3d and 5d Gauge Theory Partition Functions as q-deformed CFT Correlators
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  • 作者：Fabrizio Nieri (1)
    Sara Pasquetti (1)
    Filippo Passerini (2) (3) (4)

    1. Department of Mathematics     ; University of Surrey ; Guildford ; Surrey ; GU2 7XH ; UK
    2. PH-TH Division     ; CERN ; 1211 ; Geneva ; Switzerland
    3. Department of Physics     ; Princeton University ; Princeton ; NJ ; 08544 ; USA
    4. Laboratoire de Physique Th茅orique     ; Unit茅 Mixte du CNRS et de l鈥橢cole Normale Sup茅rieure associ茅e 脿 l鈥橴niversit茅 Pierre et Marie Curie 6 ; UMR 8549 ; Ecole Normale Sup茅rieure ; 75005 ; Paris ; France
  • 关键词：81T60 ; 81T40 ; 81T20 ; 81R10 ; 17B68 ; gauge theory ; supersymmetry ; localization ; conformal field theory ; deformed Virasoro algebra
  • 刊名：Letters in Mathematical Physics
  • 出版年：2015
  • 出版时间：January 2015
  • 年：2015
  • 卷：105
  • 期：1
  • 页码：109-148
  • 全文大小：487 KB
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  • 刊物类别：Physics and Astronomy
  • 刊物主题：Physics
    Mathematical and Computational Physics
    Statistical Physics
    Geometry
    Group Theory and Generalizations
  • 出版者：Springer Netherlands
  • ISSN：1573-0530
文摘
3d \({\mathcal{N}=2}\) partition functions on the squashed three-sphere \({S^{3}_{b}}\) and on the twisted product \({S^{2} \times S^{1}}\) have been shown to factorize into sums of squares of solid tori partition functions, the so-called holomorphic blocks. The same set of holomorphic blocks realizes \({S^{3}_{b}}\) and \({S^{2} \times S^{1}}\) partition functions but the two cases involve different inner products, the S-pairing and the id-pairing, respectively. We define a class of q-deformed CFT correlators where chiral blocks are controlled by a deformation of Virasoro symmetry and are paired by S-pairing and id-pairing, respectively. Applying the bootstrap approach to a class of degenerate correlators we are able to derive three-point functions. We show that degenerate correlators can be mapped to 3d partition functions while the crossing symmetry of correlators corresponds to the flop symmetry of 3d gauge theories. We explore how non-degenerate q-deformed correlators are related to 5d partition functions. We argue that id-pairing correlators are associated with the superconformal index on \({S^{4} \times S^{1}}\) while S-pairing three-point function factors capture the one-loop part of S 5 partition functions. This is consistent with the interpretation of \({S^{2} \times S^{1}}\) and \({S^{3}_{b}}\) gauge theories as codimension two defect theories inside \({S^{4} \times S^{1}}\) and S 5, respectively.

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