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On the Boundedness of Effective Potentials Arising from String Compactifications

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Abstract

We study effective potentials coming from compactifications of string theory. We show that, under mild assumptions, such potentials are bounded from below in four dimensions, giving an affirmative answer to a conjecture proposed by the second author in Douglas (JHEP 3:71, 2010). We also derive some sufficient conditions for the existence of critical points. All proofs and mathematical hypotheses are discussed in the context of their relevance to the physics of the problem.

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Authors and Affiliations

  1. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Marcelo M. Disconzi

  2. Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, 11794, USA

    Michael R. Douglas

  3. I.H.E.S., Le Bois-Marie, 91440, Bures-sur-Yvette, France

    Michael R. Douglas

  4. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794, USA

    Vamsi Pingali

  5. Department of Mathematics, Johns Hopkins University, 404 Krieger Hall, Baltimore, MD, 21218, USA

    Vamsi Pingali

Authors
  1. Marcelo M. Disconzi
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  2. Michael R. Douglas
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  3. Vamsi Pingali
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Correspondence to Michael R. Douglas.

Additional information

Communicated by N. A. Nekrasov

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Disconzi, M.M., Douglas, M.R. & Pingali, V. On the Boundedness of Effective Potentials Arising from String Compactifications. Commun. Math. Phys. 325, 847–878 (2014). https://doi.org/10.1007/s00220-013-1866-z

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  • DOI: https://doi.org/10.1007/s00220-013-1866-z

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