Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM

Abstract

It is argued that $4d$ $SU(N)$ $\mathcal{N}=4$ SYM has an accumulation line of zero-temperature topologically ordered phases. Each of these phases corresponds to $N$ bound states charged under electromagnetic ${\mathbb{Z}}_N^{(1)}$ one-form symmetries. Each of the $N$ bound states is made of two Dyonic flux components each of them extended over a two dimensional surface. They are localized at the fixed loci of a rotational action, and are argued to correspond to conformal blocks (or primaries) of an $SU(N{)}_1$ WZNW model on a two-torus.

arXiv comment43pp. Improved version: A sharper explanation of the emergence of topological order given in the newly added section 2

References in corpus (59)

• Non-Abelian Anyons and Topological Quantum Computation
• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Generalized Global Symmetries
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• An Index for 4 dimensional Super Conformal Theories
• Counting chiral primaries in N=1 d=4 superconformal field theories
• Rigid Supersymmetric Theories in Curved Superspace
• Supersymmetric vacua and Bethe ansatz
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• Supersymmetric AdS5 black holes
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• A topologically twisted index for three-dimensional supersymmetric theories
• Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
• Duality, Monopoles, Dyons, Confinement and Oblique Confinement in Supersymmetric SO(N_c) Gauge Theories
• Localization on Hopf surfaces
• Derivation of the Verlinde Formula from Chern-Simons Theory and the G/G model
• An extremization principle for the entropy of rotating BPS black holes in AdS${}_5$
• Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills
• Charged Kerr-de Sitter Black Holes in Five Dimensions
• Gauge Theory and Integrability, II
• Gauge Theory and Integrability, I
• The asymptotic growth of states of the 4d N=1 superconformal index
• Supersymmetric partition functions and the three-dimensional A-twist
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• The BPS limit of rotating AdS black hole thermodynamics
• Correlation functions for a strongly correlated boson system
• The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric Localization
• A 4d N=1 Cardy Formula
• Charged Rotating Black Holes in Five Dimensional U(1)^3 Gauged N=2 Supergravity
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• EFT and the SUSY Index on the 2nd Sheet
• Factorisation and holomorphic blocks in 4d
• The sl(n)-WZNW Fusion Ring: a combinatorial construction and a realisation as quotient of quantum cohomology
• Supersymmetric phases of 4d N=4 SYM at large N
• Fractional quantum Hall effect and nonabelian statistics
• Asymptotic growth of the 4d $\mathcal{N}=4$ index and partially deconfined phases
• Higgs Bundles, Gauge Theories and Quantum Groups
• A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index
• AdS black holes and finite N indices
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• A Bethe Ansatz type formula for the superconformal index
• The Cardy limit of the topologically twisted index and black strings in AdS${}_5$
• Higgs branch localization of $\mathcal{N}=1$ theories on $S^3\times S^1$
• Residues, modularity, and the Cardy limit of the 4d $\mathcal{N}=4$ superconformal index
• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index
• The topologically twisted index of $\mathcal{N}=4$ super-Yang-Mills on $T^2\times S^2$ and the elliptic genus
• $G/G$--Topological Field Theories by Cosetting $G_k$
• AdS${}_5$ Black Hole Entropy near the BPS Limit
• AdS${}_7$ Black-Hole Entropy and 5D $\mathcal{N}=2$ Yang-Mills
• Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
• $SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index
• Superconformal index of low-rank gauge theories via the Bethe Ansatz
• G/G gauged WZW model and Bethe Ansatz for the phase model
• Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM

Cited by in corpus (5)

• Supersymmetric phases of AdS${}_4$/CFT${}_3$
• Boundary Description of Microstates of the Two-Dimensional Black Hole
• Hawking-Page transition on a spin chain
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• Off-shell phase diagram of BPS black holes in AdS${}_5$