System of a D-brane in bosonic string theory on a constant $B$ field background is studied in order to obtain further insight into the bulk-boundary duality. Boundary states which describe arbitrary numbers of open-string tachyons and gluons are given. UV behaviors of field theories on the non-commutative world-volume are investigated by using these states. We take zero-slope limits of generating functions of one-loop amplitudes of gluons (and open-string tachyons) in which the region of the small open-string proper time is magnified. Existence of $B$ field allows the limits to be slightly different from the standard field theory limits of closed-string. They enable us to capture world-volume theories at a trans-string scale. In this limit the generating functions are shown to be factorized by two curved open Wilson lines (and their analogues) and become integrals on the space of paths with a Gaussian distribution around straight lines. These indicate a possibility that field theories on the non-commutative world-volume are topological at such a trans-string scale. We also give a proof of the Dhar-Kitazawa conjecture by making an explicit correspondence between the closed-string states and the paths. Momentum eigenstates of closed-string or momentum loops also play an important role in these analyses.
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机译:研究了在恒定的$ B $场背景下的玻色弦理论中的D膜系统,以便进一步了解体边界对偶性。给出了描述任意数量的开弦短子和胶子的边界状态。通过使用这些状态,研究了场理论在非交换世界体上的紫外线行为。我们采用零斜率极限来生成胶子(和开弦短子)的一环振幅函数,其中小的开弦适当时间的区域被放大了。 $ B $字段的存在允许该限制与封闭字符串的标准字段理论限制稍有不同。它们使我们能够以跨字符串的规模来捕捉世界量理论。在此极限下,生成函数显示为由两条弯曲的开放威尔逊线(及其类似物)分解,并在路径空间上以直线为高斯分布成为积分。这些表明非交换世界卷上的场论在这种跨字符串尺度上是拓扑学的可能性。我们还通过在闭弦状态与路径之间建立明确的对应关系来证明Dhar-Kitazawa猜想。闭弦或动量环的动量本征态在这些分析中也起着重要作用。
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