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Non-perturbative defect one-point functions in planar N=4 super-Yang-Mills
Nuclear Physics B ( IF 2.8 ) Pub Date : 2020-07-28 , DOI: 10.1016/j.nuclphysb.2020.115120
Shota Komatsu , Yifan Wang

The four dimensional N=4 super-Yang-Mills (SYM) theory exhibits rich dynamics in the presence of codimension-one conformal defects. The new structure constants of the extended operator algebra consist of one-point functions of local operators which are nonvanishing due to the defect insertion and carry nontrivial coupling dependence. We study an important class of half-BPS superconformal defects engineered by D5 branes that share three common directions with the D3 branes and involve Nahm pole configurations for the SYM fields on the D3 brane worldvolume. In the planar large N limit, we obtain non-perturbative results in the 't Hooft coupling λ for the defect one-point functions of both BPS and non-BPS operators, building upon recent progress in localization [1] and integrability methods [2], [3].

For BPS operator insertions in the SYM with D5-brane type boundary or interface, we derive an effective two dimensional defect-Yang-Mills (dYM) theory from supersymmetric localization, which gives an efficient way to extract defect observables and generates a novel matrix model for the defect one-point function. By solving the matrix model in the large N limit, we obtain exact results in λ which interpolate between perturbative Feynman diagram contributions in the weak coupling limit and IIB string theory predictions on AdS5×S5 in the strong coupling regime, providing a precision test of AdS/CFT with interface defects. For general non-BPS operators, we develop a non-perturbative bootstrap-type program for integrable boundary states on the worldsheet of the IIB string theory, corresponding to the interface defects in the planar SYM. Such integrable boundary states are constrained by a set of general consistency conditions for which we present explicit solutions that reproduce and extend the known results at weak coupling from integrable spin-chain methods.



中文翻译:

平面中的非扰动缺陷一点函数 ñ=4 超级杨米尔斯

四个维度 ñ=4在余维一共形缺陷的存在下,超级杨米尔斯(SYM)理论显示出丰富的动力学。扩展算子代数的新结构常数由局部算子的单点函数组成,这些函数由于缺陷的插入而消失,并具有非平凡的耦合依赖性。我们研究了由D5黄铜制造的一类重要的半BPS超共形缺陷,这些缺陷与D3黄铜具有三个共同的方向,并且涉及D3黄铜世界上SYM场的Nahm极配置。在平面大N极限中,我们基于定位[1]和可积性方法[2]的最新进展,针对BPS和非BPS算子的缺陷单点函数在't Hooft耦合λ中获得了非扰动结果。],[3]。

对于B5算子类型边界或界面的SYM中的BPS运算符插入,我们从超对称定位中推导出了有效的二维缺陷-杨-米尔斯(dYM)理论,该理论提供了一种有效的方法来提取缺陷可观察值并生成新的矩阵模型用于缺陷单点功能。通过在大N极限处求解矩阵模型,我们获得了λ的精确结果,该结果插值在弱耦合极限中的微扰动费曼图贡献和关于Ib弦理论的预测之间一种d小号5×小号5在强耦合条件下,可对带有界面缺陷的AdS / CFT进行精确测试。对于一般的非BPS算子,我们针对IIB弦理论的世界表上的可积边界状态开发了一个非扰动的自举类型程序,该程序对应于平面SYM中的界面缺陷。这样的可积边界状态受一组一般一致性条件的约束,为此,我们提出了显式解,这些解在可积分自旋链方法的弱耦合下重现并扩展了已知结果。

更新日期:2020-08-03
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