Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
hub Canonical reference
Theta, Time Reversal, and Temperature
Canonical reference. 100% of citing Pith papers cite this work as background.
23
Pith papers citing it
Background
100% of classified citations
abstract
$SU(N)$ gauge theory is time reversal invariant at $\theta=0$ and $\theta=\pi$. We show that at $\theta=\pi$ there is a discrete 't Hooft anomaly involving time reversal and the center symmetry. This anomaly leads to constraints on the vacua of the theory. It follows that at $\theta=\pi$ the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at $\theta=0$ is gapped, non-degenerate, and trivial.) Due to the anomaly, the theory admits nontrivial domain walls supporting lower-dimensional theories. Depending on the nature of the vacuum at $\theta=\pi$, several phase diagrams are possible. Assuming area law for space-like loops, one arrives at an inequality involving the temperatures at which CP and the center symmetry are restored. We also analyze alternative scenarios for $SU(2)$ gauge theory. The underlying symmetry at $\theta=\pi$ is the dihedral group of 8 elements. If deconfined loops are allowed, one can have two $O(2)$-symmetric fixed points. It may also be that the four-dimensional theory around $\theta=\pi$ is gapless, e.g. a Coulomb phase could match the underlying anomalies.
hub tools
citation-role summary
background 12
citation-polarity summary
roles
background 12polarities
background 12representative citing papers
Coleman's puzzles are solved: at θ=π with equal masses the model shows spontaneous charge conjugation breaking and no confinement with mass gap ~m exp(-0.111 g²/m²) at strong coupling; at θ=0 a level crossing occurs between isosinglet states; isospin-breaking effects are quantified for unequal mass.
Proposes torus and lens-space twisted partition functions as criteria for center-vortex and monopole condensation and proves vortex condensation implies monopole condensation in gapped phases.
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.
Lattice computation of Wilson-'t Hooft loops supplies numerical evidence for dyon condensation at theta=2pi in SU(2) Yang-Mills.
The local moduli space of charge-r/N self-dual instantons on a twisted T^4 is identified with the Higgs branch of a 4d N=2 theory on intersecting D5-branes, reproducing prior field-theory results with manifest hyper-Kähler structure.
Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.
Automorphisms of gauge groups extend to higher or non-invertible symmetries in topological gauge theories and enable transversal non-Clifford gates in 2+1d Z_N qudit Clifford stabilizer models for N greater than or equal to 3.
Simulations of a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion show the Polyakov loop remains near zero for periodic boundary conditions as the compactified circle shrinks, supporting adiabatic continuity of the confined phase.
In self-dual Yang-Mills the S-algebra becomes an algebra of 1-form symmetries whose 2-form currents link integrability to the equality of Carrollian corner charges and celestial chiral algebra modes.
Ultra-local lattice Maxwell theory with a theta term has exact SL(2,Z) duality after a non-local redefinition of the S-transformation, with Wilson and 't Hooft loops transforming up to a self-linking phase.
Numerical lattice study shows fractional instantons on twisted T^4 morph into monopole-instantons and center vortices as geometry interpolates between R^{4-k} x T^k, with some transitions discontinuous under deformation.
The paper verifies the bound fS/|n| ≤ (π/(2 κ_d)) sqrt((d-1)/(d-2)) for axion instantons and sharpens it to fS/|n| ≤ (1/κ_4) sqrt(7/2) for supersymmetric 4d instantons using three approaches in the string landscape.
A 5D bottom-up holographic model with a theta-sourced scalar reproduces the lattice result that the deconfinement temperature drops quadratically with θ/N, and predicts θ-dependence of the transition rate.
A holographic toy model is constructed for third-order photonic exceptional points in ternary microrings, with numerical spectra, phase rigidity, and connections to the theta-vacuum of QCD via topological structures and a second-order EP in a perturbed model.
In a parity-symmetric model with TeV-scale lepton number violation, a 10 TeV μ+μ+ collider can probe W' boson masses up to 16 TeV via on-shell and off-shell lepton number violating production.
Abelian 2d gauge theories show rich phase structure with c=1 and c=1/2 critical lines; chiral versions realize symmetric mass generation for fermions.
Analyses of specific chiral gauge theories using generalized symmetries and anomaly matching yield rich infrared effective theories, RG flows, and light spectra.
Holographic consistency checks confirm confinement (area law), domain-wall dynamics matching YM-CS theory, and absence of stable axionic strings in a D3/O7-conifold gauge/gravity dual.
Derives a generic chiral anomaly formula incorporating multiple Feynman diagrams, from which abelian, singlet, consistent, and covariant forms follow, with topological discussion and FeynCalc code.
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.
citing papers explorer
-
Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
-
The two-flavor Schwinger model at 50: Solving Coleman's puzzles
Coleman's puzzles are solved: at θ=π with equal masses the model shows spontaneous charge conjugation breaking and no confinement with mass gap ~m exp(-0.111 g²/m²) at strong coupling; at θ=0 a level crossing occurs between isosinglet states; isospin-breaking effects are quantified for unequal mass.
-
Monopoles, Center Vortices, Confinement in (3+1)d, and the Lens-Space Twisted Partition Function
Proposes torus and lens-space twisted partition functions as criteria for center-vortex and monopole condensation and proves vortex condensation implies monopole condensation in gapped phases.
-
Hilbert Space Fragmentation from Generalized Symmetries
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
-
Non-invertible symmetries in the axiverse, and the imaginary wormholes
Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.
-
Numerical Hints for Dyon Condensation at $\theta=2\pi$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory
Lattice computation of Wilson-'t Hooft loops supplies numerical evidence for dyon condensation at theta=2pi in SU(2) Yang-Mills.
-
D-branes and fractional instantons on a twisted four torus: the moduli space as an N=2 supersymmetric Higgs branch
The local moduli space of charge-r/N self-dual instantons on a twisted T^4 is identified with the Higgs branch of a 4d N=2 theory on intersecting D5-branes, reproducing prior field-theory results with manifest hyper-Kähler structure.
-
Generalized Families of QFTs
Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.
-
Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates
Automorphisms of gauge groups extend to higher or non-invertible symmetries in topological gauge theories and enable transversal non-Clifford gates in 2+1d Z_N qudit Clifford stabilizer models for N greater than or equal to 3.
-
Adiabatic continuity in a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion
Simulations of a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion show the Polyakov loop remains near zero for periodic boundary conditions as the compactified circle shrinks, supporting adiabatic continuity of the confined phase.
-
Celestial 1-form symmetries
In self-dual Yang-Mills the S-algebra becomes an algebra of 1-form symmetries whose 2-form currents link integrability to the equality of Carrollian corner charges and celestial chiral algebra modes.
-
Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation
Ultra-local lattice Maxwell theory with a theta term has exact SL(2,Z) duality after a non-local redefinition of the S-transformation, with Wilson and 't Hooft loops transforming up to a self-linking phase.
-
Metamorphosis of fractional instantons on a twisted $T^4$ with a double-trace deformation: a numerical study
Numerical lattice study shows fractional instantons on twisted T^4 morph into monopole-instantons and center vortices as geometry interpolates between R^{4-k} x T^k, with some transitions discontinuous under deformation.
-
Sharpening the Supersymmetric Axion Weak Gravity Conjecture
The paper verifies the bound fS/|n| ≤ (π/(2 κ_d)) sqrt((d-1)/(d-2)) for axion instantons and sharpens it to fS/|n| ≤ (1/κ_4) sqrt(7/2) for supersymmetric 4d instantons using three approaches in the string landscape.
-
Confinement in Holographic Theories at Finite Theta
A 5D bottom-up holographic model with a theta-sourced scalar reproduces the lattice result that the deconfinement temperature drops quadratically with θ/N, and predicts θ-dependence of the transition rate.
-
Photonic Exceptional Points in Holography and QCD
A holographic toy model is constructed for third-order photonic exceptional points in ternary microrings, with numerical spectra, phase rigidity, and connections to the theta-vacuum of QCD via topological structures and a second-order EP in a perturbed model.
-
Lepton number violating signals of a parity symmetric model at $\mu$TRISTAN
In a parity-symmetric model with TeV-scale lepton number violation, a 10 TeV μ+μ+ collider can probe W' boson masses up to 16 TeV via on-shell and off-shell lepton number violating production.
-
Phases of 2d Gauge Theories and Symmetric Mass Generation
Abelian 2d gauge theories show rich phase structure with c=1 and c=1/2 critical lines; chiral versions realize symmetric mass generation for fermions.
-
Infrared spectra of some strongly--coupled chiral gauge theories
Analyses of specific chiral gauge theories using generalized symmetries and anomaly matching yield rich infrared effective theories, RG flows, and light spectra.
-
Confinement in a finite duality cascade
Holographic consistency checks confirm confinement (area law), domain-wall dynamics matching YM-CS theory, and absence of stable axionic strings in a D3/O7-conifold gauge/gravity dual.
-
The Polymorphic Chiral Anomaly
Derives a generic chiral anomaly formula incorporating multiple Feynman diagrams, from which abelian, singlet, consistent, and covariant forms follow, with topological discussion and FeynCalc code.
-
Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
-
Lectures on Generalized Symmetries
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.