Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N} = 4$ super-Yang-Mills

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 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.

Aspects of Nonrelativistic Strings

“…5.28. Finally, a new approach has recently been developed for the explicit construction of Spin Matrix theories using a classical reduction of N 4 followed by a suitable quantization and normal ordering procedure [102][103][104][105]. This construction reproduces earlier results obtained [85] from limits of the one-loop spectrum of N 4 and also leads to a two-dimensional field theory formulation of the SU(1, 1) sectors, suggesting a natural dual description for SMT strings on the three-dimensional SU(1, 1) geometry in Table 1 at large N.…”