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Radiative brane-mass terms in \(D>5\) orbifold gauge theories. (English) Zbl 1005.81053

Summary: A gauge theory with gauge group \(G\) defined in \(D>4\) space-time dimensions can be broken to a subgroup \(H\) on four-dimensional fixed point branes, when compactified on an orbifold. Mass terms for extra-dimensional components of gauge fields \(A_i\) (brane scalars) might acquire (when allowed by the brane symmetries) quadratically divergent radiative masses and thus jeopardize the stability of the four-dimensional theory. We have analyzed \(Z_2\) compactifications and identified the brane symmetries remnants of the higher-dimensional gauge invariance. No mass term is allowed for \(D=5\) while for \(D>5\) a tadpole \(\propto F_{ij}^{\alpha}\) can appear when there are \(U_{\alpha}(1)\) factors in \(H\). A detailed calculation is done for the \(D=6\) case and it is established that the tadpole is related, although does not coincide, with the \(U_{\alpha}(1)\) anomaly induced on the brane by the bulk fermions. In particular, no tadpole is generated from gauge bosons or fermions in real representations.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
83E30 String and superstring theories in gravitational theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E15 Kaluza-Klein and other higher-dimensional theories
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