Abstract
We study a four-dimensional low-energy effective field theory derived from extra dimensional field theories with general gauge backgrounds. We find that products among fermionic zero-modes and lightest scalar modes are expanded by other fermionic zero-modes and lightest scalar modes. Using this aspect, we show that higher-order couplings among the fermionic zero-modes and the lightest scalar mode can be decomposed into three-point couplings. This selection rule originating from a structure of the Dirac-type operators indicates the operator product expansion the underlying conformal field theory.
Highlights
The Standard Model (SM) is the most successful model of particle physics
We studied the properties of the fourdimensional effective field theories from extradimensional field theories
III, we found the selection rule for higher-order couplings from the structure of the lightest-mode solutions of the Dirac-type equations
Summary
The Standard Model (SM) is the most successful model of particle physics. the origin of the structures of the SM is a mystery. It is known that the lightest-mode solutions of Dirac-type equations have a structure that is similar to an operator product expansion in conformal field theory [1,7]. Let us consider the Dirac-type equations for bosons with two different Uð1Þ gauge backgrounds A and A0, i.e., DAi φAI 1⁄4 ð∂i − iAiÞφAI 1⁄4 0; ð15Þ In this case, we can obtain zero-mode solutions of DAþA0 by considering the product of φAI and φAJ 0. We show that three-point couplings and higher-order couplings of the lightest modes in a four-dimensional theory can be constructed from sAIJK and tAIJK
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