Symmetry structure of the interactions in near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills

Abstract

We consider limits of $\mathcal{N}=4$ super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic near-BPS 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. We perform the sphere reduction for the near-BPS limit with $\mathrm{SU}(1,2|2)$ symmetry, which has several new features compared to the previously considered cases with $\mathrm{SU}(1,1)$ symmetry, including a dynamical gauge field. We discover a new structure in the classical limit of the interaction term. We show that the interaction term is built from certain blocks that comprise an irreducible representation of the $\mathrm{SU}(1,2|2)$ algebra. Moreover, the full interaction term can be interpreted as a norm in the linear space of this representation, explaining its features including the positive definiteness. This means one can think of the interaction term as a distance squared from saturating the BPS bound. The $\mathrm{SU}(1,1|1)$ near-BPS theory, and its subcases, is seen to inherit these features. These observations point to a way to solve the strong coupling dynamics of these near-BPS theories.

arXiv comment54 pages, 4 figures. V2: minor comments added

References in corpus (40)

• An Index for 4 dimensional Super Conformal Theories
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• General Non-Extremal Rotating Black Holes in Minimal Five-Dimensional Gauged Supergravity
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• The su(2|3) Dynamic Spin Chain
• Spin chains and string theory
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• The Bethe ansatz for superconformal Chern-Simons
• Supersymmetric multi-charge AdS_5 black holes
• Five-Dimensional Gauged Supergravity Black Holes with Independent Rotation Parameters
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• An extremization principle for the entropy of rotating BPS black holes in AdS${}_5$
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Relating non-relativistic string theories
• Comments on 1/16 BPS Quantum States and Classical Configurations
• Counting 1/8-BPS Dual-Giants
• Factorisation and holomorphic blocks in 4d
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• 1/16 BPS States in N=4 SYM
• Large AdS black holes from QFT
• N=4 SYM on R x S^3 and Theories with 16 Supercharges
• On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM
• An elliptic Virasoro symmetry in 6d
• Decoupling limits of N=4 super Yang-Mills on R x S^3
• Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT
• Matching gauge theory and string theory in a decoupling limit of AdS/CFT
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Interacting Giant Gravitons from Spin Matrix Theory
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• Near-Extremal Vanishing Horizon AdS5 Black Holes and Their CFT Duals
• Nonrelativistic near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills with $SU(1,1)$ symmetry
• Probing the EVH limit of supersymmetric AdS black holes
• Renormalization properties of a Galilean Wess-Zumino model
• Nonrelativistic Corners of $\mathcal{N}=4$ Supersymmetric Yang--Mills Theory
• Modularity of supersymmetric partition functions
• Supersymmetric Casimir Energy and $\mathrm{SL}(3,\mathbb{Z})$ Transformations
• The growth of the $\frac{1}{16}$-BPS index in 4d $\mathcal{N}=4$ SYM
• Elliptic Genus Derivation of 4d Holomorphic Blocks

Cited by in corpus (1)

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