Nonrelativistic near-BPS corners of \(\mathcal{N} = 4\) super-Yang-Mills with SU(1,1) symmetry

DOI10.1007/JHEP02(2021)188zbMATH Open1460.81097arXiv2009.03799OpenAlexW3084332797MaRDI QIDQ2026064

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Publication date: 17 May 2021

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Abstract: We consider limits of $mathcalN=4$ super Yang-Mills (SYM) theory that approach BPS bounds and for which an $SU(1,1)$ structure is preserved. The resulting near-BPS theories become non-relativistic, with a $U(1)$ symmetry emerging in the limit that implies the conservation of particle number. They are obtained by reducing $mathcalN=4$ SYM on a three-sphere and subsequently integrating out fields that become non-dynamical as the bounds are approached. Upon quantization, and taking into account normal-ordering, they are consistent with taking the appropriate limits of the dilatation operator directly, thereby corresponding to Spin Matrix theories, found previously in the literature. In the particular case of the $SU(1,1|1)$ near-BPS/Spin Matrix theory, we find a superfield formulation that applies to the full interacting theory. Moreover, for all the theories we find tantalizingly simple semi-local formulations as theories living on a circle. Finally, we find positive-definite expressions for the interactions in the classical limit for all the theories, which can be used to explore their strong coupling limits. This paper will have a companion paper in which we explore BPS bounds for which a $SU(2,1)$ structure is preserved.

Full work available at URL: https://arxiv.org/abs/2009.03799

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