Publications

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Fractionalization of coset non-invertible symmetry and exotic Hall conductance

Po-Shen Hsin, Ryohei Kobayashi, Carolyn Zhang

SciPost Phys. 17, 095 (2024) · published 27 September 2024 | · pdf

We investigate fractionalization of non-invertible symmetry in (2+1)D topological orders. We focus on coset non-invertible symmetries obtained by gauging non-normal subgroups of invertible $0$-form symmetries. These symmetries can arise as global symmetries in quantum spin liquids, given by the quotient of the projective symmetry group by a non-normal subgroup as invariant gauge group. We point out that such coset non-invertible symmetries in topological orders can exhibit symmetry fractionalization: each anyon can carry a "fractional charge" under the coset non-invertible symmetry given by a gauge invariant superposition of fractional quantum numbers. We present various examples using field theories and quantum double lattice models, such as fractional quantum Hall systems with charge conjugation symmetry gauged and finite group gauge theory from gauging a non-normal subgroup. They include symmetry enriched $S_3$ and $O(2)$ gauge theories. We show that such systems have a fractionalized continuous non-invertible coset symmetry and a well-defined electric Hall conductance. The coset symmetry enforces a gapless edge state if the boundary preserves the continuous non-invertible symmetry. We propose a general approach for constructing coset symmetry defects using a "sandwich" construction: non-invertible symmetry defects can generally be constructed from an invertible defect sandwiched by condensation defects. The anomaly free condition for finite coset symmetry is also identified.

1 citation
Higgs-confinement transitions in QCD from symmetry protected topological phases

Thomas T. Dumitrescu, Po-Shen Hsin

SciPost Phys. 17, 093 (2024) · published 26 September 2024 | · pdf

In gauge theories with fundamental matter there is typically no sharp way to distinguish confining and Higgs regimes, e.g. using generalized global symmetries acting on loop order parameters. It is standard lore that these two regimes are continuously connected, as has been explicitly demonstrated in certain lattice and continuum models. We point out that Higgsing and confinement sometimes lead to distinct symmetry protected topological (SPT) phases -- necessarily separated by a phase transition -- for ordinary global symmetries. We present explicit examples in 3+1 dimensions, obtained by adding elementary Higgs fields and Yukawa couplings to QCD while preserving parity $\mathsf{P}$ and time reversal $\mathsf{T}$. In a suitable scheme, the confining phases of these theories are trivial SPTs, while their Higgs phases are characterized by non-trivial $\mathsf{P}$- and $\mathsf{T}$-invariant theta-angles $\theta_f, \theta_g = \pi$ for flavor or gravity background gauge fields, i.e. they are topological insulators or superconductors. Finally, we consider conventional three-flavor QCD (without elementary Higgs fields) at finite $U(1)_B$ baryon-number chemical potential $\mu_B$, which preserves $\mathsf{P}$ and $\mathsf{T}$. At very large $\mu_B$, three-flavor QCD is known to be a completely Higgsed color superconductor that also spontaneously breaks $U(1)_B$. We argue that this high-density phase is in fact a gapless SPT, with a gravitational theta-angle $\theta_g = \pi$ that safely co-exists with the $U(1)_B$ Nambu-Goldstone boson. We explain why this SPT motivates unexpected transitions in the QCD phase diagram, as well as anomalous surface modes at the boundary of quark-matter cores inside neutron stars.

5 citations
On perturbation around closed exclusion processes

Masataka Watanabe

SciPost Phys. 17, 092 (2024) · published 25 September 2024 | · pdf

We derive the formula for the stationary states of particle-number conserving exclusion processes infinitesimally perturbed by inhomogeneous adsorption and desorption. The formula not only proves but also generalises the conjecture proposed in [Phys. Rev. E 97, 032135] to account for inhomogeneous adsorption and desorption. As an application of the formula, we draw part of the phase diagrams of the open asymmetric simple exclusion process with and without Langmuir kinetics, correctly reproducing known results.

1 citation
Background independent tensor networks

Chris Akers, Annie Y. Wei

SciPost Phys. 17, 090 (2024) · published 25 September 2024 | · pdf

Conventional holographic tensor networks can be described as toy holographic maps constructed from many small linear maps acting in a spatially local way, all connected together with "background entanglement", i.e. links of a fixed state, often the maximally entangled state. However, these constructions fall short of modeling real holographic maps. One reason is that their "areas" are trivial, taking the same value for all states, unlike in gravity where the geometry is dynamical. Recently, new constructions have ameliorated this issue by adding degrees of freedom that "live on the links". This makes areas non-trivial, equal to the background entanglement piece plus a new positive piece that depends on the state of the link degrees of freedom. Nevertheless, this still has the downside that there is background entanglement, and hence it only models relatively limited code subspaces in which every area has a definite minimum value. In this note, we simply point out that a version of these constructions goes one step further: they can be background independent, with no background entanglement in the holographic map. This is advantageous because it allows tensor networks to model holographic maps for larger code subspaces. In addition to pointing this out, we address some subtleties involved in making it work.

3 citations
Higher-form symmetry and chiral transport in real-time Abelian lattice gauge theory

Arpit Das, Adrien Florio, Nabil Iqbal, Napat Poovuttikul

SciPost Phys. 17, 085 (2024) · published 19 September 2024 | · pdf

We study classical lattice simulations of theories of electrodynamics coupled to charged matter at finite temperature, interpreting them using the higher-form symmetry formulation of magnetohydrodynamics (MHD). We compute transport coefficients using classical Kubo formulas on the lattice and show that the properties of the simulated plasma are in complete agreement with the predictions from effective field theories. In particular, the higher-form formulation allows us to understand from hydrodynamic considerations the relaxation rate of axial charge in the chiral plasma observed in previous simulations. A key point is that the resistivity of the plasma – defined in terms of Kubo formulas for the electric field in the 1-form formulation of MHD – remains a well-defined and predictive quantity at strong electromagnetic coupling. However, the Kubo formulas used to define the conventional conductivity vanish at low frequencies due to electrodynamic fluctuations, and thus the concept of the conductivity of a gauged electric current must be interpreted with care.

1 citation
Two infinite families of facets of the holographic entropy cone

Bartlomiej Czech, Yu Liu, Bo Yu

SciPost Phys. 17, 084 (2024) · published 19 September 2024 | · pdf

We verify that the recently proven infinite families of holographic entropy inequalities are maximally tight, i.e. they are facets of the holographic entropy cone. The proof is technical but it offers some heuristic insight. On star graphs, both families of inequalities quantify how concentrated/spread information is with respect to a dihedral symmetry acting on subsystems. In addition, toric inequalities viewed in the K-basis show an interesting interplay between four-party and six-party perfect tensors.

3 citations
Emergent generalized symmetries in ordered phases and applications to quantum disordering

Salvatore D. Pace

SciPost Phys. 17, 080 (2024) · published 13 September 2024 | · pdf

We explore the rich landscape of higher-form and non-invertible symmetries that emerge at low energies in generic ordered phases. Using that their charge is carried by homotopy defects (i.e., domain walls, vortices, hedgehogs, etc.), in the absence of domain walls we find that their symmetry defects in $D$-dimensional spacetime are described by $(D-1)$-representations of a $(D-1)$-group that depends only on the spontaneous symmetry-breaking (SSB) pattern of the ordered phase. These emergent symmetries are not spontaneously broken in the ordered phase. We show that spontaneously breaking them induces a phase transition into a nontrivial disordered phase that can have symmetry-enriched (non-)Abelian topological orders, photons, and even more emergent symmetries. This SSB transition is between two distinct SSB phases--an ordinary and a generalized one--making it a possible generalized deconfined quantum critical point. We also investigate the 't Hooft anomalies of these emergent symmetries and conjecture that there is always a mixed anomaly between them and the microscopic symmetry spontaneously broken in the ordered phase. One way this anomaly can manifest is through the fractionalization of the microscopic symmetry's quantum numbers. Our results demonstrate that even the most exotic generalized symmetries emerge in ordinary phases and provide a valuable framework for characterizing them and their transitions.

9 citations
RG flows in de Sitter: C-functions and sum rules

Manuel Loparco

SciPost Phys. 17, 079 (2024) · published 12 September 2024 | · pdf

We study the renormalization group flow of unitary Quantum Field Theories on two-dimensional de Sitter (dS) spacetime. We prove the existence of two functions of the radius of dS that interpolate between the central charges of the UV and IR fixed points of the flow when tuning the radius $R$ while keeping the mass scales fixed. The first is constructed from certain components of the two-point function of the stress tensor evaluated at antipodal separation. The second is the spectral weight of the stress tensor in the $\Delta=2$ discrete series. This last fact implies that the stress tensor of any unitary QFT in dS$_2$ must interpolate between the vacuum and states in the $\Delta=2$ discrete series irrep. We verify that the c-functions are monotonic for intermediate radii in the free massive boson and free massive fermion theories, but we lack a general proof of said monotonicity. We derive a variety of sum rules that relate the central charges and the c-functions to integrals of the two-point function of the trace of the stress tensor and to integrals of its spectral densities. The positivity of these formulas implies $c^{UV}≥ c^{IR}$. In the infinite radius limit the sum rules reduce to the well known formulas in flat space. Throughout the paper, we prove some general properties of the spectral decomposition of the stress tensor in dS$_{d+1}$.

2 citations
Lorentzian contours for tree-level string amplitudes

Lorenz Eberhardt, Sebastian Mizera

SciPost Phys. 17, 078 (2024) · published 11 September 2024 | · pdf

We engineer compact contours on the moduli spaces of genus-zero Riemann surfaces that achieve analytic continuation from Euclidean to Lorentzian worldsheets. These generalized Pochhammer contours are based on the combinatorics of associahedra and make the analytic properties of tree-level amplitudes entirely manifest for any number and type of external strings. We use them in practice to perform first numerical computations of open and closed string amplitudes directly in the physical kinematics for $n=4,5,6,7,8,9$. We provide a code that allows anyone to do such computations.

1 citation
On a $\mathbb{Z}_3$-valued discrete topological term in 10d heterotic string theories

Yuji Tachikawa, Hao Y. Zhang

SciPost Phys. 17, 077 (2024) · published 11 September 2024 | · pdf

We show that the low-energy effective actions of two ten-dimensional supersymmetric heterotic strings are different by a $\mathbb{Z}_3$-valued discrete topological term even after we turn off the $E_8×E_8$ and $Spin(32)/\mathbb{Z}_2$ gauge fields. This will be demonstrated by considering the inflow of normal bundle anomaly to the respective NS5-branes from the bulk. This result will be used to show further that the $Spin(16)×Spin(16)$ non-tachyonic non-supersymmetric heterotic string has the same non-zero $\mathbb{Z}_3$-valued discrete topological term. We will also explain the relation of our findings to the theory of topological modular forms. The paper is written as a string theory paper, except for an appendix translating the content in mathematical terms. We will explain there that our finding identifies a representative of the $\mathbb{Z}/3$-torsion element of $\pi_{-32}\mathrm{TMF}$ as a particular self-dual vertex operator superalgebra of $c=16$ and how we utilize string duality to arrive at this statement.

2 citations

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