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arXiv 1006.5672hep-th
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与物质耦合的Chern-Simons理论中的重整化群与共形对称破缺

Renormalization Group and Conformal Symmetry Breaking in the Chern-Simons Theory Coupled to Matter

A. G. Dias, A. F. Ferrari

摘要:

为了研究共形对称破缺和有效势的稳定性,考虑了任意电荷的标量场和费米子场耦合的三维阿贝尔Chern-Simons理论.本文提出了一种改进的有效势计算方法,它是基于两圈计算和重整化群方程:重整化群方程允许我们对有效势中的一系列项求和,这些项的幂分别比耦合常数的总幂小一个、两个和三个单位(即,领先、次领先和次领先的下一个下一个领先队列)。为了计算,我们确定了费米子-费米子-标量-标量相互作用的β函数和标量场的反常维数。我们表明,改进的有效势提供了一个更精确的确定的理论的性质在破相,相比直接从循环计算得到的标准有效势。这是因为这里讨论的改进大大减少了动力学对称性破缺的参数空间区域。

英文摘要:

The three-dimensional Abelian Chern-Simons theory coupled to a scalar and a fermionic field of arbitrary charge is considered in order to study conformal symmetry breakdown and the effective potential stability. We present an improved effective potential computation based on two-loop calculations and the renormalization group equation: the later allows us to sum up series of terms in the effective potential where the power of the logarithms are one, two and three units smaller than the total power of coupling constants (i.e., leading, next-to-leading and next-to-next-to-leading logarithms). For the sake of this calculation we determined the beta function of the fermion-fermion-scalar-scalar interaction and the anomalous dimension of the scalar field. We shown that the improved effective potential provides a much more precise determination of the properties of the theory in the broken phase, compared to the standard effective potential obtained directly from the loop calculations. This happens because the region of the parameter space where dynamical symmetry breaking occurs is drastically reduced by the improvement discussed here.

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