Proceedings of the International Workshop on Quantum Systems : new trends and methods, Minsk, Belarus, 3-7 June 1996

Y. S. Kim

Published Jan 1, 1997• 0 citations

Abstract

Numerical gauge theories with topological fidelity, A.P. Balachandran Lee-Yang Zeros and phase structure of non-compact lattice QED, I. Barbour Intrinsic irreversibility of quantum systems, A. Bohn Nonrelativistic quantum dynamics on manifolds, H-D. Doebner Underground particle astrophysics, G. Giacomelli Decoherence and time scales, Y.S. Kim Search for neutral Higgs Bosons, M. Krawczyk Integrals of motion and quantum tomography, V. Man'ko Coherent states map for MIC-Kepler system, A. Odzijewicz Two-photon decay of the MSSM Higgs particle, P. Osland Shielding and the Aharonov-Bohm effect, M. Peshkin Interacting Wess-Zumino-Witten systems, L.O'Raifeartaigh Particle physics in international collaboration - the future, D. Saxon Long-range spin-dependent forces, J. Sucher.

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Proceedings of the International Workshop on Quantum Systems : new trends and methods, Minsk, Belarus, 3-7 June 1996

Y. S. Kim

Published Jan 1, 1997• 0 citations

OpenAlex

Abstract

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Dual topological nonlinear sigma models of $\text{QED}$ theory by dimensional reduction and monopole operatorsDual topological nonlinear sigma models of $\text{QED}$ theory by dimensional reduction and monopole operators

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Nonlinear $σ$ models (NLSM) with topological terms, i.e., Wess-Zumino-Witten (WZW) terms, or topological NLSM, are potent descriptions of many critical points and phases beyond the Landau paradigm. These critical systems include the deconfined quantum critical points (DQCP) between the Neel order and valance bond solid, and the Dirac spin liquid, in which the topological NLSMs are dual descriptions of the corresponding fermionic models or $\text{QED}$ theory. In this paper, we propose a dimensional reduction scheme to derive the $\text{U}(1)$ gauged topological NLSM in $n$ -dimensional spacetime on a general target space represented by a Hermitian matrix from the dual QED theory. Compared with the famous Abanov-Wiegmann (AW) mechanism, which generally requires the fermions to be Dirac fermions in the infrared (IR), our method is also applicable to non-relativistic fermions in IR, which can have quadratic dispersion or even a Fermi surface. As concrete examples, we construct several two dimensional lattice models, whose IR theories are all the $N_f=4$ $\text{QED}_3$ with fermions of quadratic dispersion and show that its topological NLSM dual description has level-2 WZW terms on the Grassmannian manifold $\frac{\text{U(4)}}{\text{U(2)}\times \text{U(2)}}$ coupled with a dynamical $\text{U(1)}$ gauge field. We also study 't Hooft anomaly matching and the same effect of defects in both theories, such as interface, gauge monopoles and skyrmions, which further support our duality. Finally, we discuss how the macroscopic symmetries act on the $\text{U(1)}$ monopole operators and the corresponding quantum number.Nonlinear $σ$ models (NLSM) with topological terms, i.e., Wess-Zumino-Witten (WZW) terms, or topological NLSM, are potent descriptions of many critical points and phases beyond the Landau paradigm. These critical systems include the deconfined quantum critical points (DQCP) between the Neel order and valance bond solid, and the Dirac spin liquid, in which the topological NLSMs are dual descriptions of the corresponding fermionic models or $\text{QED}$ theory. In this paper, we propose a dimensional reduction scheme to derive the $\text{U}(1)$ gauged topological NLSM in $n$-dimensional spacetime on a general target space represented by a Hermitian matrix from the dual QED theory. Compared with the famous Abanov-Wiegmann (AW) mechanism, which generally requires the fermions to be Dirac fermions in the infrared (IR), our method is also applicable to non-relativistic fermions in IR, which can have quadratic dispersion or even a Fermi surface. As concrete examples, we construct several two dimensional lattice models, whose IR theories are all the $N_f=4$ $\text{QED}_3$ with fermions of quadratic dispersion and show that its topological NLSM dual description has level-2 WZW terms on the Grassmannian manifold $\frac{\text{U(4)}}{\text{U(2)}\times \text{U(2)}}$ coupled with a dynamical $\text{U(1)}$ gauge field. We also study 't Hooft anomaly matching and the same effect of defects in both theories, such as interface, gauge monopoles and skyrmions, which further support our duality. Finally, we discuss how the macroscopic symmetries act on the $\text{U(1)}$ monopole operators and the corresponding quantum number.

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Dual topological nonlinear sigma models of

\text{QED}

theory by dimensional reduction and monopole operators

Nonlinear

σ

models (NLSM) with topological terms, i.e., Wess-Zumino-Witten (WZW) terms, or topological NLSM, are potent descriptions of many critical points and phases beyond the Landau paradigm. These critical systems include the deconfined quantum critical points (DQCP) between the Neel order and valance bond solid, and the Dirac spin liquid, in which the topological NLSMs are dual descriptions of the corresponding fermionic models or

\text{QED}

theory. In this paper, we propose a dimensional reduction scheme to derive the

\text{U}(1)

gauged topological NLSM in

n

-dimensional spacetime on a general target space represented by a Hermitian matrix from the dual QED theory. Compared with the famous Abanov-Wiegmann (AW) mechanism, which generally requires the fermions to be Dirac fermions in the infrared (IR), our method is also applicable to non-relativistic fermions in IR, which can have quadratic dispersion or even a Fermi surface. As concrete examples, we construct several two dimensional lattice models, whose IR theories are all the

N_f=4

\text{QED}_3

with fermions of quadratic dispersion and show that its topological NLSM dual description has level-2 WZW terms on the Grassmannian manifold

\frac{\text{U(4)}}{\text{U(2)}\times \text{U(2)}}

coupled with a dynamical

\text{U(1)}

gauge field. We also study 't Hooft anomaly matching and the same effect of defects in both theories, such as interface, gauge monopoles and skyrmions, which further support our duality. Finally, we discuss how the macroscopic symmetries act on the

\text{U(1)}

monopole operators and the corresponding quantum number.

\mathrm{SU}(n)

excitations are driven by an underlying multibody interaction. As a minimal model in the infrared, we explore the realization of an archetypical strong-coupling quantum field theory, the

\mathrm{SU}(n)

Wess-Zumino-Witten model, and discuss a diagnostic tool to map the conformal data of the field theory to the static and dynamical correlators of the fluctuating photons in the guided mode.