From 4d superconformal indices to 3d partition functions

Apr, 2011
11 pages
Published in:
  • Phys.Lett.B 704 (2011) 234-241
e-Print:
Report number:
  • AEI-2011-019

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Abstract: (Elsevier)
An exact formula for partition functions in 3 d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific q -hypergeometric integrals whose key building block is the double sine function (or the hyperbolic gamma function). Elliptic hypergeometric integrals, discovered by the second author, define 4 d superconformal indices. Using their reduction to the hyperbolic level, we describe a general scheme of reducing 4 d superconformal indices to 3 d partition functions which imply an efficient way of getting 3 d N=2 supersymmetric dualities for both SYM and CS theories from the “parent” 4 d N=1 dualities for SYM theories. As an example, we consider explicitly the duality pattern for 3 d N=2 SYM and CS theories with SP(2N) gauge group with the antisymmetric tensor matter.
Note:
  • Latex 14 pages/ v. 2 explanations added, version to appear in Phys. Lett. B
  • dimension: 3
  • gauge field theory: Yang-Mills: supersymmetry
  • supersymmetry: 2
  • gauge field theory: Sp(2N)
  • partition function
  • conformal
  • superfield: chiral
  • supersymmetry: duality
  • U(1) x U(1)
  • SU(6)