Nonrelativistic near-BPS corners of N = 4 super-Yang-Mills with SU(1, 1) symmetry

Stefano Baiguera, Troels Harmark, Nico Wintergerst

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We consider limits of N = 4 super Yang-Mills (SYM) theory that approach BPS bounds and for which an SU(1,1) structure is preserved. The resulting near-BPS theories become non-relativistic, with a U(1) symmetry emerging in the limit that implies the conservation of particle number. They are obtained by reducing N = 4 SYM on a three-sphere and subsequently integrating out fields that become non-dynamical as the bounds are approached. Upon quantization, and taking into account normal-ordering, they are consistent with taking the appropriate limits of the dilatation operator directly, thereby corresponding to Spin Matrix theories, found previously in the literature. In the particular case of the SU(1,1—1) near-BPS/Spin Matrix theory, we find a superfield formulation that applies to the full interacting theory. Moreover, for all the theories we find tantalizingly simple semi-local formulations as theories living on a circle. Finally, we find positive-definite expressions for the interactions in the classical limit for all the theories, which can be used to explore their strong coupling limits. This paper will have a companion paper in which we explore BPS bounds for which a SU(2,1) structure is preserved.

Original languageEnglish
Article number188
JournalJournal of High Energy Physics
Issue number2
StatePublished - 1 Feb 2021
Externally publishedYes


  • AdS-CFT Correspondence
  • Field Theories in Lower Dimensions
  • Superspaces
  • Supersymmetric Gauge Theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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