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

Abstract

We consider limits of $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ 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 $$ \frac{1}{8} $$ 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.

Words to describe a black hole

“…Finally, the one-loop Beisert Hamiltonian in various subsectors has been explored in [75][76][77][78], and dubbed as the "spin matrix theory" that describes the dynamics of near-BPS states. We have shown that the Beisert Hamiltonian takes a very simple form (3.2) and (3.3) in terms of the BPS superfield Ψ, which efficiently organizes all the BPS letters.…”

Supersymmetric Galilean Electrodynamics

“…In recent years, it has been shown that decoupling limits of N = 4 SYM lead to quantum mechanical models, called Spin Matrix Theories (SMT), which have non-relativistic symmetries and are closed under the action of the one-loop dilatation operator [48]. The effective Hamiltonian of these sectors in the near-BPS limit have been derived in [33][34][35][36], leading in some cases to field theory and superfield formulations. It would be interesting to find a link between these decoupling limits of N = 4 SYM and a null reduction JHEP09(2022)237 procedure, and study the quantum properties of both theories.…”

“…Therefore, it does not appear surprising that several investigations of theories which are both supersymmetric and non-relativistic had a great revival in recent years. Starting from the first investigations involving the SUSY generalization of the Galilean algebra and limits of the relativistic models [23][24][25], there have been studies of superconformal anyons [26], spontaneous SUSY breaking [27], the analysis of the renormalization properties of supersymmetric Galilean or Lifshitz-invariant models [28,29], supergravity [30,31] and the study of non-relativistic corners of N = 4 super Yang-Mills (SYM) theory [32][33][34][35][36].…”

Aspects of Nonrelativistic Strings

“…To further establish this corner of NR strings in the holographic correspondence, this result should also be obtained from a direct quantization of the SMT string sigma model on the FF U (1)-Galilean backgrounds (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 threedimensional SU (1, 1) geometry in Table 1 at large N .…”