A
bstract
We investigate a higher-group structure of massless axion electrodynamics in (3 + 1) dimensions. By using the background gauging method, we show that the higher-form symmetries necessarily ...have a global semistrict 3-group (2-crossed module) structure, and exhibit ’t Hooft anomalies of the 3-group. In particular, we find a cubic mixed ’t Hooft anomaly between 0-form and 1-form symmetries, which is specific to the higher-group structure.
A
bstract
We systematically derive the collision term for the axial kinetic theory, a quantum kinetic theory delineating the coupled dynamics of the vector/axial charges and spin transport carried by ...the massive spin-1/2 fermions traversing a medium. We employ the Wigner-function approach and propose a consistent power-counting scheme where the axial-charge distribution function, a non-conserved quantity for massive particles, is accounted as the first-order quantity in the
ħ
expansion, while the vector-charge distribution function the zeroth-order quantity. This specific power-counting scheme allows us to organize a reduced
ħ
expansion for the collision term and to formally identity the spin- diffusion effect and the spin-polarization effect at the same order. We confirm that the obtained collisional axial kinetic theory smoothly reduces to the chiral kinetic theory in the massless limit, serving as a consistency check. In the absence of electromagnetic fields, we further present the simplified axial kinetic equations suitable for tracking dynamical spin polarization of heavy and light fermions, respectively. As an application to the weakly coupled quark-gluon plasma at high temperature, we compute the spin-diffusion term for massive quarks within the leading-log approximation. The formal expression for the first- order terms provides a path toward evaluation of the spin polarization effect in quantum chromodynamics.
A
bstract
We study the Hamiltonian lattice Yang-Mills theory based on spin networks that provide a useful basis to represent the physical states satisfying the Gauss law constraints. We focus on ...SU(2) Yang-Mills theory in (2 + 1) dimensions. Following the string-net model, we introduce a regularization of the Kogut-Susskind Hamiltonian of lattice Yang-Mills theory based on the
q
deformation, which respects the (discretized) SU(2) gauge symmetry as quantum group, i.e., SU(2)
k
, and enables implementation of the lattice Yang-Mills theory both in classical and quantum algorithms by referring to those of the string-net model. Using the regularized Hamiltonian, we study quantum scars in a nonabelian gauge theory. Quantum scars are nonthermal energy eigenstates arising in the constrained quantum many-body systems. We find that quantum scars from zero modes, which have been found in abelian gauge theories arise even in a nonabelian gauge theory. We also show the spectrum of a single-plaquette model for SU(2)
k
and SU(3)
k
with naive cutoff and that based on the
q
-deformation to discuss cutoff dependence of the formulation.
The chiral kinetic theory of Weyl fermions with collisions in the presence of weak electric and magnetic fields is derived from quantum field theories. It is found that the side-jump terms in the ...perturbative solution of Wigner functions play a significant role for the derivation. Moreover, such terms manifest the breaking of Lorentz symmetry for distribution functions. The Lorentz covariance of Wigner functions thus leads to modified Lorentz transformation associated with side-jump phenomena further influenced by background fields and collisions.
A
bstract
We study SU(3) Yang-Mills theory in (2 + 1) dimensions based on networks of Wilson lines. With the help of the
q
deformation, networks respect the (discretized) SU(3) gauge symmetry as a ...quantum group, i.e., SU(3)
k
, and may enable implementations of SU(3) Yang-Mills theory in quantum and classical algorithms by referring to those of the stringnet model. As a demonstration, we perform a mean-field computation of the groundstate of SU(3)
k
Yang-Mills theory, which is in good agreement with the conventional Monte Carlo simulation by taking sufficiently large
k
. The variational ansatz of the mean-field computation can be represented by the tensor networks called infinite projected entangled pair states. The success of the mean-field computation indicates that the essential features of Yang-Mills theory are well described by tensor networks, so that they may be useful in numerical simulations of Yang-Mills theory.
We study higher-form symmetries in a low-energy effective theory of a massless axion coupled with a photon in (3+1) dimensions. It is shown that the higher-form symmetries of this system are ...accompanied by a semistrict 3-group (2-crossed module) structure, which can be found by the correlation functions of symmetry generators of the higher-form symmetries. We argue that the Witten effect and anomalous Hall effect in the axion electrodynamics can be described in terms of 3-group transformations.
We study higher-form symmetries and a higher group in the low energy limit of a (3+1)-dimensional axion electrodynamics with a massive axion and a massive photon. A topological field theory ...describing topological excitations with the axion-photon coupling, which we call a topological axion electrodynamics, is obtained in the low energy limit. Higher-form symmetries of the topological axion electrodynamics are specified by equations of motion and Bianchi identities. We find that there are induced anyons on the intersections of symmetry generators. By a link of worldlines of the anyons, we show that the worldvolume of an axionic domain wall is topologically ordered. We further specify the underlying mathematical structure elegantly describing all salient features of the theory to be a 4-group.
A
bstract
We show detailed derivation of the electric conductivity of quark matter at finite temperature and density under a magnetic field. We especially focus on the longitudinal electric ...conductivity along the magnetic direction and establish the field-theoretical description of the negative magnetoresistance as observed in chiral materials. With increasing magnetic field our microscopic calculation leads to changing behavior from approximately quadratic to asymptotically linear dependence of the electric conductivity, while the magnetic dependence is quadratic in the conventional relaxation time approximation. The presented formulation founds a firm basis for the physical interpretation of the negative magnetoresistance in terms of the particle and the hydrodynamic contributions, as well as it offers general methodology applicable for various transport coefficients.
We discuss the effect of rapid rotation on the phase diagram of hadronic matter. The energy dispersion relation is shifted by an effective chemical potential induced by rotation. This suggests that ...rotation should lower the critical temperature of chiral restoration, but it is still controversial how the deconfinement temperature should change as a function of angular velocity. We adopt the hadron resonance gas model as an approach free from fitting parameters. We identify the deconfinement from the thermodynamic behavior and find that rotation decreases the deconfinement temperature. We also discuss the spatial inhomogeneity of the pressure and give a semi-quantitative estimate of the moment of inertia.
A
bstract
We propose an effective field theory for branes with higher-form symmetry as a generalization of ordinary Landau theory, which is an extension of the previous work by Iqbal and McGreevy for ...one-dimensional objects to an effective theory for
p
-dimensional objects. In the case of a
p
-form symmetry, the fundamental field
ψ
C
p
is a functional of
p
-dimensional closed brane
C
p
embedded in a spacetime. As a natural generalization of ordinary field theory, we call this theory the
brane field theory
. In order to construct an action that is invariant under higher-form transformation, we generalize the idea of
area derivative
for one-dimensional objects to higher-dimensional ones. Following this, we discuss various fundamental properties of the brane field based on the higher-form invariant action. It is shown that the classical solution exhibits the area law in the unbroken phase of U(1)
p
-form symmetry, while it indicates a constant behavior in the broken phase for the large volume limit of
C
p
. In the latter case, the low-energy effective theory is described by the
p
-form Maxwell theory. We also discuss brane-field theories with a discrete higher-form symmetry and show that the low-energy effective theory becomes a BF-type topological field theory, resulting in topological order. Finally, we present a concrete brane-field model that describes a superconductor from the point of view of higher-form symmetry.
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