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Seiberg-Witten geometries revisited

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Abstract

We provide a uniform solution to 4d \( \mathcal{N} = 2 \) gauge theory with a single gauge group G = A, D, E when the one-loop contribution to the beta function from any irreducible component R of the hypermultiplets is less than or equal to half of that of the adjoint representation. The solution is given by a non-compact Calabi-Yau geometry, whose defining equation is built from explicitly known polynomials W G and X R , associated respectively to the gauge group G and each irreducible component R. We provide many pieces of supporting evidence, for example by analyzing the system from the point of view of the 6d \( \mathcal{N} = \left( {2,0} \right) \) theory compactified on a sphere.

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Authors and Affiliations

  1. IPMU, University of Tokyo, Chiba, 277-8583, Japan

    Yuji Tachikawa

  2. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan

    Seiji Terashima

Authors
  1. Yuji Tachikawa
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  2. Seiji Terashima
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Correspondence to Yuji Tachikawa.

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Dedicated to the memory of Professor Sung-Kil Yang

ArXiv ePrint: 1108.2315

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Tachikawa, Y., Terashima, S. Seiberg-Witten geometries revisited. J. High Energ. Phys. 2011, 10 (2011). https://doi.org/10.1007/JHEP09(2011)010

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