Dilatation operator in (super-)Yang–Mills theories on the light-cone
Dilatation operator in (super-)Yang–Mills theories on the light-cone
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光锥上的（超）杨-米尔斯理论中的膨胀算子
DOI：
10.1016/j.nuclphysb.2004.11.034
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
A. Manashov
中科院分区：
文献类型：
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作者：
A. Belitsky;S. Derkachov;G. Korchemsky;A. Manashov
规范/弦对应表明，超共形SU（2，2）规范理论中的伸缩算符|N）对称性应具有普适的可积性。我们通过计算光锥上所有（超）对称杨-米尔斯理论中的单圈扩张算子，从gluodynamics一直到最大超对称N=4理论，进一步支持了这一猜想。我们证明，膨胀算子采取一个非常简单的形式时，实现在空间由单迹产品的超场分离的类光距离。后者是最大洛伦兹自旋的Wilson算符的生成函数，两者的尺度依赖性是一一对应的。在N=4的最大超对称理论中，所有的非定域光锥算符都是由一个CPT自共轭超场构成的，而对于N= 0，1，2，我们必须处理两个不同的超场，并区分三种不同类型的光锥算符。我们发现，对于由单一超场构成的光锥算符，单圈伸缩算符在所有SYM理论中具有相同的普遍形式，并且在多色极限下可映射到SL（2）的哈密顿量|N）海森堡（超）自旋链，其长度等于所涉及的超场的数量。对于包含两个超场的“混合”光锥算符，N 2的伸缩算符从光锥上的超场之间的交换相互作用中得到额外的贡献，这破坏了它的可积性对称性，并在反常维度的光谱中产生了质量间隙。
The gauge/string correspondence hints that the dilatation operator in gauge theories with the superconformal SU(2,2|N) symmetry should possess universal integrability properties for different N. We provide further support for this conjecture by computing a one-loop dilatation operator in all (super)symmetric Yang–Mills theories on the light-cone ranging from gluodynamics all the way to the maximally supersymmetric N=4 theory. We demonstrate that the dilatation operator takes a remarkably simple form when realized in the space spanned by single-trace products of superfields separated by light-like distances. The latter operators serve as generating functions for Wilson operators of the maximal Lorentz spin and the scale dependence of the two are in the one-to-one correspondence with each other. In the maximally supersymmetric, N=4 theory all nonlocal light-cone operators are built from a single CPT self-conjugated superfield while for N=0,1,2 one has to deal with two distinct superfields and distinguish three different types of such operators. We find that for the light-cone operators built from only one species of superfields, the one-loop dilatation operator takes the same, universal form in all SYM theories and it can be mapped in the multi-color limit into a Hamiltonian of the SL(2|N) Heisenberg (super)spin chain of length equal to the number of superfields involved. For “mixed” light-cone operators involving both superfields the dilatation operator for N⩽2 receives an additional contribution from the exchange interaction between superfields on the light-cone which breaks its integrability symmetry and creates a mass gap in the spectrum of anomalous dimensions.
辐射物理化学21-1-2。
DOI：
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