(In)validity of large N orientifold equivalence

Abstract

It has been argued that the bosonic sectors of supersymmetric SU(N) Yang-Mills theory, and of QCD with a single fermion in the antisymmetric (or symmetric) tensor representation, are equivalent in the $N\to \infty$ limit. If true, this correspondence can provide useful insight into properties of real QCD (with fundamental representation fermions), such as predictions [with O(1/N) corrections] for the non-perturbative vacuum energy, the chiral condensate, and a variety of other observables. Several papers asserting to have proven this large N ``orientifold equivalence'' have appeared. By considering theories compactified on $R^3\times S^1$, we show explicitly that this large N equivalence fails for sufficiently small radius, where our analysis is reliable, due to spontaneous symmetry breaking of charge conjugation symmetry in QCD with an antisymmetric (or symmetric) tensor representation fermion. This theory is also chirally symmetric for small radius, unlike super-Yang-Mills. The situation is completely analogous to large-N equivalences based on orbifold projections: simple symmetry realization conditions are both necessary and sufficient for the validity of the large N equivalence. Whether these symmetry realization conditions are satisfied depends on the specific non-perturbative dynamics of the theory under consideration. Unbroken charge conjugation symmetry is necessary for validity of the large N orientifold equivalence. Whether or not this condition is satisfied on $R^4$ (or $R^3\times S^1$ for sufficiently large radius) is not currently known.

arXiv comment23 pages, added discussion of P, T symmetry realization

References in corpus (27)

• 4d Conformal Field Theories and Strings on Orbifolds
• On Conformal Theories in Four Dimensions
• Gluino Condensate and Magnetic Monopoles in Supersymmetric Gluodynamics
• Large N limit of orbifold field theories
• Exact Results in Non-Supersymmetric Large N Orientifold Field Theories
• String Expansion as Large N Expansion of Gauge Theories
• SUSY Relics in One-Flavor QCD from a New 1/N Expansion
• Monopoles, affine algebras and the gluino condensate
• Large N reduction in the continuum three dimensional Yang-Mills theory
• Duality of Non-Supersymmetric Large N Gauge Theories
• Necessary and sufficient conditions for non-perturbative equivalences of large N orbifold gauge theories
• Refining the Proof of Planar Equivalence
• Super Yang-Mills on the lattice with domain wall fermions
• Effective Lagrangians for Orientifold Theories
• The Deconfinement Phase Transition in One-Flavour QCD
• QCD Quark Condensate from SUSY and the Orientifold Large-N Expansion
• Non-perturbative equivalences among large N gauge theories with adjoint and bifundamental matter fields
• Closed String Tachyons, AdS/CFT, and Large N QCD
• Quark condensate in two-flavor QCD
• Higher Representations: Confinement and Large N
• On Methods for Extracting Exact Non-perturbative Results in Non-supersymmetric Gauge Theories
• Can large Nc equivalence between supersymmetric Yang-Mills theory and its orbifold projections be valid?
• Comments on Condensates in Non-Supersymmetric Orbifold Field Theories
• Spontaneous Z2 Symmetry Breaking in the Orbifold Daughter of N=1 Super Yang-Mills Theory, Fractional Domain Walls and Vacuum Structure
• Nonperturbative Tests of the Parent/Orbifold Correspondence in Supersymmetric Gauge Theories
• Small volume expansion of almost supersymmetric large N theories
• An insight on the Proof of Orientifold Planar Equivalence on the Lattice

Cited by in corpus (80)

• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Volume independence in large Nc QCD-like gauge theories
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• The order of the Roberge-Weiss endpoint (finite size transition) in QCD
• Finite size phase transitions in QCD with adjoint fermions
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Universality of Phases in QCD and QCD-like Theories
• High-temperature asymptotics of supersymmetric partition functions
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• The Roberge-Weiss endpoint in N_f = 2 QCD
• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Towards multi-scale dynamics on the baryonic branch of Klebanov-Strassler
• Dynamical Stabilization of the Fermi Scale: Phase Diagram of Strongly Coupled Theories for (Minimal) Walking Technicolor and Unparticles
• Large-N reduction in QCD-like theories with massive adjoint fermions
• Orbifold equivalence and the sign problem at finite baryon density
• Non-perturbative volume-reduction of large-N QCD with adjoint fermions
• Introductory lectures to large-N QCD phenomenology and lattice results
• 2d affine XY-spin model/ 4d gauge theory duality and deconfinement
• Large N Volume Independence and an Emergent Fermionic Symmetry
• Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications
• On Yang-Mills Theories with Chiral Matter at Strong Coupling
• QCD with one compact spatial dimension
• Phases of $\Nc= \infty$ QCD-like gauge theories on $S^3\times S^1$ and nonperturbative orbifold-orientifold equivalences
• Baryon currents in QCD with compact dimensions
• The 't Hooft vertex revisited
• Alternative Large Nc Schemes and Chiral Dynamics
• Semiclassics with 't Hooft flux background for QCD with $2$-index quarks
• Phases of Gauge Theories
• RG Limit Cycles and Unconventional Fixed Points in Perturbative QFT
• A possible phase for adjoint QCD
• SO(N) gauge theories in 2+1 dimensions: glueball spectra and confinement
• Lattice Study of Planar Equivalence: The Quark Condensate
• Sign problem and phase quenching in finite-density QCD: models, holography, and lattice
• Non-Supersymmetric Seiberg Duality, Orientifold QCD and Non-Critical Strings
• Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
• Metastable nonconfining states in SU(3) lattice gauge theory with sextet fermions
• Quantum phase transitions and new scales in QCD-like theories
• Phase Transitions of Orientifold Gauge Theories at Large N in Finite Volume
• Spin contribution to light baryons in different large-$N$ limits
• A note on C-Parity Conservation and the Validity of Orientifold Planar Equivalence
• Thermal order in large N conformal gauge theories
• The three-dimensional, three state Potts model in a negative external field
• On the weak N-dependence of SO(N) and SU(N) gauge theories in 2+1 dimensions
• Classification of compactified $su(N_c)$ gauge theories with fermions in all representations
• A Chiral SU(N) Gauge Theory Planar Equivalent to Super-Yang-Mills
• Non-Perturbative Planar Equivalence and the Absence of Closed String Tachyons
• SO(2N) and SU(N) gauge theories in 2+1 dimensions
• Degeneracy Between the Regge Slope of Mesons and Baryons from Supersymmetry
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Alternative large Nc baryons and holography
• Holographic realization of large-Nc orbifold equivalence with non-zero chemical potential
• More about QCD on compact spaces
• Center symmetry and Hagedorn spectrum
• QCD in magnetic field, Landau levels and double-life of unbroken center-symmetry
• Nonperturbative results for two-index conformal windows
• Conformal windows of SP(2N) and SO(N) gauge theories from topological excitations on R3 * S1
• Wilson loop expectations in $SU(N)$ lattice gauge theory
• A numerical investigation of orientifold planar equivalence for quenched mesons
• Phases of $\mathbf{U}({\mathbf{N}}_{\mathbf{c}})$ QCD${}_3$ from Type 0 Strings and Seiberg Duality
• S-duality of nonsupersymmetric gauge theories
• Discrete symmetry breaking and baryon currents in U(N) and SU(N) gauge theories
• The Quark Condensate in Multi-Flavour QCD - Planar Equivalence Confronting Lattice Simulations
• The deconfining phase transition of SO(N) gauge theories in 2+1 dimensions
• Some Theoretical Developments in SUSY
• Center symmetry and the orientifold planar equivalence
• Domain Walls and Metastable Vacua in Hot Orientifold Field Theories
• Spectrum of orientifold QCD in the strong coupling and hopping expansion approximation
• Spontaneous breaking of discrete symmetries in QCD on a small volume
• Large Nc gauge theory with quarks in high representations
• The one-flavor quark condensate and related problems
• Emergent Supersymmetry at Large $N$
• Large-Nc equivalence and the sign problem at finite baryon density
• Theoretical Developments in SUSY
• Universality of phase diagrams in QCD and QCD-like theories
• About Orientifold Planar Equivalence on the Lattice
• Phase diagram of adjoint QCD at weak coupling and finite volume
• Orientifold Planar Equivalence: The Chiral Condensate