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Compactified rotating branes in the matrix model, and excitation spectrum towards one loop

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Abstract

We study compactified brane solutions of type \(\mathbb{R}^{4} \times K\) in the IIB matrix model, and obtain explicitly the bosonic and fermionic fluctuation spectrum required to compute the one-loop effective action. We verify that the one-loop contributions are UV finite for \(\mathbb{R}^{4} \times T^{2}\), and supersymmetric for \(\mathbb{R}^{3} \times S^{1}\). The higher Kaluza–Klein modes are shown to have a gap in the presence of flux on T 2, and potential problems concerning stability are discussed.

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Notes

  1. This is expected to hold also in the presence of compactified extra dimensions, due to the non-commutativity of the brane.

  2. One-loop finiteness holds even on 6D backgrounds, but not for higher loops. This is consistent with well-known results [14–16] for SYM theory.

  3. Note that \(\mathcal{M}= \mathbb {R}^{3} \times S^{1}\) is symplectic while \(\mathbb {R}^{3}\) is not. Thus one can raise or lower indices by introducing an effective metric G μν on \(\mathcal{M}\) following [7]. In this paper we short-cut these geometrical considerations, and use a tilde to indicate that a momentum is in \(T^{*}_{\mathcal{M}}\) rather than \(T_{\mathcal{M}}\).

  4. In fact we will only need Γ 0,…,Γ 6 for the computations ahead.

  5. The crossing of the corresponding energy shells at p μ=0 will lead to mixing of the corresponding modes. This corresponds to the mixing of gravitational modes found in [8].

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Acknowledgements

D.N. Blaschke is a recipient of an APART fellowship of the Austrian Academy of Sciences, and is also grateful for the hospitality of the theory division of LANL and its partial financial support. The work of H.S. is supported by the Austrian Fonds für Wissenschaft und Forschung under grant P24713.

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Authors and Affiliations

  1. Theory Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Daniel N. Blaschke

  2. Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria

    Harold C. Steinacker

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  1. Daniel N. Blaschke
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  2. Harold C. Steinacker
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Correspondence to Daniel N. Blaschke.

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Blaschke, D.N., Steinacker, H.C. Compactified rotating branes in the matrix model, and excitation spectrum towards one loop. Eur. Phys. J. C 73, 2414 (2013). https://doi.org/10.1140/epjc/s10052-013-2414-x

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