论文标题
通用鱼网CFT的织机
The Loom for General Fishnet CFTs
论文作者
论文摘要
我们提出了$ su（n）$ aepancoint标量字段的$ d $ d $二维形式的范围的广泛类别，从而将4 $ d $ d $ fishnet CFT（FCFT）推广。 Gürdogan和其中一位作者是$γ$ formed $ \ MATHCAL {N} = 4 $ SYM理论的特殊限制。在平面$ n \ to \ infty $中，fcfts由``渔网''平面feynman图形所主导。作为``编织''的``织机''，``与某些类型的繁殖者的feynman图表，在任何$ d $中都有$ M $不同的斜率非独立的，对数CFT享有某些现实属性，因为它们的对称性类似于C. Bender提出的非hermitian hamiltonians的PT，我们更详细地讨论了由$ M = 2,3,4 $的织机产生的理论，以及form fcfts for Spinning spinning $ d $ d $ d $ d $ d $。
We propose a broad class of $d$-dimensional conformal field theories of $SU(N)$ adjoint scalar fields generalising the 4$d$ Fishnet CFT (FCFT) discovered by Ö. Gürdogan and one of the authors as a special limit of $γ$-deformed $\mathcal{N}=4$ SYM theory. In the planar $N\to\infty $ limit the FCFTs are dominated by the ``fishnet" planar Feynman graphs. These graphs are explicitly integrable, as was shown long ago by A. Zamolodchikov. The Zamolodchikov's construction, based on the dual Baxter lattice (straight lines on the plane intersecting at arbitrary slopes) and the star-triangle identities, can serve as a ``loom" for ``weaving" the Feynman graphs of these FCFTs, with certain types of propagators, at any $d$. The Baxter lattice with $M$ different slopes and any number of lines parallel to those, generates an FCFT consisting of $M(M-1)$ fields and a certain number of chiral vertices of different valences with distinguished couplings. These non-unitary, logarithmic CFTs enjoy certain reality properties for their spectrum due to a symmetry similar to the PT-invariance of non-hermitian hamiltonians proposed by C. Bender. We discuss in more detail the theories generated by a loom with $M=2,3,4$, and the generalisation of the loom FCFTs for spinning fields in 4$d$.
