Abstract
We consider limits of mathcal{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 mathcal{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 frac{1}{8} -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.
Highlights
Newton-Cartan gravity single trace operators survive the limit, and the system can be interpreted as a periodic spin chain [5, 6]
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
When supersymmetry is preserved in the spin group, we found a concrete realization in terms of superfields
Summary
In the cases described by eq (1.2), the quantization of the dilatation operator and the corresponding action of the Hamiltonian on a spin chain were considered in [52, 53] for the SU(2|3) sector, and in [54–56] for the PSU(1, 1|2) sector. It was shown for the SU(1, 1) sector and some of its extensions that the results coming from the quantization of the dilatation operator can be equivalently derived by performing the sphere reduction of classical N = 4 SYM, and giving a prescription for the quantization [1, 2].
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