The 2-dimensionalN=2 supersymmetric Yang-Mills model on the discrete space-time lattice

Iwamoto, Hiroaki; Aratyn, H.; Zímerman, A. H.

doi:10.1007/bf01559598

Cited by 2 publications

(3 citation statements)

References 9 publications

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“…(96) It is more instructive to focus first on the linear stress tensor, thinking of its role in problems of adhesion and of contact in general. In this case, the linear stress tensor is given by (77), unchanged in its form with respect to the homogenous case,…”

Section: Applications: Heterogenous Membranes External Forcesmentioning

confidence: 99%

“…As a second example of an external force acting on a lipid membrane, we consider a spatially varying external magnetic field B(X), to illustrate the formulation. The lipid membrane is considered as a diamagnetic material, and the effect of the magnetic field on the lipid constituents is described by an alignment energy density [75][76][77] F…”

Section: External Forces and Constraintsmentioning

confidence: 99%

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Elastic Bending Energy: A Variational Approach

Capovilla¹

2017

JGSP

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Geometric continuum models for fluid lipid membranes are considered using classical field theory, within a covariant variational approach. The approach is cast as a higher-derivative Lagrangian formulation of continuum classical field theory, and it can be seen as a covariant version of the field theoretical variational approach that uses the height representation. This novel Lagrangian formulation is presented first for a generic reparametrization invariant geometric model, deriving its equilibrium condition equation, or shape equation, and its linear and angular stress tensors, using the classical Canham-Helfrich elastic bending energy for illustration. The robustness of the formulation is established by extending it to the presence of external forces, and to the case of heterogenous lipid membranes, breaking reparametrization invariance. In addition, a useful and compact general expression for the second variation of the free energy is obtained within the Lagrangian formulation, as a first step towards the study of the stability of membrane configurations. The simple structure of the expressions derived for the basic entities that appear in the mechanics of a lipid membrane is a direct consequence of the well established power of a Lagrangian variational approach. The paper is self-contained, and it is meant to provide, besides a new framework, also a convenient introduction to the mechanics of lipid membranes.

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Section: Applications: Heterogenous Membranes External Forcesmentioning

confidence: 99%

Section: External Forces and Constraintsmentioning

confidence: 99%

Elastic Bending Energy: A Variational Approach

Capovilla¹

2017

JGSP

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“…Attempts were made to construct such theories in a Hamiltonian formalism in [28,29]. A similar approach was used in [30] to construct a SYM model in Euclidean space using only some of the component Kähler-Dirac fields. However it is only in the context of twisted supersymmetry that the full power of the Kähler-Dirac approach can be realized.…”

Section: Interpretation In Terms Kähler-dirac Fieldsmentioning

confidence: 99%

A geometrical approach toN=2 super Yang-Mills theory on the two dimensional lattice

Catterall

2004

J. High Energy Phys.

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We propose a discretization of two dimensional Euclidean Yang-Mills theories with N = 2 supersymmetry which preserves exactly both gauge invariance and an element of supersymmetry. The approach starts from the twisted form of the continuum super Yang Mills action which we show may be written in terms of two real Kähler-Dirac fields whose components transform into each other under the twisted supersymmetry. Once the theory is written in this geometrical language it is straightforward to discretize by mapping the component tensor fields to appropriate geometrical structures in the lattice and by replacing the continuum exterior derivative and its adjoint by appropriate lattice covariant difference operators. The lattice action is local and possesses a unique vacuum state while the use of Kähler-Dirac fermions ensures the model does not exhibit spectrum doubling.

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The 2-dimensionalN=2 supersymmetric Yang-Mills model on the discrete space-time lattice

Cited by 2 publications

References 9 publications

Elastic Bending Energy: A Variational Approach

Elastic Bending Energy: A Variational Approach

A geometrical approach toN=2 super Yang-Mills theory on the two dimensional lattice

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