RG Domain Walls and Hybrid Triangulations
RG Domain Walls and Hybrid Triangulations
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RG 畴壁和混合三角剖分
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
R. Veen
中科院分区：
文献类型：
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作者：
Tudor Dimofte;D. Gaiotto;R. Veen
本文研究了用六维（2,0）SCFT的扭曲紧化进行几何描述的三维和四维N=2规范理论之间的相互作用。我们的主要目标是构建与任何三维共体相关的三维畴壁。我们发现我们可以建立各种三维理论来表示给定域壁上的局部自由度在各种四维二元框架中，包括UV s -双框架和IR Seiberg-Witten电磁双框架。我们特别关注由具有位置依赖耦合的四维拉格朗日量定义的Janus区域壁。如果在不同的UV对偶框架中，壁面两侧的耦合较弱，则Janus畴壁将减少为s -对偶壁，即编码UV对偶性的畴壁。如果一侧的耦合在IR和另一侧的耦合在UV下都很弱，那么Janus结构域壁就会减少到RG壁，即编码RG流特性的结构域壁。我们推导了与这两种类型的畴壁相关的三维几何形状，并通过基本的场论考虑和与量子Teichmuller理论的比较，在简单的例子中测试了它们的性质。我们的主要数学工具是基于理想三角剖分的框架平面SL(K)连接的参数化和量化。
This paper studies the interplay between the N=2 gauge theories in three and four dimensions that have a geometric description in terms of twisted compactification of the six-dimensional (2,0) SCFT. Our main goal is to construct the three-dimensional domain walls associated to any three-dimensional cobordism. We find that we can build a variety of 3d theories that represent the local degrees of freedom at a given domain wall in various 4d duality frames, including both UV S-dual frames and IR Seiberg-Witten electric-magnetic dual frames. We pay special attention to Janus domain walls, defined by four-dimensional Lagrangians with position-dependent couplings. If the couplings on either side of the wall are weak in different UV duality frames, Janus domain walls reduce to S-duality walls, i.e. domain walls that encode the properties of UV dualities. If the couplings on one side are weak in the IR and on the other weak in the UV, Janus domain walls reduce to RG walls, i.e. domain walls that encode the properties of RG flows. We derive the 3d geometries associated to both types of domain wall, and test their properties in simple examples, both through basic field-theoretic considerations and via comparison with quantum Teichmuller theory. Our main mathematical tool is a parametrization and quantization of framed flat SL(K) connections on these geometries based on ideal triangulations.
4D 规范理论和 2D CFT 缺陷的优点
影响因子：
5.4
作者：
Drukker N
通讯作者：
Drukker N