in the passive transformation on the spacetime coordinates; but together with a charge conjugation C, the total C-P-R-T symmetries have enriched active transformations on fields in representations of the spacetime-internal symmetry groups of quantum field theories (QFTs). In this work, we derive that these symmetries can be further fractionalized, especially in the presence of the fermion parity $(-1)^{\rm F}$. We elaborate on examples including relativistic Lorentz invariant QFTs (e.g., spin-1/2 Dirac or Majorana spinor fermion theories) and nonrelativistic quantum many-body systems (involving Majorana zero modes), and comment on applications to spin-1 Maxwell electromagnetism (QED) or interacting Yang-Mills (QCD) gauge theories. We discover various C-P-R-T-$(-1)^{\rm F}$ group structures, e.g., Dirac spinor is in a projective representation of $\mathbb{Z}_2^{\rm C}\times \mathbb{Z}_2^{\rm P} \times \mathbb{Z}_2^{\rm T}$ but in an (anti)linear representation of an order-16 nonabelian finite group, as the central product between an order-8 dihedral (generated by C and P) or quaternion group and an order-4 group generated by T with T$^2=(-1)^{\rm F}$. The general theme may be coined as C-P-T or C-R-T fractionalization.

hep-th↗

arXiv2022

Proton Stability: From the Standard Model to Beyond Grand Unification

A proton is known for its longevity, but what is its lifetime? While many Grand Unified Theories predict the proton decay with a finite lifetime, we show that the Standard Model (SM) and some versions of Ultra Unification (which replace sterile neutrinos with new exotic gapped/gapless sectors, e.g., topological or conformal field theory under global anomaly cancellation constraints) with a discrete baryon plus lepton symmetry permit a stable proton. For the 4d SM with $N_f$ families of 15 or 16 Weyl fermions, in addition to the continuous baryon minus lepton U(1)$_{\bf B - L}$ symmetry, there is also a compatible discrete baryon plus lepton $\mathbb{Z}_{2N_f, \bf B + L}$ symmetry. The $\mathbb{Z}_{2N_f, \bf B + L}$ is discrete due to the ABJ anomaly under the BPST SU(2) instanton. Although both U(1)$_{\bf B - L}$ and $\mathbb{Z}_{2N_f, \bf B + L}$ symmetries are anomaly-free under the dynamical SM gauge field, it is important to check whether they have mixed anomalies with the gravitational background field and higher symmetries (whose charged objects are Wilson electric or 't Hooft magnetic line operators) of SM. We can also replace the U(1)$_{\bf B - L}$ with a discrete variant $\mathbb{Z}_{4,X}$ for $X \equiv 5({\bf B - L})-\frac{2}{3} {\tilde Y}$ of electroweak hypercharge ${\tilde Y}$. We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM's deformation class. We discuss the proton stability of the SM and Ultra Unification in the presence of discrete ${\bf B + L}$ symmetry protection, in particular (U(1)$_{\bf B - L} \times \mathbb{Z}_{2N_f,\bf B + L})/{\mathbb{Z}_2^{\rm F}}$ or $(\mathbb{Z}_{4,X} \times \mathbb{Z}_{2N_f, \bf B + L})/{\mathbb{Z}_2^{\rm F}}$ symmetry with the fermion parity $\mathbb{Z}_2^{\rm F}$.

hep-ph↗

arXiv2022

Cobordism and Deformation Class of the Standard Model

't Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a $d$d spacetime are known to be classified by a $d+1$d cobordism group TP$_{d+1}$(G), whose group generator is a $d+1$d cobordism invariant written as an invertible topological field theory (iTFT) Z$_{d+1}$. The deformation class of QFT is recently proposed to be specified by its symmetry G and an iTFT Z$_{d+1}$. Seemingly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. In this work, we ask which deformation class controls the 4d ungauged or gauged (SU(3)$\times$SU(2)$\times$U(1))/$\mathbb{Z}_q$ Standard Model (SM) for $q=1,2,3,6$ with a continuous or discrete $(\bf{B}-\bf{L})$ symmetry. We show that the answer contains some combination of 5d iTFTs: two $\mathbb{Z}$ classes associated with $(\bf{B}-\bf{L})^3$ and $(\bf{B}-\bf{L})$-(gravity)$^2$ 4d perturbative local anomalies, a mod 16 class Atiyah-Patodi-Singer $η$ invariant and a mod 2 class Stiefel-Whitney $w_2w_3$ invariant associated with 4d nonperturbative global anomalies, and additional $\mathbb{Z}_3\times\mathbb{Z}_2$ classes involving higher symmetries whose charged objects are Wilson electric or 't Hooft magnetic line operators. Out of $\mathbb{Z}$ classes of local anomalies and 24576 classes of global anomalies, we pin down a deformation class of SM labeled by $(N_f,n_{ν_{R}},$ p$',q)$, the family and "right-handed sterile" neutrino numbers, magnetic monopole datum, and mod $q$ relation. Grand Unifications and Ultra Unification that replaces sterile neutrinos with new exotic gapped/gapless sectors (e.g., topological or conformal field theory) or gravitational sectors with topological or cobordism constraints, all reside in an SM deformation class. Neighbor phases/transitions/critical regions near SM exhibit beyond SM phenomena.

hep-th↗

arXiv2022

Non-Liquid Cellular States

The existence of quantum non-liquid states and fracton orders, both gapped and gapless states, challenges our understanding of phases of entangled matter. We generalize the cellular topological states to liquid or non-liquid cellular states. We propose a mechanism to construct more general non-abelian states by gluing gauge-symmetry-breaking vs gauge-symmetry-extension interfaces as extended defects in a cellular network, including defects of higher-symmetries, in any dimension. Our approach also naturally incorporates the anyonic particle/string condensations and composite string (related to particle-string or p-string)/membrane condensations. This approach shows gluing the familiar extended topological quantum field theory or conformal field theory data via topology, geometry, and renormalization consistency criteria (via certain modified group cohomology or cobordism theory data) in a tensor network can still guide us to analyze the non-liquid states. (Part of the abelian construction can be understood from the K-matrix Chern-Simons theory approach and the coupled-layer-by-junction constructions.) This approach may also lead us toward a unifying framework for quantum systems of both higher-symmetries and sub-system/sub-dimensional symmetries.

cond-mat.str-el↗

arXiv2022

Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction

Prior work [arXiv:2106.16248] shows that the Standard Model (SM) naturally arises near a gapless quantum critical region between Georgi-Glashow (GG) $su(5)$ and Pati-Salam (PS) $su(4) \times su(2) \times su(2)$ models of quantum vacua (in a phase diagram or moduli space), by implementing a modified $so(10)$ Grand Unification (GUT) with a Spin(10) gauge group plus a new discrete Wess-Zumino Witten term matching a 4d nonperturbative global mixed gauge-gravity $w_2 w_3$ anomaly. In this work, we include Barr's flipped $su(5)$ model into the quantum landscape, showing these four GUT-like models arise near the quantum criticality near SM. Highlights include: First, we find the precise GG or flipped $u(5)$ gauge group requires to redefine a Lie group U(5)$_{\hat q}$ with $\hat q=2$ or $3$ (instead of non-isomorphic analog $\hat q=1$ or 4), and different $\hat q$ are related by multiple covering. Second, we show that the GG and flipped $u(5)$ are two different symmetry-breaking vacua of the same order parameter separated by a first-order Landau-Ginzburg transition. We also show that analogous 3+1d deconfined quantum criticalities, both between GG and PS, and between the flipped $u(5)$ and PS, are beyond Landau-Ginzburg paradigm. Third, topological quantum criticality occurs by tuning between the 15n vs 16n scenarios. Fourth, we explore the generalized higher global symmetries in the SM and GUTs. Gauging the $\mathbb{Z}_2$ flip symmetry between GG and flipped $u(5)$ models, leads to a potential categorical higher symmetry that is a non-invertible global symmetry: within a gauge sector $(u(1) \times u(1)) \rtimes \mathbb{Z}_2$, the fusion rule of 2d topological surface operator splits. However, the un-Higgs Spin(10) at UV retracts this categorical symmetry.

hep-th↗

arXiv2022

3+1d Boundaries with Gravitational Anomaly of 4+1d Invertible Topological Order for Branch-Independent Bosonic Systems

We study bosonic systems on a spacetime lattice defined by path integrals of commuting fields. We introduce branch-independent bosonic (BIB) systems, whose path integral is independent of the branch structure of the spacetime simplicial complex, even for a spacetime with boundaries. In contrast, a generic lattice bosonic (GLB) system's path integral may depend on the branch structure. We find the invertible topological order characterized by the Stiefel-Whitney cocycle (e.g., 4+1d w$_2$w$_3$) to be nontrivial for BIB systems, but this topological order and a trivial gapped tensor product state belong to the same phase for GLB systems. The invertible topological orders in GLB systems are not classified by the oriented cobordism. The branch dependence on a lattice may be related to the orthonormal frame of smooth manifolds and the framing anomaly of continuum field theories. The branch structure on a discretized lattice may be related to a frame structure on a smooth manifold that trivializes any Stiefel-Whitney classes. We construct BIB systems to realize the w$_2$w$_3$ topological order, and its 3+1d gapped or gapless boundaries. A 3+1d $\mathbb{Z}_2$ gauge theory with (1) fermionic $\mathbb{Z}_2$ gauge charge particle trivializes w$_2$ and (2) fermionic $\mathbb{Z}_2$ gauge flux line trivializes w$_3$. In particular, if the flux loop's worldsheet is unorientable, then an orientation-reversal 1d worldline corresponds to a fermion worldline carrying no $\mathbb{Z}_2$ gauge charge. Spin and Spin$^c$ structures trivialize the w$_2$w$_3$ global pure gravitational anomaly to zero (which helps to construct 3+1d $\mathbb{Z}_2$ and all-fermion U(1) gauge theories), but the Spin$^h$ and Spin$\times_{\mathbb{Z}_2}$Spin$(n \geq 3)$ structures modify the w$_2$w$_3$ into a global mixed gauge-gravitational anomaly, which helps to constrain Grand Unifications (e.g., $n=10,18$) or construct new models.

cond-mat.str-el↗

arXiv2022

Symmetric Mass Generation

The most well-known mechanism for fermions to acquire a mass is the Nambu-Goldstone-Anderson-Higgs mechanism, i.e. after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group. This new mechanism is generally referred to as the "Symmetric Mass Generation (SMG)." It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes current numerical results, introduces a novel unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and overviews various features and applications of SMG.

cond-mat.str-el↗

arXiv2022

Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model

Lattice regularization of chiral fermions has been a long-standing problem in physics. In this work, we present the density matrix renormalization group (DMRG) simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of (2+1)D lattice model of multi-layer Chern insulator, whose finite-width implies the quantum system is effectively (1+1)D. By introducing carefully designed two sets of six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation (SMG) mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. We determine the evolution of Luttinger parameters before the transition, which confirms that the transition happens exactly at the point when the interaction term becomes marginal. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless, which provides the desired lattice regularization of chiral fermions.

cond-mat.str-el↗

arXiv2022

Deconfined Quantum Criticality among Grand Unified Theories

This article overviews the recent developments in applying the idea of deconfined quantum criticality in condensed matter physics to understand quantum phase transitions among grand unified theories in high energy physics in the 4-dimensional spacetime. In particular, dictated by a mod 2 class nonperturbative global mixed gauge-gravitational anomaly, there can be a gapless deconfined quantum critical region between Georgi-Glashow and Pati-Salam models -- not only the Standard Model occurs as a neighbor phase, but also beyond the Standard Model phenomena (such as deconfined dark gauge force and fractionalized/fragmentary fermionic partons) emerge near the critical region.

hep-ph↗

arXiv2022

Gauge Enhanced Quantum Criticality Beyond the Standard Model

Standard lore views our 4d quantum vacuum governed by one of the candidate Standard Models (SMs), while lifting towards some Grand Unification-like structure (GUT) at higher energy scales. In contrast, in our work, we introduce an alternative view that the SM arises from various neighbor vacua competition in a quantum phase diagram. In general, we regard the SM arising near the gapless quantum criticality (either critical points or critical regions) between the competing neighbor vacua. In particular, we demonstrate how the $su(3)\times su(2)\times u(1)$ SM with 16n Weyl fermions arises near the quantum criticality between the GUT competition of Georgi-Glashow (GG) $su(5)$ and Pati-Salam (PS) $su(4)\times su(2)\times su(2)$. We propose two enveloping toy models. Model I is a conventional $so(10)$ GUT with a Spin(10) gauge group plus GUT-Higgs potential inducing various Higgs transitions. Model II modifies Model I plus a 4d discrete torsion Wess-Zumino-Witten-like term built from GUT-Higgs field (that matches a nonperturbative global mixed gauge-gravity anomaly captured by a 5d invertible topological field theory $w_2w_3$), which manifests a Beyond-Landau-Ginzburg criticality between GG and PS models, with extra Beyond-the-Standard-Model (BSM) excitations emerging near a quantum critical region. If the internal symmetries were treated as global symmetries, we show a gapless 4d deconfined quantum criticality with new BSM fractionalized fragmentary excitations of Color-Flavor separation, and gauge enhancement including a Dark Gauge force sector, altogether requiring a double fermionic Spin structure named DSpin. If the internal symmetries are dynamically gauged, we show a 4d boundary criticality such that only appropriately gauge enhanced dynamical GUT gauge fields propagate into an extra-dimensional 5d bulk. The phenomena may be regarded as SM deformation or morphogenesis.

hep-th↗

arXiv2022

Ultra Unification

Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number ${\bf B}-{\bf L}$, the electroweak hypercharge $Y$, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT, or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed "sterile" neutrinos, gapless unparticle physics, more general interacting conformal field theories, or gravity with topological cobordism constraints, or their combinations to altogether cancel the mixed gauge-gravitational anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations) or gapless conformal matter. Physical characterizations of these gapped extended objects require the mathematical theories of cohomology, cobordism, or category. Although weaker than the weak force, Topological Force is infinite-range or long-range which does not decay in the distance, and mediates between the linked worldvolume trajectories via fractional or categorical statistical interactions.

hep-th↗

arXiv2021

Boundary supersymmetry of 1+1 d fermionic SPT phases

We prove that the boundaries of all non-trivial 1+1 dimensional intrinsically fermionic symmetry-protected-topological phases, protected by finite on-site symmetries (unitary or anti-unitary), are supersymmetric quantum mechanical systems. This supersymmetry does not require any fine-tuning of the underlying Hamiltonian, arises entirely as a consequence of the boundary 't Hooft anomaly that classifies the phase and is related to a `Bose-Fermi' degeneracy different in nature from other well known degeneracies such as Kramers doublets.

cond-mat.str-el↗

arXiv2021

Higher-Rank Tensor Non-Abelian Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauging

With a view toward a fracton theory in condensed matter, we introduce a higher-moment polynomial degree-p global symmetry, acting on complex scalar/vector/tensor fields (e.g., ordinary or vector global symmetry for p$=0$ and p$=1$ respectively). We relate this higher-moment global symmetry of $n$-dimensional space, to a lower degree (either ordinary or higher-moment, e.g., degree-(p-$\ell$)) subdimensional or subsystem global symmetry on layers of $(n-\ell)$-submanifolds. These submanifolds are algebraic affine varieties (i.e., solutions of polynomials). The structure of layers of submanifolds as subvarieties can be studied via mathematical tools of embedding, foliation, and algebraic geometry. We also generalize Noether's theorem for this higher-moment polynomial global symmetry. We can promote the higher-moment global symmetry to a local symmetry, and derive a new family of higher-rank-m symmetric tensor gauge theory by gauging, with m = p$+1$. By further gauging a discrete $\mathbb{Z}_2^C$ charge conjugation (particle-hole) symmetry, we derive a new general class of rank-m tensor non-abelian gauge field theory (the gauge structure is non-commutative thus non-abelian but not an ordinary group): a hybrid class of (symmetric or non-symmetric) higher-rank-m tensor gauge theory and anti-symmetric tensor topological field theory, generalizing [arXiv:1909.13879], interplaying between gapless and gapped sectors.

hep-th↗

arXiv2020

Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force

Standard lore uses local anomalies to check the kinematic consistency of gauge theories coupled to chiral fermions, e.g. Standard Models (SM). Based on a systematic cobordism classification, we examine constraints from invertible quantum anomalies (including all perturbative local and nonperturbative global anomalies) for gauge theories. We also clarify the different uses of these anomalies: including (1) anomaly cancellations of dynamical gauge fields, (2) 't Hooft anomaly matching conditions of background fields of global symmetries, and others. We apply several 4d $\mathbb{Z}_{n}$ anomaly constraints of $n=16,4,2$ classes, beyond the familiar Feynman-graph perturbative $\mathbb{Z}$ class local anomalies. As an application, for (SU(3)$\times$SU(2)$\times$U(1))/$\mathbb{Z}_q$ SM (with $q=1,2,3,6$) and SU(5) Grand Unification with 15n chiral Weyl fermions and with a discrete baryon minus lepton number $X=5({\bf B}- {\bf L})-4Y$ preserved, we discover a new hidden gapped sector previously unknown to the SM and Georgi-Glashow model. The gapped sector at low energy contains either (1) 4d non-invertible topological quantum field theory (TQFT, above the energy gap with heavy fractionalized anyon excitations from 1d particle worldline and 2d string worldsheet, inaccessible directly from Dirac or Majorana mass gap of the 16th Weyl fermions [i.e., right-handed neutrinos], but accessible via a topological quantum phase transition), or (2) 5d invertible TQFT in extra dimensions. Above a higher energy scale, the discrete $X$ becomes dynamically gauged, the entangled Universe in 4d and 5d is mediated by Topological Force. Our model potentially resolves puzzles, surmounting sterile neutrinos and dark matter, in fundamental physics.

hep-th↗

arXiv2020

Unwinding Fermionic SPT Phases: Supersymmetry Extension

We show how 1+1-dimensional fermionic symmetry-protected topological states (SPTs, i.e. nontrivial short-range entangled gapped phases of quantum matter whose boundary exhibits 't Hooft anomaly and whose bulk cannot be deformed into a trivial tensor product state under finite-depth local unitary transformations only in the presence of global symmetries), indeed can be unwound to a trivial state by enlarging the Hilbert space via adding extra degrees of freedom and suitably extending the global symmetries. The extended projective global symmetry on the boundary can become supersymmetric in a specific sense, i.e., it contains group elements that do not commute with the fermion number parity $(-1)^F$, while the anti-unitary time-reversal symmetry becomes fractionalized. This also means we can uplift and remove certain exotic fermionic anomalies (e.g., "parity" anomaly in time-reversal or reflection symmetry) via appropriate supersymmetry extensions in terms of group extensions. We work out explicit examples for multi-layers of 1+1d Majorana fermion chains, then comment on models with Sachdev-Ye-Kitaev (SYK) interactions, intrinsic fermionic gapless SPTs protected by supersymmetry, and generalizations to higher spacetime dimensions via a cobordism theory.

cond-mat.str-el↗

arXiv2020

Non-Abelian Gauged Fracton Matter Field Theory: New Sigma Models, Superfluids and Vortices

By gauging a higher-moment polynomial degree global symmetry and a discrete charge conjugation (i.e., particle-hole) symmetry coupled to matter fields (two symmetries mutually non-commutative), we derive a new class of higher-rank tensor non-abelian gauge field theory with dynamically gauged fractonic matter fields: Non-abelian gauged fractons interact with a hybrid class of higher-rank (symmetric or generic non-symmetric) tensor gauge theory and anti-symmetric tensor topological field theory, generalizing [arXiv:1909.13879, 1911.01804]. We also apply a quantum phase transition similar to that between insulator v.s. superfluid/superconductivity (U(1) symmetry disordered phase described by a topological gauge theory or a disordered Sigma model v.s. U(1) global/gauge symmetry-breaking ordered phase described by a Sigma model with a U(1) target space underlying Goldstone modes): We can regard our tensor gauge theories as disordered phases, and we transient to their new ordered phases by deriving new Sigma models in continuum field theories. While one low energy theory is captured by degrees of freedom of rotor or scalar modes, another side of low energy theory has vortices and superfluids -- we explore non-abelian vortices (two types of vortices mutually interacting non-commutatively beyond an ordinary group structure) and their Cauchy-Riemann relation.

cond-mat.str-el↗