Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions

Abstract

We investigate QCD with adjoint Dirac fermions on ${\mathbb{R}}^3\times S^1$ with generic boundary conditions for fermions along $S^1$. By means of perturbation theory, semiclassical methods and a chiral effective model, we elucidate a rich phase structure in the space spanned by the $S^1$ compactification scale $L$, twisted fermionic boundary condition $\varphi$ and the fermion mass $m$. We found various phases with or without chiral and center symmetry breaking, separated by first- and second-order phase transitions, which in specific limits ($\varphi =0$, $\varphi =\pi$, $L\to 0$ and $m\to \infty$) reproduce known results in the literature. In the center-symmetric phase at small $L$, we show that Unsal's bion-induced confinement mechanism is at work but is substantially weakened at $\varphi \ne 0$ by a linear potential between monopoles. Through an analytic and numerical study of the PNJL model, we show that the order parameters for center and chiral symmetries (i.e., Polyakov loop and chiral condensate) are strongly intertwined at $\varphi \ne 0$. Due to this correlation, a deconfined phase can intervene between a weak-coupling center-symmetric phase at small $L$ and a strong-coupling one at large $L$. Whether this happens or not depends on the ratio of the dynamical fermion mass to the energy scale of the Yang-Mills theory. Implication of this possibility for resurgence in gauge theories is briefly discussed. In an appendix, we study the index of the adjoint Dirac operator on ${\mathbb{R}}^3\times S^1$ with twisted boundary conditions, which is important for semiclassical analysis of monopoles.

arXiv comment43 pages, 14 figures. v2: references added, Section 3.1 expanded. The version to appear in JHEP

References in corpus (108)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• QCD Phenomenology based on a Chiral Effective Lagrangian
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Chiral effective model with the Polyakov loop
• Strong Dynamics and Electroweak Symmetry Breaking
• Phases of QCD: lattice thermodynamics and a field theoretical model
• The QCD phase diagram for small densities from imaginary chemical potential
• Finite density QCD via imaginary chemical potential
• Physics of Strongly coupled Quark-Gluon Plasma
• Periodic Instantons with non-trivial Holonomy
• SU(2) Calorons and Magnetic Monopoles
• SU(N) gauge theories at large N
• Measurement of $J/\psi$ helicity distributions in inelastic photoproduction at HERA
• QCD-like Theories at Finite Baryon Density
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Chiral Symmetry Restoration and $Z_N$ Symmetry
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Monopole Constituents inside SU(n) Calorons
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Gauge Dynamics And Compactification To Three Dimensions
• Imaginary chemical potential and finite fermion density on the lattice
• Gluino Condensate and Magnetic Monopoles in Supersymmetric Gluodynamics
• Aharonov-Bohm effect and nucleon-nucleon phase shifts on the lattice
• 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 at Finite Baryon and Isospin Density
• Monopoles and Instantons on Partially Compactified D-Branes
• Phenomenological Equations of State for the Quark-Gluon Plasma
• Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential
• Phase diagram of SU(2) with 2 flavors of dynamical adjoint quarks
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Numerical Study of Dense Adjoint Matter in Two Color QCD
• Evolution of the coupling constant in SU(2) lattice gauge theory with two adjoint fermions
• QCD thermodynamics from an imaginary mu_B: results on the four flavor lattice model
• Deconfinement and Chiral Symmetry Restoration in an SU(3) Gauge Theory with Adjoint Fermions
• Continuity, Deconfinement, and (Super) Yang-Mills Theory
• Renormalized Polyakov loops in many representations
• A semiclassical realization of infrared renormalons
• QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations
• Quantum weights of dyons and of instantons with non-trivial holonomy
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Conformal vs confining scenario in SU(2) with adjoint fermions
• Monopoles, affine algebras and the gluino condensate
• Spectrum of SU(2) lattice gauge theory with two adjoint Dirac flavours
• Conformality or confinement: (IR)relevance of topological excitations
• Dual quark condensate and dressed Polyakov loops
• Infrared fixed point in SU(2) gauge theory with adjoint fermions
• Linking confinement to spectral properties of the Dirac operator
• Finite size phase transitions in QCD with adjoint fermions
• Index theorem for topological excitations on R^3 * S^1 and Chern-Simons theory
• Confining ensemble of dyons
• New Phases of SU(3) and SU(4) at Finite Temperature
• Topology and confinement
• Phase diagram of QCD at finite temperature and chemical potential from lattice simulations with dynamical Wilson quarks
• The Chiral Phase Transition and Instanton Anti-instanton Molecules
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Singular values of the Dirac operator in dense QCD-like theories
• Phase diagram in the imaginary chemical potential region and extended Z3 symmetry
• Complex Langevin dynamics and other approaches at finite chemical potential
• Large-N volume independence in conformal and confining gauge theories
• Microscopic Structure of Magnetic Bions
• Gauge dynamics in the PNJL model: Color neutrality and Casimir scaling
• Polyakov loops and the Hosotani mechanism on the lattice
• Weyl-Dirac zero-mode for calorons
• How to get from imaginary to real chemical potential
• Scaling and Goldstone effects in a QCD with two flavours of adjoint quarks
• Large-N reduction in QCD-like theories with massive adjoint fermions
• An effective gluon potential and hybrid approach to Yang-Mills thermodynamics
• A New Method for Determining $F_{\pi }$ on the Lattice
• Large N Volume Independence and an Emergent Fermionic Symmetry
• Polyakov Loop and Gluon Quasiparticles in Yang-Mills Thermodynamics
• (S)QCD on R^3 x S^1: Screening of Polyakov loop by fundamental quarks and the demise of semi-classics
• Lüscher's finite size method with twisted boundary conditions: an application to $J/\psi$-$\varphi$ system to search for narrow resonance
• Dual quark condensate in the Polyakov-loop extended Nambu--Jona-Lasinio model
• Large-N reduction in QCD with two adjoint Dirac fermions
• Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories
• Near the sill of the conformal window: gauge theories with fermions in two-index representations
• Fermionic boundary conditions and the finite temperature transition of QCD
• QCD-like theories at nonzero temperature and density
• Multiflavor QCD* on R_3 x S_1: Studying Transition From Abelian to Non-Abelian Confinement
• The finite-temperature chiral transition in QCD with adjoint fermions
• Twisted space-time reduced model of large N QCD with two adjoint Wilson fermions
• QCD with one compact spatial dimension
• Extracting $F_{\pi }$ from small lattices: unquenched results
• Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills
• String Tension Scaling in High-Temperature Confined SU(N) Gauge Theories
• Chiral condensate and dressed Polyakov loop in the Nambu--Jona-Lasinio model
• Phase structure of the N=1 supersymmetric Yang-Mills theory at finite temperature
• Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases
• The 't Hooft vertex revisited
• Quarks with Twisted Boundary Conditions in the Epsilon Regime
• A PNJL Model for Adjoint Fermions with Periodic Boundary Conditions
• Adjoint fermion zero-modes for SU(N) calorons
• Phase structure and Hosotani mechanism in gauge theories with compact dimensions revisited
• BCS-BEC crossover in relativistic Fermi systems
• Confinement and deconfinement for any gauge group from dyons viewpoint
• Quantum phase transitions and new scales in QCD-like theories
• Remarks on Adjoint QCD with k Flavors, k>= 2
• Adjoint quarks and fermionic boundary conditions
• Physical interpretation of the dressed Polyakov loop in the Nambu--Jona-Lasinio model
• Gluino zero-modes for non-trivial holonomy calorons
• Instantons and constituent monopoles
• Twisted reduction in large N QCD with adjoint Wilson fermions
• Statistical physics of dyons and confinement
• Exact high temperature expansion of the one-loop thermodynamic potential with complex chemical potential
• On the Relation of the Deconfinement and the Chiral Phase Transition in Gauge Theories with Fundamental and Adjoint Matter
• Gluino zero-modes for calorons at finite temperature
• Gauge theories with fermions in two-index representations

Cited by in corpus (54)

• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Anomaly constraints on deconfinement and chiral phase transition
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Circle compactification and 't Hooft anomaly
• Complexified path integrals, exact saddles and supersymmetry
• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• QCD on a small circle
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• On exact-WKB analysis, resurgent structure, and quantization conditions
• Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• $\theta$ dependence in trace deformed $SU(3)$ Yang-Mills theory: a lattice study
• Compactified N=1 supersymmetric Yang-Mills theory on the lattice: Continuity and the disappearance of the deconfinement transition
• Fractional instantons and bions in the principal chiral model on ${\mathbb{R}}^2\times S^1$ with twisted boundary conditions
• Anderson Localization in high temperature QCD: background configuration properties and Dirac eigenmodes
• From 3d dualities to hadron physics
• Exact-WKB analysis for SUSY and quantum deformed potentials: Quantum mechanics with Grassmann fields and Wess-Zumino terms
• $\theta$-dependence and center symmetry in Yang-Mills theories
• Critical behavior of gauge theories and Coulomb gases in three and four dimensions
• String tensions in deformed Yang-Mills theory
• Bose-Fermi Degeneracies in Large $N$ Adjoint QCD
• Bose-Fermi cancellations without supersymmetry
• Vacuum structure of Yang-Mills theory as a function of $\theta$
• Dihedral symmetry in $SU(N)$ Yang-Mills theory
• Properties of size-dependent models having quasiperiodic boundary conditions
• On the Global Structure of Deformed Yang-Mills Theory and QCD(adj) on ${\mathbb{R}}^3\times {\mathbb{S}}^1$
• Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV
• Strongly coupled QFT dynamics via TQFT coupling
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• The absence of IR renormalons in gauge theories on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and what it means for resurgence
• Phases of circle-compactified QCD with adjoint fermions at finite density
• Spectrum of Trace Deformed Yang-Mills Theories
• Exploring gauge theories with adjoint matter on the lattice
• Symmetry Crossover Protecting Chirality in Dirac Spectra
• The thermal instanton determinant in compact form
• Monopole-vortex continuity of $\mathcal{N}=1$ super Yang-Mills theory on ${\mathbb{R}}^2\times S^1\times S^1$ with 't Hooft twist
• Consistency of $\chi$SB in chiral Yang-Mills theory with adiabatic continuity
• Infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• ${\mathbb{Z}}_N$ stability and continuity in twisted Eguchi-Kawai model with two-flavor adjoint fermions
• More on the infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• Deconfinement on ${\mathbb{R}}^2\times S_L^1\times S_{\beta }^1$ for all gauge groups and duality to double Coulomb Gas
• Exact WKB in all sectors I: Potentials with degenerate saddles
• Boundary conditions and electromagnetic effects on the phase transition of a zero spin bosonic system
• Exact-WKB Analysis of Two-level Floquet Systems
• Exact WKB in all sectors II: Potentials with non-degenerate saddles
• On the perturbative aspects of deformed Yang-Mills theory