A gauge theory for shallow water

Tong, David

doi:10.21468/scipostphys.14.5.102

Cited by 10 publications

(14 citation statements)

References 40 publications

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“…The first equation (1a) is the mass conservation equation, that the 3 dimensional fluid is incompressible and (1b) is Newton's second law (Navier-Stokes or Euler equation), in which g is the gravitational constant and f is the Coriolis parameter, which is a constant. 1 As we see these equations are nonlinear for both variables H, u i . This theory has two global Noether currents which satisfy…”

Section: Shallow Water Gauge Theory: a Reviewmentioning

confidence: 85%

“…These two conservation equations, upon Noether's theorem, may be associated with symmetries of the system. In an interesting recent paper [1], it was argued that these two conservation equations may be naturally described by a 2 + 1 dimensional u(1) × u(1) gauge theory. In this gauge theory description Kelvin's theorem corresponds to the Gauss law.…”

mentioning

confidence: 99%

“…Shallow water system is governed by nonlinear equations but is well approximated by a linear system when amplitude of the waves is much smaller than the height of the fluid. The linear system is described by a 2+1 dimensional Maxwell-Chern-Simons (MCS) gauge theory [1]. The study in [1] was motivated by bridging between the two dimensional condensed matter systems, in particular quantum Hall system, and the shallow water mechanics focusing on the topological features of the two sides (for further discussion see [5,6]).…”

mentioning

confidence: 99%

“…The linear system is described by a 2+1 dimensional Maxwell-Chern-Simons (MCS) gauge theory [1]. The study in [1] was motivated by bridging between the two dimensional condensed matter systems, in particular quantum Hall system, and the shallow water mechanics focusing on the topological features of the two sides (for further discussion see [5,6]).…”

mentioning

confidence: 99%

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Shallow water memory: Stokes and Darwin drifts

Sheikh-Jabbari,

Taghiloo,

Vahidinia

2023

SciPost Phys.

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It has been shown in [SciPost Phys. 14, 102 (2023)] that shallow water in the Euler description admits a dual gauge theory formulation. We show in the Lagrange description this gauge symmetry is a manifestation of the 2 dimensional area-preserving diffeomorphisms. We find surface charges associated with the gauge symmetry and their algebra, and study their physics in the shallow water system. In particular, we provide a reinterpretation of the Kelvin circulation theorem in terms of conserved charges. In the linear shallow water case, the charges form a u(1) current algebra with level proportional to the Coriolis parameter over the height of the fluid. We also study memory effect for the gauge theory description of the linearized shallow water and show Euler, Stokes and Darwin drifts can be understood as a memory effect and/or change of the surface charges in the gauge theory description.

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Section: Shallow Water Gauge Theory: a Reviewmentioning

confidence: 85%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Shallow water memory: Stokes and Darwin drifts

Sheikh-Jabbari,

Taghiloo,

Vahidinia

2023

SciPost Phys.

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“…If one neglects the hopping terms at very large coupling, the theory becomes ultra-local. Ultra-local models like these are called Carrollian field theories, which have recently gained interest in condensed matter [60,61], fluid dynamics [62][63][64][65], high energy [66][67][68] and gravitational physics [69,70] for diverse inquiries. In particular, fermionic models with these symmetries have been dealt with in detail in [71][72][73].…”

Section: Introductionmentioning

confidence: 99%

Entanglement of edge modes in (very) strongly correlated topological insulators

Ara,

Basu,

Mathew

et al. 2024

J. Phys.: Condens. Matter

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Identifying topological phases for a strongly correlated theory remains a non-trivial task, as defining order parameters, such as Berry phases, is not straightforward. Quantum information theory is capable of identifying topological phases for a theory that exhibits quantum phase transition with a suitable definition of order parameters that are related to different entanglement measures for the system. In this work, we study entanglement entropy for a coupled SSH model, both in the presence and absence of Hubbard interaction and at varying interaction strengths. For the free theory, edge entanglement acts as an order parameter, which is supported by analytic calculations and numerical (DMRG) studies. We calculate the symmetry-resolved entanglement and demonstrate the equipartition of entanglement for this model which itself acts as an order parameter when calculated for the edge modes. As the DMRG calculation allows one to go beyond the free theory, we study the entanglement structure of the edge modes in the presence of on-site Hubbard interaction for the same model. A sudden reduction of edge entanglement is obtained as interaction is switched on. The explanation for this lies in the change in the size of the degenerate subspaces in the presence and absence of interaction. We also study the signature of entanglement when the interaction strength becomes extremely strong and demonstrate that the edge entanglement remains protected. In this limit, the energy eigenstates essentially become a tensor product state, implying zero entanglement. However, a remnant entropy survives in the non-trivial topological phase, which is exactly due to the entanglement of the edge modes.

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What can abelian gauge theories teach us about kinematic algebras?

Armstrong-Williams,

Nagy,

White

et al. 2024

J. High Energ. Phys.

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The phenomenon of BCJ duality implies that gauge theories possess an abstract kinematic algebra, mirroring the non-abelian Lie algebra underlying the colour information. Although the nature of the kinematic algebra is known in certain cases, a full understanding is missing for arbitrary non-abelian gauge theories, such that one typically works outwards from well-known examples. In this paper, we pursue an orthogonal approach, and argue that simpler abelian gauge theories can be used as a testing ground for clarifying our understanding of kinematic algebras. We first describe how classes of abelian gauge fields are associated with well-defined subalgebras of the diffeomorphism algebra. By considering certain special subalgebras, we show that one may construct interacting theories, whose kinematic algebras are inherited from those already appearing in a related abelian theory. Known properties of (anti-)self-dual Yang-Mills theory arise in this way, but so do new generalisations, including self-dual electromagnetism coupled to scalar matter. Furthermore, a recently obtained non-abelian generalisation of the Navier-Stokes equation fits into a similar scheme, as does Chern-Simons theory. Our results provide useful input to further conceptual studies of kinematic algebras.

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A gauge theory for shallow water

Cited by 10 publications

References 40 publications

Shallow water memory: Stokes and Darwin drifts

Shallow water memory: Stokes and Darwin drifts

Entanglement of edge modes in (very) strongly correlated topological insulators

What can abelian gauge theories teach us about kinematic algebras?

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