AdS_4的扭曲积与压缩拉伸七流形的规范对偶
The Gauge Dual of A Warped Product of AdS_4 and A Squashed and Stretched Seven-Manifold
摘要：
Corrado、Pilch和Warner在2001年发现了第二个11维解，其中升力中S^7的变形几何包含S^2 x S^2。我们用Franco，Klebanov和Rodriguez-Gomez最近描述的理论确定了这种背景下的规范对偶。它是U（N）× U（N）× U（N）规范理论，其中两个SU（2）手征二重态场B_1在（N，Nbar，1）中变换，B_2在（1，N，Nbar）中变换，C_1在（1，Nbar，N）中变换，C_2在（Nbar，N，1）中变换，伴随场Φ在（1，adj，1）表示中变换.通过在伴随场Φ中加入质量项，确定了AdS_4超引力场与IR场论复合算符之间的详细对应关系。此外，我们还计算了AdS_4与压缩拉伸七维流形的翘曲积周围的自旋为2的KK模。这种SU（2）x SU（2）x U（1）R对称性的背景与具有八阶超势和Chern-Simons能级（1，1，-2）的U（N）x U（N）x U（N）N=2超共形Chern-Simons物质理论有关。AdS_4的质量平方取决于SU（2）× SU（2）× U（1）_R的量子数和KK激发数。找到了自旋为2的算符的维数。
英文摘要：
Corrado, Pilch and Warner in 2001 have found the second 11-dimensional solution where the deformed geometry of S^7 in the lift contains S^2 x S^2. We identify the gauge dual of this background with the theory described by Franco, Klebanov and Rodriguez-Gomez recently. It is the U(N) x U(N) x U(N) gauge theory with two SU(2) doublet chiral fields B_1 transforming in the (N, Nbar, 1), B_2 transforming in the (1, N, Nbar), C_1 in the (1, Nbar, N) and C_2 in the (Nbar, N, 1) as well as an adjoint field Φin the (1, adj, 1) representation. By adding the mass term for adjoint field Φ, the detailed correspondence between fields of AdS_4 supergravity and composite operators of the IR field theory is determined. Moreover, we compute the spin-2 KK modes around a warped product of AdS_4 and a squashed and stretched seven-manifold. This background with global SU(2) x SU(2) x U(1)_R symmetry is related to a U(N) x U(N) x U(N) N=2 superconformal Chern-Simons matter theory with eighth-order superpotential and Chern-Simons level (1,1,-2). The mass-squared in AdS_4 depends on SU(2) x SU(2) x U(1)_R quantum numbers and KK excitation number. The dimensions of spin-2 operators are found.
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