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.
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Theta, Time Reversal, and Temperature
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$SU(N)$ 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.
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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.
Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
Holographic 5D model shows confinement critical temperature falls quadratically with vacuum angle, matches lattice QCD, and allows time-dependent theta to trigger supercooling and altered gravitational-wave spectra.
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.
The local moduli space of self-dual fractional instantons (Q = r/N) on a twisted four-torus is the Higgs branch of an N=2 supersymmetric theory, obtained via wrapped intersecting D-brane configurations.
Holographic checks confirm area-law confinement, anomaly-matching domain walls via 2+1D TQFT, and unstable axionic strings implying no massless axions in this finite duality cascade model.
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.
The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking.
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.
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.
citing papers explorer
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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.
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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.
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Generalized Families of QFTs
Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.
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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.
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Confinement in Holographic Theories at Finite Theta
Holographic 5D model shows confinement critical temperature falls quadratically with vacuum angle, matches lattice QCD, and allows time-dependent theta to trigger supercooling and altered gravitational-wave spectra.
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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.
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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 self-dual fractional instantons (Q = r/N) on a twisted four-torus is the Higgs branch of an N=2 supersymmetric theory, obtained via wrapped intersecting D-brane configurations.
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Confinement in a finite duality cascade
Holographic checks confirm area-law confinement, anomaly-matching domain walls via 2+1D TQFT, and unstable axionic strings implying no massless axions in this finite duality cascade model.
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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.
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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.
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Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation
The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking.
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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.
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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.
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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.
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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.
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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.