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Vacuum energy for Yang-Mills fields inR d×S 1: One-loop, two-loop, and beyond

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Zeitschrift für Physik C Particles and Fields

Abstract

The vacuum energy is calculated for Yang-Mills (YM) system defined inD dimensional space-time ofS 1×R d (D=d+1), where the possibility of the YM fields to acquire the vacuum expectation values onS 1 is taken into account. The vacuum energy has already been obtained to the order of one-loop in many people. Here we calculate the vacuum energy inD dimensions to two-loop order. With an intention to reach higher loops, an approximation method is proposed, which is especially effective in higher dimensions. By this method, we can treat the higher-loop contributions of YM interactions as easily as we treat one-loop effect. As a check, we show reproduction of the two-loop contribution (D-dependence of the coefficient as well as the functional form) when the coupling constant is small. This approximation method is useful not only for the Kaluza-Klein theories but also for the finite temperature-density system (as a quark-gluon plasma).

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Author notes

  1. K. Shiraishi

    Present address: Institute for Cosmic Ray Research, University of Tokyo, Midori-cho, 188, Tanashi-shi, Tokyo, Japan

  2. S. Hirenzaki

    Present address: The Institute of Physical and Chemical Research, 351-01, Wakoh-shi, Saitama, Japan

Authors and Affiliations

  1. Department of Physics, Faculty of Science, Ochanomizu University, 1-1 Otsuka 2, Bunkyo-ku, 112, Tokyo, Japan

    K. Shiraishi

  2. Department of Physics, Tokyo Metropolitan University, Fukazawa, Setagaya-ku, 158, Tokyo, Japan

    S. Hirenzaki

Authors
  1. K. Shiraishi
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  2. S. Hirenzaki
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Minami-Ohsawa Hachioji-shi, Tokyo 92-03 Japan

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Shiraishi, K., Hirenzaki, S. Vacuum energy for Yang-Mills fields inR d×S 1: One-loop, two-loop, and beyond. Z. Phys. C - Particles and Fields 53, 91–96 (1992). https://doi.org/10.1007/BF01483877

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  • DOI: https://doi.org/10.1007/BF01483877

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