Built on

P. Goddard, J. Nuyts and D. I. Olive, Gauge Theories and Magnetic Charge , Nucl. Phys. B125
1977
Earlier work this paper cites.
A. D’Adda, M. Luscher and P. Di Vecchia, A 1/n Expandable Series of Nonlinear Sigma Models with Instantons , Nucl. Phys. B146
1978
Earlier work this paper cites.
G. ’t Hooft, On the Phase Transition Towards Permanent Quark Confinement , Nucl. Phys. B138
1978
Earlier work this paper cites.
A. M. Polyakov, Thermal Properties of Gauge Fields and Quark Liberation , Phys. Lett. 72B
1978
Earlier work this paper cites.
E. Witten, Instantons, the Quark Model, and the 1/n Expansion , Nucl. Phys. B149
1979
Earlier work this paper cites.
E. Witten, Current Algebra Theorems for the U(1) Goldstone Boson , Nucl. Phys. B156
1979
Earlier work this paper cites.
E. Witten, Dyons of Charge e theta/2 pi , Phys. Lett. 86B
1979
Earlier work this paper cites.
E. Witten, Large N Chiral Dynamics , Annals Phys. 128
1980
Earlier work this paper cites.
M. Creutz, Quark masses and chiral symmetry , Phys. Rev. D52
1995
Earlier work this paper cites.
K.-M. Lee and P. Yi, Monopoles and instantons on partially compactified D-branes , Phys. Rev. D56
1997
Earlier work this paper cites.
E. Witten, Theta dependence in the large N limit of four-dimensional gauge theories , Phys. Rev. Lett. 81
1998
Earlier work this paper cites.
T. C. Kraan and P. van Baal, Periodic instantons with nontrivial holonomy , Nucl.Phys. B533
1998
Earlier work this paper cites.
M. A. Shifman, Domain walls and decay rate of the excited vacua in the large N Yang-Mills theory , Phys. Rev. D59
1999
Earlier work this paper cites.
A. V. Smilga, QCD at theta similar to pi , Phys. Rev. D59
1999
Earlier work this paper cites.
N. M. Davies, T. J. Hollowood, V. V. Khoze and M. P. Mattis, Gluino condensate and magnetic monopoles in supersymmetric gluodynamics , Nucl. Phys. B559
1999
Earlier work this paper cites.
N. Dorey, An Elliptic superpotential for softly broken N=4 supersymmetric Yang-Mills theory , JHEP 07
1999
Earlier work this paper cites.
L. Del Debbio, H. Panagopoulos and E. Vicari, theta dependence of SU(N) gauge theories , JHEP 08
2002
Earlier work this paper cites.
N. M. Davies, T. J. Hollowood and V. V. Khoze, Monopoles, affine algebras and the gluino condensate , J. Math. Phys. 44
2003
Earlier work this paper cites.
M. Unsal and L. G. Yaffe, Center-stabilized Yang-Mills theory: Confinement and large N volume independence , Phys. Rev. D78
Original
2008
Earlier work this paper cites.
M. Unsal, Abelian duality, confinement, and chiral symmetry breaking in QCD(adj) , Phys.Rev.Lett. 100
Original
2008
Earlier work this paper cites.
M. Shifman and M. Unsal, QCD-like Theories on R(3) x S(1): A Smooth Journey from Small to Large r(S(1)) with Double-Trace Deformations , Phys. Rev. D78
Original
2008
Earlier work this paper cites.
E. Vicari and H. Panagopoulos, Theta dependence of SU(N) gauge theories in the presence of a topological term , Phys. Rept. 470
Original
2009
Earlier work this paper cites.
M. Unsal, Magnetic bion condensation: A New mechanism of confinement and mass gap in four dimensions , Phys. Rev. D80
Original
2009
Earlier work this paper cites.
M. Shifman and M. Unsal, On Yang-Mills Theories with Chiral Matter at Strong Coupling , Phys. Rev. D79
Original
2009
Earlier work this paper cites.
M. Shifman and M. Unsal, Multiflavor QCD* on R(3) x S(1): Studying Transition From Abelian to Non-Abelian Confinement , Phys. Lett. B681
Original
2009
Earlier work this paper cites.

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Then

H. Kouno, T. Misumi, K. Kashiwa, T. Makiyama, T. Sasaki and M. Yahiro, Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories , Phys. Rev. D88
Original
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Later among the works it cites.
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Later among the works it cites.

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2018

Vacuum structure of Yang-Mills theory as a function of $\theta$

Aitken, Kyle, Cherman, Aleksey, Ünsal, Mithat

Understand

It is believed that in $SU(N)$ Yang-Mills theory observables are $N$-branched functions of the topological $\theta$ angle.

This is supposed to be due to the existence of a set of locally-stable candidate vacua, which compete for global stability as a function of $\theta$.
We study the number of $\theta$ vacua, their interpretation, and their stability properties using systematic semiclassical analysis in the context of adiabatic circle compactification on $\mathbb{R}^3 \times S^1$.
We find that while observables are indeed N-branched functions of $\theta$, there are only $\approx N/2$ locally-stable candidate vacua for any given $\theta$.

Built on

P. Goddard, J. Nuyts and D. I. Olive, Gauge Theories and Magnetic Charge , Nucl. Phys. B125
1977
Earlier work this paper cites.
A. D’Adda, M. Luscher and P. Di Vecchia, A 1/n Expandable Series of Nonlinear Sigma Models with Instantons , Nucl. Phys. B146
1978
Earlier work this paper cites.
G. ’t Hooft, On the Phase Transition Towards Permanent Quark Confinement , Nucl. Phys. B138
1978
Earlier work this paper cites.
A. M. Polyakov, Thermal Properties of Gauge Fields and Quark Liberation , Phys. Lett. 72B
1978
Earlier work this paper cites.
E. Witten, Instantons, the Quark Model, and the 1/n Expansion , Nucl. Phys. B149
1979
Earlier work this paper cites.
E. Witten, Current Algebra Theorems for the U(1) Goldstone Boson , Nucl. Phys. B156
1979
Earlier work this paper cites.
E. Witten, Dyons of Charge e theta/2 pi , Phys. Lett. 86B
1979
Earlier work this paper cites.
E. Witten, Large N Chiral Dynamics , Annals Phys. 128
1980
Earlier work this paper cites.
M. Creutz, Quark masses and chiral symmetry , Phys. Rev. D52
1995
Earlier work this paper cites.
K.-M. Lee and P. Yi, Monopoles and instantons on partially compactified D-branes , Phys. Rev. D56
1997
Earlier work this paper cites.
E. Witten, Theta dependence in the large N limit of four-dimensional gauge theories , Phys. Rev. Lett. 81
1998
Earlier work this paper cites.
T. C. Kraan and P. van Baal, Periodic instantons with nontrivial holonomy , Nucl.Phys. B533
1998
Earlier work this paper cites.
M. A. Shifman, Domain walls and decay rate of the excited vacua in the large N Yang-Mills theory , Phys. Rev. D59
1999
Earlier work this paper cites.
A. V. Smilga, QCD at theta similar to pi , Phys. Rev. D59
1999
Earlier work this paper cites.
N. M. Davies, T. J. Hollowood, V. V. Khoze and M. P. Mattis, Gluino condensate and magnetic monopoles in supersymmetric gluodynamics , Nucl. Phys. B559
1999
Earlier work this paper cites.
N. Dorey, An Elliptic superpotential for softly broken N=4 supersymmetric Yang-Mills theory , JHEP 07
1999
Earlier work this paper cites.
L. Del Debbio, H. Panagopoulos and E. Vicari, theta dependence of SU(N) gauge theories , JHEP 08
2002
Earlier work this paper cites.
N. M. Davies, T. J. Hollowood and V. V. Khoze, Monopoles, affine algebras and the gluino condensate , J. Math. Phys. 44
2003
Earlier work this paper cites.
M. Unsal and L. G. Yaffe, Center-stabilized Yang-Mills theory: Confinement and large N volume independence , Phys. Rev. D78
Original
2008
Earlier work this paper cites.
M. Unsal, Abelian duality, confinement, and chiral symmetry breaking in QCD(adj) , Phys.Rev.Lett. 100
Original
2008
Earlier work this paper cites.
M. Shifman and M. Unsal, QCD-like Theories on R(3) x S(1): A Smooth Journey from Small to Large r(S(1)) with Double-Trace Deformations , Phys. Rev. D78
Original
2008
Earlier work this paper cites.
E. Vicari and H. Panagopoulos, Theta dependence of SU(N) gauge theories in the presence of a topological term , Phys. Rept. 470
Original
2009
Earlier work this paper cites.
M. Unsal, Magnetic bion condensation: A New mechanism of confinement and mass gap in four dimensions , Phys. Rev. D80
Original
2009
Earlier work this paper cites.
M. Shifman and M. Unsal, On Yang-Mills Theories with Chiral Matter at Strong Coupling , Phys. Rev. D79
Original
2009
Earlier work this paper cites.
M. Shifman and M. Unsal, Multiflavor QCD* on R(3) x S(1): Studying Transition From Abelian to Non-Abelian Confinement , Phys. Lett. B681
Original
2009
Earlier work this paper cites.

Similar

G. Cossu and M. D’Elia, Finite size phase transitions in QCD with adjoint fermions , JHEP 07
Original
2009
Cited alongside, same era.
J. C. Myers and M. C. Ogilvie, Phase diagrams of SU(N) gauge theories with fermions in various representations , JHEP 07
Original
2009
Cited alongside, same era.
M. Unsal and L. G. Yaffe, Large-N volume independence in conformal and confining gauge theories , JHEP 08
Original
2010
Cited alongside, same era.
T. Azeyanagi, M. Hanada, M. Unsal and R. Yacoby, Large-N reduction in QCD-like theories with massive adjoint fermions , Phys. Rev. D82
Original
2010
Cited alongside, same era.
H. Panagopoulos and E. Vicari, The 4D SU(3) gauge theory with an imaginary θ \theta term , JHEP 11

Then

H. Kouno, T. Misumi, K. Kashiwa, T. Makiyama, T. Sasaki and M. Yahiro, Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories , Phys. Rev. D88
Original
2013
Later among the works it cites.
G. Cossu, H. Hatanaka, Y. Hosotani and J.-I. Noaki, Polyakov loops and the Hosotani mechanism on the lattice , Phys. Rev. D89
Original
2014
Later among the works it cites.
M. M. Anber, E. Poppitz and B. Teeple, Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups , JHEP 09
Original
2014
Later among the works it cites.
G. Bergner and S. Piemonte, Compactified 𝒩 = 1 \mathcal{N}=1 supersymmetric Yang-Mills theory on the lattice: continuity and the disappearance of the deconfinement transition , JHEP 12
Original
2014
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

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Later among the works it cites.

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