Built on

K. Yonekura, “Anomaly matching in QCD thermal phase transition,” JHEP
Original
1901
Earlier work this paper cites.
T. Sulejmanpasic and C. Gattringer, “Abelian gauge theories on the lattice: θ \theta -terms and compact gauge theory with(out) monopoles,” Nucl. Phys
Original
1901
Earlier work this paper cites.
H. Nishimura and Y. Tanizaki, “High-temperature domain walls of QCD with imaginary chemical potentials,” JHEP
Original
1903
Earlier work this paper cites.
A. Karasik and Z. Komargodski, “The bi-fundamental gauge theory in 3+1 dimensions: The vacuum structure and a cascade,” JHEP
Original
1904
Earlier work this paper cites.
T. Misumi, Y. Tanizaki, and M. Ünsal, “Fractional θ \theta angle, ’t Hooft anomaly, and quantum instantons in charge- q q multi-flavor Schwinger model,” JHEP
Original
1905
Earlier work this paper cites.
C. Cordova, D. S. Freed, H. T. Lam, and N. Seiberg, “Anomalies in the Space of Coupling Constants and Their Dynamical Applications I,” arXiv:1905.09315 [hep-th]
Original
1905
Earlier work this paper cites.
A. Cherman, T. Jacobson, Y. Tanizaki, and M. Ünsal, “Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD,” arXiv:1908.09858 [hep-th]
Original
1908
Earlier work this paper cites.
A. A. Cox, E. Poppitz, and S. S. Wong, “Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow,” arXiv:1909.10979 [hep-th]
Original
1909
Earlier work this paper cites.
E. Sharpe, “Undoing decomposition,” arXiv:1911.05080 [hep-th]
Original
1911
Earlier work this paper cites.
S. L. Adler, “Axial vector vertex in spinor electrodynamics,” Phys. Rev
1969
Earlier work this paper cites.
J. S. Bell and R. Jackiw, “A PCAC puzzle: π 0 → γ γ \pi^{0}\to\gamma\gamma in the σ \sigma model,” Nuovo Cim
1969
Earlier work this paper cites.
G. ’t Hooft, “Magnetic Monopoles in Unified Gauge Theories,” Nucl. Phys
1974
Earlier work this paper cites.
A. M. Polyakov, “Particle Spectrum in the Quantum Field Theory,” JETP Lett
1974
Earlier work this paper cites.
A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Yu. S. Tyupkin, “Pseudoparticle Solutions of the Yang-Mills Equations,” Phys. Lett
1975
Earlier work this paper cites.
A. M. Polyakov, “Compact Gauge Fields and the Infrared Catastrophe,” Phys. Lett
1975
Earlier work this paper cites.
C. G. Callan, Jr., R. F. Dashen, and D. J. Gross, “The Structure of the Gauge Theory Vacuum,” Phys. Lett
1976
Earlier work this paper cites.
R. Jackiw and C. Rebbi, “Vacuum Periodicity in a Yang-Mills Quantum Theory,” Phys. Rev. Lett
1976
Earlier work this paper cites.
G. ’t Hooft, “Symmetry Breaking Through Bell-Jackiw Anomalies,” Phys. Rev. Lett
1976
Earlier work this paper cites.
R. D. Peccei and H. R. Quinn, “CP Conservation in the Presence of Instantons,” Phys. Rev. Lett
1977
Earlier work this paper cites.
R. D. Peccei and H. R. Quinn, “Constraints Imposed by CP Conservation in the Presence of Instantons,” Phys. Rev
1977
Earlier work this paper cites.
G. ’t Hooft, “On the phase transition towards permanent quark confinement,” Nucl.Phys.B
1978
Earlier work this paper cites.
E. Witten, “Large N Chiral Dynamics,” Annals Phys
1980
Earlier work this paper cites.
Y. Frishman, A. Schwimmer, T. Banks, and S. Yankielowicz, “The Axial Anomaly and the Bound State Spectrum in Confining Theories,” Nucl. Phys
1981
Earlier work this paper cites.
D. J. Gross, R. D. Pisarski, and L. G. Yaffe, “QCD and Instantons at Finite Temperature,” Rev. Mod. Phys
1981
Earlier work this paper cites.
A. Gonzalez-Arroyo and M. Okawa, “Large N N reduction with the Twisted Eguchi-Kawai model,” JHEP
Original
1981
Earlier work this paper cites.
P. van Baal, “Some Results for SU(N) Gauge Fields on the Hypertorus,” Commun. Math. Phys
1982
Earlier work this paper cites.
T. Eguchi and H. Kawai, “Reduction of Dynamical Degrees of Freedom in the Large N Gauge Theory,” Phys. Rev. Lett
1982
Earlier work this paper cites.
E. Witten, “Constraints on Supersymmetry Breaking,” Nucl. Phys
1982
Earlier work this paper cites.
A. Gonzalez-Arroyo and M. Okawa, “The Twisted Eguchi-Kawai Model: A Reduced Model for Large N Lattice Gauge Theory,” Phys. Rev
1983
Earlier work this paper cites.
A. Gonzalez-Arroyo and M. Okawa, “A Twisted Model for Large N N Lattice Gauge Theory,” Phys. Lett
1983
Earlier work this paper cites.
K.-M. Lee and P. Yi, “Monopoles and instantons on partially compactified D-branes,” Phys. Rev
1997
Earlier work this paper cites.
E. Witten, “Theta dependence in the large N limit of four-dimensional gauge theories,” Phys. Rev. Lett
1998
Earlier work this paper cites.
K.-M. Lee and C.-h. Lu, “SU(2) calorons and magnetic monopoles,” Phys. Rev
1998
Earlier work this paper cites.
T. C. Kraan and P. van Baal, “Exact T duality between calorons and Taub - NUT spaces,” Phys. Lett
1998
Earlier work this paper cites.
T. C. Kraan and P. van Baal, “Periodic instantons with nontrivial holonomy,” Nucl. Phys
1998
Earlier work this paper cites.

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T. C. Kraan and P. van Baal, “Monopole constituents inside SU(n) calorons,” Phys. Lett
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Then

A. Cherman, D. Dorigoni, and M. Unsal, “Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles,” JHEP
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2019

Modified instanton sum in QCD and higher-groups

Tanizaki, Yuya, Ünsal, Mithat

Understand

We consider the $SU(N)$ Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of $p$.

We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both $2\pi$-periodic scalar and $3$-form gauge fields.
This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory.
The theory has not only $\mathbb{Z}_N$ $1$-form symmetry but also $\mathbb{Z}_p$ $3$-form symmetry, and we study the global nature of this theory from the recent 't Hooft anomaly matching.

Built on

K. Yonekura, “Anomaly matching in QCD thermal phase transition,” JHEP
Original
1901
Earlier work this paper cites.
T. Sulejmanpasic and C. Gattringer, “Abelian gauge theories on the lattice: θ \theta -terms and compact gauge theory with(out) monopoles,” Nucl. Phys
Original
1901
Earlier work this paper cites.
H. Nishimura and Y. Tanizaki, “High-temperature domain walls of QCD with imaginary chemical potentials,” JHEP
Original
1903
Earlier work this paper cites.
A. Karasik and Z. Komargodski, “The bi-fundamental gauge theory in 3+1 dimensions: The vacuum structure and a cascade,” JHEP
Original
1904
Earlier work this paper cites.
T. Misumi, Y. Tanizaki, and M. Ünsal, “Fractional θ \theta angle, ’t Hooft anomaly, and quantum instantons in charge- q q multi-flavor Schwinger model,” JHEP
Original
1905
Earlier work this paper cites.
C. Cordova, D. S. Freed, H. T. Lam, and N. Seiberg, “Anomalies in the Space of Coupling Constants and Their Dynamical Applications I,” arXiv:1905.09315 [hep-th]
Original
1905
Earlier work this paper cites.
A. Cherman, T. Jacobson, Y. Tanizaki, and M. Ünsal, “Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD,” arXiv:1908.09858 [hep-th]
Original
1908
Earlier work this paper cites.
A. A. Cox, E. Poppitz, and S. S. Wong, “Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow,” arXiv:1909.10979 [hep-th]
Original
1909
Earlier work this paper cites.
E. Sharpe, “Undoing decomposition,” arXiv:1911.05080 [hep-th]
Original
1911
Earlier work this paper cites.
S. L. Adler, “Axial vector vertex in spinor electrodynamics,” Phys. Rev
1969
Earlier work this paper cites.
J. S. Bell and R. Jackiw, “A PCAC puzzle: π 0 → γ γ \pi^{0}\to\gamma\gamma in the σ \sigma model,” Nuovo Cim
1969
Earlier work this paper cites.
G. ’t Hooft, “Magnetic Monopoles in Unified Gauge Theories,” Nucl. Phys
1974
Earlier work this paper cites.
A. M. Polyakov, “Particle Spectrum in the Quantum Field Theory,” JETP Lett
1974
Earlier work this paper cites.
A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Yu. S. Tyupkin, “Pseudoparticle Solutions of the Yang-Mills Equations,” Phys. Lett
1975
Earlier work this paper cites.
A. M. Polyakov, “Compact Gauge Fields and the Infrared Catastrophe,” Phys. Lett
1975
Earlier work this paper cites.
C. G. Callan, Jr., R. F. Dashen, and D. J. Gross, “The Structure of the Gauge Theory Vacuum,” Phys. Lett
1976
Earlier work this paper cites.
R. Jackiw and C. Rebbi, “Vacuum Periodicity in a Yang-Mills Quantum Theory,” Phys. Rev. Lett
1976
Earlier work this paper cites.
G. ’t Hooft, “Symmetry Breaking Through Bell-Jackiw Anomalies,” Phys. Rev. Lett
1976
Earlier work this paper cites.
R. D. Peccei and H. R. Quinn, “CP Conservation in the Presence of Instantons,” Phys. Rev. Lett
1977
Earlier work this paper cites.
R. D. Peccei and H. R. Quinn, “Constraints Imposed by CP Conservation in the Presence of Instantons,” Phys. Rev
1977
Earlier work this paper cites.
G. ’t Hooft, “On the phase transition towards permanent quark confinement,” Nucl.Phys.B
1978
Earlier work this paper cites.
E. Witten, “Large N Chiral Dynamics,” Annals Phys
1980
Earlier work this paper cites.
Y. Frishman, A. Schwimmer, T. Banks, and S. Yankielowicz, “The Axial Anomaly and the Bound State Spectrum in Confining Theories,” Nucl. Phys
1981
Earlier work this paper cites.
D. J. Gross, R. D. Pisarski, and L. G. Yaffe, “QCD and Instantons at Finite Temperature,” Rev. Mod. Phys
1981
Earlier work this paper cites.
A. Gonzalez-Arroyo and M. Okawa, “Large N N reduction with the Twisted Eguchi-Kawai model,” JHEP
Original
1981
Earlier work this paper cites.
P. van Baal, “Some Results for SU(N) Gauge Fields on the Hypertorus,” Commun. Math. Phys
1982
Earlier work this paper cites.
T. Eguchi and H. Kawai, “Reduction of Dynamical Degrees of Freedom in the Large N Gauge Theory,” Phys. Rev. Lett
1982
Earlier work this paper cites.
E. Witten, “Constraints on Supersymmetry Breaking,” Nucl. Phys
1982
Earlier work this paper cites.
A. Gonzalez-Arroyo and M. Okawa, “The Twisted Eguchi-Kawai Model: A Reduced Model for Large N Lattice Gauge Theory,” Phys. Rev
1983
Earlier work this paper cites.
A. Gonzalez-Arroyo and M. Okawa, “A Twisted Model for Large N N Lattice Gauge Theory,” Phys. Lett
1983
Earlier work this paper cites.
K.-M. Lee and P. Yi, “Monopoles and instantons on partially compactified D-branes,” Phys. Rev
1997
Earlier work this paper cites.
E. Witten, “Theta dependence in the large N limit of four-dimensional gauge theories,” Phys. Rev. Lett
1998
Earlier work this paper cites.
K.-M. Lee and C.-h. Lu, “SU(2) calorons and magnetic monopoles,” Phys. Rev
1998
Earlier work this paper cites.
T. C. Kraan and P. van Baal, “Exact T duality between calorons and Taub - NUT spaces,” Phys. Lett
1998
Earlier work this paper cites.
T. C. Kraan and P. van Baal, “Periodic instantons with nontrivial holonomy,” Nucl. Phys
1998
Earlier work this paper cites.

Similar

T. C. Kraan and P. van Baal, “Monopole constituents inside SU(n) calorons,” Phys. Lett
1998
Cited alongside, same era.
R. Brower, S. Chandrasekharan, J. W. Negele, and U. J. Wiese, “QCD at fixed topology,” Phys. Lett
2003
Cited alongside, same era.
N. M. Davies, T. J. Hollowood, and V. V. Khoze, “Monopoles, affine algebras and the gluino condensate,” J. Math. Phys
2003
Cited alongside, same era.
Cambridge University Press, 5, 2005
S. Weinberg, The Quantum Theory of Fields, Volume 2: Modern Applications · 2005
Cited alongside, same era.
T. Pantev and E. Sharpe, “GLSM’s for Gerbes (and other toric stacks),” Adv. Theor. Math. Phys
2006
Cited alongside, same era.
T. Pantev and E. Sharpe, “String compactifications on Calabi-Yau stacks,” Nucl. Phys
2006