TY - JOUR

T1 - Spin Matrix Theory in near 1/8-BPS corners of N=4 super-Yang-Mills

AU - Baiguera, Stefano

AU - Harmark, Troels

AU - Lei, Yang

PY - 2022/2/24

Y1 - 2022/2/24

N2 - 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 1/8-BPS subsectors, which include the PSU(1,1 vertical bar 2) and SU(2 vertical bar 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 vertical bar 2) case, we prove the positivity of the spectrum by constructing cubic supercharges using the enhanced PSU(1 vertical bar 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.

AB - 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 1/8-BPS subsectors, which include the PSU(1,1 vertical bar 2) and SU(2 vertical bar 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 vertical bar 2) case, we prove the positivity of the spectrum by constructing cubic supercharges using the enhanced PSU(1 vertical bar 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.

KW - AdS-CFT Correspondence

KW - Field Theories in Lower Dimensions

KW - Supersymmetric Effective Theories

KW - Supersymmetric Gauge Theory

KW - DILATATION OPERATOR

KW - HAGEDORN TRANSITION

U2 - 10.1007/JHEP02(2022)191

DO - 10.1007/JHEP02(2022)191

M3 - Journal article

VL - 2022

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

SN - 1126-6708

IS - 2

M1 - 191

ER -