Abstract
We carry out a systematic study of SU(6) Yang-Mills theory endowed with fermions in the adjoint and 3-index antisymmetric mixed-representation. The fermion bilinear in the 3-index antisymmetric representation vanishes identically, which leads to interesting new phenomena. We first study the theory on a small circle, i.e., on \( {\mathrm{\mathbb{R}}}^3\times {\mathbbm{S}}_L^1 \), employing symmetry-twisted boundary conditions and semi-classical techniques. We find that the ground state is 3-fold degenerate, which can be explained as a consequence of a 1-form/0-form mixed ’t Hooft anomaly. In addition, the theory may admit massless bosonic and fermionic degrees of freedom, depending on the number of flavors, and confines the electric probes in the infrared. Empowered by ’t Hooft anomaly matching conditions along with the 2-loop β-function, we further examine the possible infrared symmetry realizations on ℝ4 for various number of adjoint and 3-index antisymmetric fermions. The infrared theory is either a conformal field theory, which is expected for a large number of flavors, or it is confining with or without chiral symmetry breaking. In a few cases, we are able to give enough evidence for adiabatic continuity between the small- and large-circle limits.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. ’t Hooft et al. eds., Recent developments in gauge theories, in Proceedings, Nato Advanced Study Institute, Cargese, France, 26 August–8 September 1979 [NATO Sci. Ser.B 59 (1980) 1] [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized global symmetries, JHEP02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
D. Gaiotto, A. Kapustin, Z. Komargodski and N. Seiberg, Theta, time reversal and temperature, JHEP05 (2017) 091 [arXiv:1703 .00501] [INSPIRE].
Y. Tanizaki, Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking, JHEP08 (2018) 171 [arXiv:1807.07666] [INSPIRE].
F. Benini, C. Córdova and P.-S. Hsin, On 2-group global symmetries and their anomalies, JHEP03 (2019) 118 [arXiv:1803.09336] [INSPIRE].
C. Choi, D. Delmastro, J. Gomis and Z. Komargodski, Dynamics of QCD3with rank-two quarks and duality, arXiv:1810.07720 [INSPIRE].
Z. Komargodski, T. Sulejmanpasic and M. Ünsal, Walls, anomalies and deconfinement in quantum antiferromagnets, Phys. Rev.B 97 (2018) 054418 [arXiv:1706.05731] [INSPIRE].
H. Shimizu and K. Yonekura, Anomaly constraints on deconfinement and chiral phase transition, Phys. Rev.D 97 (2018) 105011 [arXiv:1706 .06104] [INSPIRE].
Z. Komargodski, A. Sharon, R. Thorngren and X. Zhou, Comments on Abelian Higgs models and persistent order, SciPost Phys.6 (2019) 003 [arXiv: 1705 .04786] [INSPIRE].
Y. Kikuchi and Y. Tanizaki, Global inconsistency, ’t Hooft anomaly and level crossing in quantum mechanics, PTEP2017 (2017) 113B05 [arXiv:1708 .01962] [INSPIRE].
K. Aitken, A. Cherman and M. Ünsal, Dihedral symmetry in SU(N) Yang-Mills theory, arXiv: 1804.05845 [INSPIRE].
Y. Tanizaki and T. Sulejmanpasic, Anomaly and global inconsistency matching: θ-angles, SU(3)/U(1)2nonlinear σ-model, SU(3) chains and its generalizations, Phys. Rev.B 98 (2018) 115126 [arXiv:1805.11423] [INSPIRE].
T. Sulejmanpasic and Y. Tanizaki, C-P-T anomaly matching in bosonic quantum field theory and spin chains, Phys. Rev.B 97 (2018) 144201 [arXiv:1802 .02153] [INSPIRE].
Y. Tanizaki, Y. Kikuchi, T. Misumi and N. Sakai, Anomaly matching for the phase diagram of massless ZN-QCD, Phys. Rev.D 97 (2018) 054012 [arXiv:1711.10487] [INSPIRE].
M.M. Anber and E. Poppitz, Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj), JHEP05 (2019) 151 [arXiv:1811.10642] [INSPIRE].
M.M. Anber and E. Poppitz, Anomaly matching, (axial) Schwinger models and high- T super Yang-Mills domain walls, JHEP09 (2018) 076 [arXiv:1807 .00093] [INSPIRE].
A. Karasik and Z. Komargodski, The hi-fundamental gauge theory in 3 + 1 dimensions: the vacuum structure and a cascade, JHEP05 (2019) 144 [arXiv:1904 .09551] [INSPIRE].
C. Córdova, D.S. Freed, H.T. Lam and N. Seiberg, Anomalies in the space of coupling constants and their dynamical applications I, arXiv:1905.09315 [INSPIRE].
C. Córdova, D.S. Freed, H.T. Lam and N. Seiberg, Anomalies in the space of coupling constants and their dynamical applications II, arXiv:1905 .13361 [INSPIRE].
T. Misumi, Y. Tanizaki and M. Ünsal, Fractional θ angle, ’t Hooft anomaly and quantum instantons in charge-q multi-flavor Schwinger model, JHEP07 (2019) 018 [arXiv: 1905 .05781] [INSPIRE].
H. Nishimura and Y. Tanizaki, High-temperature domain walls of QCD with imaginary chemical potentials, JHEP06 (2019) 040 [arXiv:1903. 04014] [INSPIRE].
G.V. Dunne, Y. Tanizaki and M. Ünsal, Quantum distillation of Hilbert spaces, semi-classics and anomaly matching, JHEP08 (2018) 068 [arXiv: 1803 .02430] [INSPIRE].
M.M. Anber, E. Poppitz and T. Sulejmanpasic, Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD, Phys. Rev.D 92 (2015) 021701 [arXiv: 1501.06773] [INSPIRE].
A. Cherman, T. Schäfer and M. Ünsal, Chiral lagrangian from duality and monopole operators in compactified QCD, Phys. Rev. Lett.117 (2016) 081601 [arXiv: 1604 . 06108] [INSPIRE].
M.M. Anber, E. Poppitz and M. Ünsal, 2d affine XY-spin modelj4d gauge theory duality and deconfinement, JHEP04 (2012) 040 [arXiv: 1112.6389] [INSPIRE].
E. Poppitz, T. Schäfer and M. Ünsal, Continuity, deconfinement and (super) Yang-Mills theory, JHEP10 (2012) 115 [arXiv: 1205. 0290] [INSPIRE].
M.M. Anber, S. Collier and E. Poppitz, The SU(3)/Z3QCD(adj) deconfinement transition via the gauge theory/‘affine’ XY-model duality, JHEP01 (2013) 126 [arXiv:1211. 2824] [INSPIRE].
M. Ünsal and L.G. Yaffe, Center-stabilized Yang-Mills theory: confinement and large N volume independence, Phys. Rev.D 78 (2008) 065035 [arXiv: 0803 . 0344] [INSPIRE].
M.M. Anber, S. Collier, E. Poppitz, S. Strimas-Mackey and B. Teeple, Deconfinement in N = 1 super Yang-Mills theory on R3 × S1via dual-Coulomb gas and “affine” XY-model, JHEP11 (2013) 142 [arXiv:1310 .3522] [INSPIRE].
M.M. Anber, E. Poppitz and B. Teeple, Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups, JHEP09 (2014) 040 [arXiv:1406 . 1199] [INSPIRE].
G.V. Dunne and M. Ünsal, New nonperturbative methods in quantum field theory: from large-N orbifold equivalence to bions and resurgence, Ann. Rev. Nucl. Part. Sci.66 (2016) 245 [arXiv: 1601.03414] [INSPIRE].
M.M. Anber and T. Sulejmanpasic, The renormalon diagram in gauge theories on R3 × S1, JHEP01 (2015) 139 [arXiv:1410 . 0121] [INSPIRE].
M.M. Anber and B.J. Kolligs, Entanglement entropy, dualities and deconfinement in gauge theories, JHEP08 (2018) 175 [arXiv:1804 . 01956] [INSPIRE].
K. Aitken, A. Cherman, E. Poppitz and L.G. Yaffe, QCD on a small circle, Phys. Rev.D 96 (2017) 096022 [arXiv:1707 . 08971] [INSPIRE].
Y. Tanizaki, T. Misumi and N. Sakai, Circle compactification and ’t Hooft anomaly, JHEP12 (2017) 056 [arXiv:1710 .08923] [INSPIRE].
M. Hongo, T. Misumi and Y. Tanizaki, Phase structure of the twisted SU(3) /U(1)2flag σ-model on R × S1, JHEP02 (2019) 070 [arXiv:1812 . 02259] [INSPIRE].
M.M. Anber and E. Poppitz, Two-flavor adjoint QCD, Phys. Rev.D 98 (2018) 034026 [arXiv: 1805 .12290] [INSPIRE].
M.M. Anber and L. Vincent-Genod, Classification of compactified su(Nc) gauge theories with fermions in all representations, JHEP12 (2017) 028 [arXiv: 1704. 08277] [INSPIRE].
D.D. Dietrich and F. Sannino, Conformal window of SU(N) gauge theories with fermions in higher dimensional representations, Phys. Rev.D 75 (2007) 085018 [hep-ph/0611341] [INSPIRE].
E. Poppitz and Y. Shang, Chiral lattice gauge theories via mirror-fermion decoupling: a mission (im)possible?, Int. J. Mod. Phys.A 25 (2010) 2761 [arXiv: 1003 .5896] [INSPIRE].
S. Bolognesi and K. Konishi, Dynamics and symmetries in chiral SU(N) gauge theories, arXiv: 1906 . 01485 [INSPIRE].
T.A. Ryttov and R. Shrock, Ultraviolet to infrared evolution and nonperturbative behavior of SU(N) ⨂ SU(N − 4) ⨂ U(1) chiral gauge theories, Phys. Rev.D 100 (2019) 055009 [arXiv: 1906 . 04255] [INSPIRE].
S. Yamaguchi, ’t Hooft anomaly matching condition and chiral symmetry breaking without bilinear condensate, JHEP01 (2019) 014 [arXiv: 1811.09390] [INSPIRE].
E. Poppitz and M. Ünsal, Conformality or confinement: (IR)relevance of topological excitations, JHEP09 (2009) 050 [arXiv:0906. 5156] [INSPIRE].
E. Poppitz and M. Ünsal, Conformality or confinement (II): one-flavor CFTs and mixed-representation QCD, JHEP12 (2009) 011 [arXiv:0910.1245] [INSPIRE].
J.C. Myers and M.C. Ogilvie, Phase diagrams of SU(N) gauge theories with fermions in various representations, JHEP07 (2009) 095 [arXiv:0903. 4638] [INSPIRE].
D.J. Gross and W. Taylor, Twists and Wilson loops in the string theory of two-dimensional QCD, Nucl. Phys.B 403 (1993) 395 [hep-th/9303046] [INSPIRE].
W.E. Caswell, Asymptotic behavior of non-Abelian gauge theories to two loop order, Phys. Rev. Lett.33 (1974) 244 [INSPIRE].
T. Appelquist, K.D. Lane and U. Mahanta, On the ladder approximation for spontaneous chiral symmetry breaking, Phys. Rev. Lett.61 (1988) 1553 [INSPIRE].
C. Córdova and T.T. Dumitrescu, Candidate phases for SU(2) adjoint QCD4with two flavors from N = 2 supersymmetric Yang-Mills theory, arXiv: 1806 . 09592 [INSPIRE].
Z. Bi and T. Senthil, Adventure in topological phase transitions in 3 + 1-D: non-Abelian deconfined quantum criticalities and a possible duality, Phys. Rev.X 9 (2019) 021034 [arXiv : 1808 . 07465] [INSPIRE].
Z. Wan and J. Wang, Adjoint QCD4, deconfined critical phenomena, symmetry-enriched topological quantum field theory and higher symmetry-extension, Phys. Rev.D 99 (2019) 065013 [arXiv:1812 . 11955] [INSPIRE].
E. Poppitz and T.A. Ryttov, A possible phase for adjoint QCD, arXiv: 1904.11640 [INSPIRE].
E. Poppitz and M. Ünsal, Chiral gauge dynamics and dynamical supersymmetry breaking, JHEP07 (2009) 060 [arXiv:0905 .0634] [INSPIRE].
P.C. Argyres and M. Ünsal, The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion and renormalon effects, JHEP08 (2012) 063 [arXiv: 1206 .1890] [INSPIRE].
M.F. Atiyah and I.M. Singer, The index of elliptic operators: I, Ann. Math. 87 (1968) 484.
T.M.W. Nye and M.A. Singer, An L2index theorem for Dirac operators on S1 × R3, submitted to J. Funct. Anal. (2000) [math.DG/0009144] [INSPIRE].
E. Poppitz and M. Ünsal, Index theorem for topological excitations on R3 × S1and Chern- Simons theory, JHEP03 (2009) 027 [arXiv:0812. 2085] [INSPIRE].
T.C. Kraan and P. van Baal, Periodic instantons with nontrivial holonomy, Nucl. Phys.B 533 (1998) 627 [hep-th/9805168] [INSPIRE].
M.M. Anber and E. Poppitz, Microscopic structure of magnetic bions, JHEP06 (2011) 136 [arXiv: 1105 .0940] [INSPIRE].
M.M. Anber and E. Poppitz, On the global structure of deformed Yang-Mills theory and QCD(adj) on R3 × S1, JHEP10 (2015) 051 [arXiv:1508 .00910] [INSPIRE].
M. Ünsal, Magnetic bion condensation: a new mechanism of confinement and mass gap in four dimensions, Phys. Rev.D 80 (2009) 065001 [arXiv:0709. 3269] [INSPIRE].
G. ’t Hooft, A property of electric and magnetic flux in non-Abelian gauge theories, Nucl. Phys.B 153 (1979) 141 [INSPIRE].
T.D. Cohen, Center symmetry and area laws, Phys. Rev.D 90 (2014) 047703 [arXiv: 1407 .4128] [INSPIRE].
G. Bergner, P. Giudice, G. Münster, I. Montvay and S. Piemonte, The light bound states of supersymmetric SU(2) Yang-Mills theory, JHEP03 (2016) 080 [arXiv:1512 .07014] [INSPIRE].
T. Banks and A. Zaks, On the phase structure of vector-like gauge theories with massless fermions, Nucl. Phys.B 196 (1982) 189 [INSPIRE].
L.-F. Li, Group theory of the spontaneously broken gauge symmetries, Phys. Rev.D 9 (1974) 1723 [INSPIRE].
C. Csáki and H. Murayama, Discrete anomaly matching, Nucl. Phys.B 515 (1998) 114 [hep-th/9710105] [INSPIRE].
J.L. Cardy, Is there a c theorem in four-dimensions?, Phys. Lett.B 215 (1988) 749 [INSPIRE].
Z. Wan and J. Wang, Higher anomalies, higher symmetries and cobordisms I: classification of higher-symmetry-protected topological states and their boundary fermionic jbosonic anomalies via a generalized cobordism theory, arXiv:1812.11967 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1906.10315
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Anber, M.M. Self-conjugate QCD. J. High Energ. Phys. 2019, 42 (2019). https://doi.org/10.1007/JHEP10(2019)042
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2019)042