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arXiv 0912.0417hep-th
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非仿射丛中的域。III。弦和更高膜中的有效对称性和守恒流

Fields in nonaffine bundles. III. Effective symmetries and conserved currents in strings and higher branes

Brandon Carter

摘要:

先前开发的形式主义的协变处理的多标量场(如在非线性西格玛模型)的相关目标空间是不是仿射型-但弯曲-的原则被概括。它们的应用从普通的调和模型扩展到更一般的“调和”场模型,重点是场被限制在弦或更高的膜世界片上的情况,并且相关的内部对称群是非阿贝尔的,因此相应的电荷电流守恒的条件变得相当微妙,特别是当对称性被衡量时。注意力也被给予了不同种类的电流守恒的条件--代表广义动量或能量的表面通量--与内部目标空间的对称性无关,而是与底层时空背景结构的对称性有关,包括度量和任何相关的规范场。为了使相应的电流守恒,后者不需要是明显不变的:守恒模规范调整就足够了。最简单的情况是“强”对称,即在有效李导数(普通李导数的适当规范调整修改)作用下的不变性。当有效对称性是更一般的“弱”对称性时,电流的动力学部分本身并不守恒,而只有在被来自背景的适当贡献补充之后才守恒。

英文摘要:

The principles of a previously developed formalism for the covariant treatment of multi-scalar fields for which (as in a nonlinear sigma model) the relevant target space is not of affine type -- but curved -- are recapitulated. Their application is extended from ordinary harmonic models to a more general category of "harmonious" field models, with emphasis on cases in which the field is confined to a string or higher brane worldsheet, and for which the relevant internal symmetry group is non Abelian, so that the conditions for conservation of the corresponding charge currents become rather delicate, particularly when the symmetry is gauged. Attention is also given to the conditions for conservation of currents of a different kind -- representing surface fluxes of generalised momentum or energy -- associated with symmetries not of the internal target space but of the underlying spacetime background structure, including the metric and any relevant gauge field. For the corresponding current to be conserved the latter need not be manifestly invariant: preservation modulo a gauge adjustment will suffice. The simplest case is that of "strong" symmetry, meaning invariance under the action of an effective Lie derivative (an appropriately gauge adjusted modification of an ordinary Lie derivative). When the effective symmetry is of the more general "weak" kind, the kinetic part of the current is not conserved by itself but only after being supplemented by a suitable contribution from the background.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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