Spin Matrix Theory in near 18 -BPS corners of N = 4 super-Yang-Mills

Stefano Baiguera, Troels Harmark, Yang Lei

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We consider limits of N = 4 super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix Theories. The near-BPS theories can be obtained by reducing N = 4 SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. In the previous works [1–3] we have considered various SU(1,1) and SU(1,2) types of subsectors in this limit. In the current work, we will construct the remaining Spin Matrix Theories defined near the 18-BPS subsectors, which include the PSU(1,1|2) and SU(2|3) cases. We derive the Hamiltonians by applying the spherical reduction algorithm and show that they match with the spin chain result, coming from the loop corrections to the dilatation operator. In the PSU(1,1|2) case, we prove the positivity of the spectrum by constructing cubic supercharges using the enhanced PSU(1|1)2 symmetry and show that they close to the interacting Hamiltonian. We finally analyse the symmetry structure of the sectors in view of an interpretation of the interactions in terms of fundamental blocks.

Original languageEnglish
Article number191
JournalJournal of High Energy Physics
Issue number2
StatePublished - 1 Feb 2022


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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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