The ABCDEFG of Instantons and W-algebras

Article, Preprint English OPEN
Keller, Christoph A.; Mekareeya, Noppadol; Song, Jaewon; Tachikawa, Yuji;
(2011)
  • Publisher: Springer
  • Identifiers: doi: 10.1007/JHEP03(2012)045
  • Subject: High Energy Physics - Theory
    arxiv: High Energy Physics::Theory | High Energy Physics::Phenomenology | High Energy Physics::Lattice

For arbitrary gauge groups, we check at the one-instanton level that the Nekrasov partition function of pure N = 2 super Yang-Mills is equal to the norm of a certain coherent state of the corresponding W-algebra. For non-simply-laced gauge groups, we confirm in particu... View more
  • References (67)
    67 references, page 1 of 7

    2 Instanton calculation 5 2.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 One-instanton contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    3 Free field realization of W-algebras 7 3.1 Simply laced W-algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Twisted sectors of the simply-laced W-algebras . . . . . . . . . . . . . . . . . 9 3.3 Basic properties of the Verma module . . . . . . . . . . . . . . . . . . . . . . 10

    4 Instantons and coherent states of W-algebras 11 4.1 Identification of the coherent state . . . . . . . . . . . . . . . . . . . . . . . . 11 4.2 Coherent state at the lowest level . . . . . . . . . . . . . . . . . . . . . . . . 12 4.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 A Roots of simple Lie algebras 18 A.1 Simply-laced algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 A.2 Non-simply-laced algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

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