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.

Baiguera, S., Harmark, T., Lei, Y. (2022). Spin Matrix Theory in near 18 -BPS corners of N = 4 super-Yang-Mills. JOURNAL OF HIGH ENERGY PHYSICS, 2022(2) [10.1007/JHEP02(2022)191].

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

Baiguera S.
;
Harmark T.;
2022

Abstract

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.
Articolo in rivista - Articolo scientifico
AdS-CFT Correspondence; Field Theories in Lower Dimensions; Supersymmetric Effective Theories; Supersymmetric Gauge Theory;
English
24-feb-2022
2022
2022
2
191
open
Baiguera, S., Harmark, T., Lei, Y. (2022). Spin Matrix Theory in near 18 -BPS corners of N = 4 super-Yang-Mills. JOURNAL OF HIGH ENERGY PHYSICS, 2022(2) [10.1007/JHEP02(2022)191].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/488523
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