Gradient formula for the beta function of 2D quantum field theory
Gradient formula for the beta function of 2D quantum field theory
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二维量子场论β函数的梯度公式
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. Konechny
中科院分区：
文献类型：
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作者：
D. Friedan;A. Konechny
我们给出了二维量子场论的 beta 函数的梯度公式的非微扰证明。梯度公式的形式为 ∂ic = −(gij + Δgij + bij)βj，其中 βj 是 beta 函数，c 和 gij 分别是 Zamolodchikov c 函数和度量，bij 是 Osborn 引入的反对称张量，Δgij 是某个度量校正。该公式是在应力能量守恒的假设和红外行为的某些条件下推导的，其中最重要的是场论的大距离极限不表现出自发破缺的全局共形对称性的条件。该公式专门用于非线性 sigma 模型，意味着重整化群不动点和 c 的临界点之间存在一一对应关系。
We give a non-perturbative proof of a gradient formula for beta functions of two-dimensional quantum field theories. The gradient formula has the form ∂ic = −(gij + Δgij + bij)βj where βj are the beta functions, c and gij are the Zamolodchikov c-function and metric respectively, bij is an antisymmetric tensor introduced by Osborn and Δgij is a certain metric correction. The formula is derived under the assumption of stress–energy conservation and certain conditions on the infrared behavior the most significant of which is the condition that the large-distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to nonlinear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c.