Nonrelativistic Corners of $\mathcal{N}=4$ Supersymmetric Yang--Mills Theory

Abstract

We show that $\mathcal{N}=4$ supersymmetric-Yang-Mills (SYM) theory on $\mathbb{R}\times S^3$ with gauge group $\text{SU}(N)$ is described in a near-BPS limit by a simple lower-dimensional nonrelativistic field theory with $\text{SU}(1,1)\times \text{U}(1)$ invariant interactions. In this limit, a single complex adjoint scalar field survives, and part of its interaction is obtained by exactly integrating out the gauge boson of the SYM theory. Taking into account normal ordering, the interactions match the one-loop dilatation operator of the $\text{SU}(1,1)$ sector, establishing the consistency of the limit at the quantum level. We discover a tantalizing field-theoretic structure, corresponding to a $(1+1)$-dimensional complex chiral boson on a circle coupled to a nondynamical gauge field, both in the adjoint representation of $\text{SU}(N)$. The successful construction of a lower-dimensional nonrelativistic field theory in the $\text{SU}(1,1)$ near-BPS limit provides a proof of concept for other BPS bounds. These are expected to lead to richer field theories in nonrelativistic corners of $\mathcal{N}=4$ SYM that include fermions, gauge fields and supersymmetry and can provide a novel path towards understanding strongly coupled finite-$N$ dynamics of gauge theories.

6 pages, 1 figure; v2: minor clarifications added, matches journal version

References in corpus (12)

• Galilean Conformal Algebras and AdS/CFT
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Nonrelativistic String Theory and T-Duality
• Relating non-relativistic string theories
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• Remark About Non-Relativistic String in Newton-Cartan Background and Null Reduction
• Anatomy of Deconfinement
• Growing Extra Dimensions in AdS/CFT
• N=4 SYM on R x S^3 and Theories with 16 Supercharges
• Partial Deconfinement
• Decoupling limits of N=4 super Yang-Mills on R x S^3

Cited by in corpus (14)

• Aspects of Nonrelativistic Strings
• Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT
• Aspects of Non-Relativistic Quantum Field Theories
• Matrix Theory Reloaded: A BPS Road to Holography
• Nonrelativistic near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills with $SU(1,1)$ symmetry
• The Panorama of Spin Matrix Theory
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Decoding the Spin-Matrix limit of strings on $Ad{S}_5\times S^5$
• Supersymmetric Galilean Electrodynamics
• Nonrelativistic spinning strings
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• Symmetry structure of the interactions in near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills