- Letter
- Open Access
Symmetry enhancement, symmetry-protected topological absorption, and duality in
Phys. Rev. B 112, L041113 – Published 11 July, 2025
DOI: https://doi.org/10.1103/pgm4-dtlp
Abstract
Quantum electrodynamics in dimensions () with two Dirac fermions displays time reversal symmetry, nontrivial SPT phases, and anomalies. The fate of this theory in its strongly coupled regime has been debated extensively. Surprisingly, we find that gluing together the phase diagrams of two standard Wilson-Fisher theories suffices to reproduce all the SPT phases, anomalies, and semiclassical limits. A central mechanism behind it is “SPT absorption.” The patching of the transitions makes very concrete predictions for the behavior of the theory in its strongly coupled limits; for instance, the sigma model with topology appears due to monopole condensation.
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References (65)
- A. N. Redlich, Gauge noninvariance and parity violation of three-dimensional fermions, Phys. Rev. Lett. 52, 18 (1984).
- Throughout, we do not deform the action by monopole operators, and therefore, our theory will always have a symmetry associated to the conservation of the total magnetic charge (this symmetry may or may not be broken spontaneously, though).
- T. Appelquist, D. Nash, and L. C. R. Wijewardhana, Critical behavior in (2+1)-dimensional QED, Phys. Rev. Lett. 60, 2575 (1988).
- A. M. Polyakov, Quark confinement and topology of gauge groups, Nucl. Phys. B 120, 429 (1977).
- Using RG monotones, there exist rigorous bounds on symmetry breaking phases, see e.g. [51, 52, 53].
- A related scenario for non-compact with symmetry breaking pattern has received support from lattice simulations [54, 55, 56].
- A. Karch and D. Tong, Particle-vortex duality from 3D bosonization, Phys. Rev. X 6, 031043 (2016).
- N. Seiberg, T. Senthil, C. Wang, and E. Witten, A duality web in 2+1 dimensions and condensed matter physics, Ann. Phys. 374, 395 (2016).
- C. Wang, A. Nahum, M. A. Metlitski, C. Xu, and T. Senthil, Deconfined quantum critical points: Symmetries and dualities, Phys. Rev. X 7, 031051 (2017).
- M. Akhond, A. Armoni, and S. Speziali, Phases of from type 0 strings and seiberg duality, J. High Energy Phys. 09 (2019) 111.
- T. Senthil, D. T. Son, C. Wang, and C. Xu, Duality between quantum critical points, Phys. Rep. 827, 1 (2019).
- Z. Li, Conformality and self-duality of , Phys. Lett. B 831, 137192 (2022).
- N. Karthik and R. Narayanan, No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions, Phys. Rev. D 93, 045020 (2016).
- N. Karthik and R. Narayanan, Scale-invariance of parity-invariant three-dimensional QED, Phys. Rev. D 94, 065026 (2016).
- Y. Q. Qin, Y.-Y. He, Y.-Z. You, Z.-Y. Lu, A. Sen, A. W. Sandvik, C. Xu, and Z. Y. Meng, Duality between the deconfined quantum-critical point and the bosonic topological transition, Phys. Rev. X 7, 031052 (2017).
- P. Serna and A. Nahum, Emergence and spontaneous breaking of approximate symmetry at a weakly first-order deconfined phase transition, Phys. Rev. B 99, 195110 (2019).
- We normalize the monopoles to have charge , so , which is different from the normalization used in [18, 19, 20].
- S. S. Pufu, Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics, Phys. Rev. D 89, 065016 (2014).
- E. Dupuis, R. Boyack, and W. Witczak-Krempa, Anomalous dimensions of monopole operators at the transitions between dirac and topological spin liquids, Phys. Rev. X 12, 031012 (2022).
- E. Dyer, M. Mezei, S. S. Pufu, and S. Sachdev, Scaling dimensions of monopole operators in the theory in 2 + 1 dimensions, J. High Energ. Phys. 06 (2015) 037.
- S. M. Chester and S. S. Pufu, Towards bootstrapping , J. High Energy Phys. 08 (2016) 019.
- S. Albayrak, R. S. Erramilli, Z. Li, D. Poland, and Y. Xin, Bootstrapping conformal , Phys. Rev. D 105, 085008 (2022).
- In the related case of a gauge field coupled to complex scalars, the large calculation of monopole operator scaling dimensions was shown to be accurate for all [20, 57] by comparison to lattice data, and even for by comparison to particle/vortex duality [58]. Similarly, the large and Chern-Simons level results [59, 60] were matched to the 3d bosonization duality for [58].
- D. Banerjee, S. Chandrasekharan, D. Orlando, and S. Reffert, Conformal dimensions in the large charge sectors at the O(4) Wilson-Fisher fixed point, Phys. Rev. Lett. 123, 051603 (2019).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/pgm4-dtlp for additional details about the calculation, in particular the values of monopole scaling dimensions and SPT absorption.
- In the large charge limit, we expect the scaling dimenions are controlled by a few Wilson coefficients and behave as to leading order [19, 61].
- O. Aharony, Baryons, monopoles and dualities in Chern-Simons-matter theories, J. High Energy Phys. 02 (2016) 093.
- In particular, this follows from plugging in into the first duality in equation 1.4 of [8].
- J. Alicea, O. I. Motrunich, M. Hermele, and M. P. A. Fisher, Criticality in quantum triangular antiferromagnets via fermionized vortices, Phys. Rev. B 72, 064407 (2005).
- Z. Komargodski and N. Seiberg, A symmetry breaking scenario for , J. High Energy Phys. 01 (2018)109.
- J. Gomis, Z. Komargodski, and N. Seiberg, Phases of adjoint and dualities, SciPost Phys. 5, 007 (2018).
- C. Choi, D. Delmastro, J. Gomis, and Z. Komargodski, Dynamics of with rank-two quarks and duality, J. High Energy Phys. 03 (2020) 078.
- A. Armoni, T. T. Dumitrescu, G. Festuccia, and Z. Komargodski, Metastable vacua in large-N , J. High Energy Phys. 01 (2020) 004.
- R. Argurio, A. Armoni, M. Bertolini, F. Mignosa, and P. Niro, Vacuum structure of large from holography, J. High Energy Phys. 07 (2020) 134.
- The map for other operators that are charged under the global symmetry, such as monopoles or the adjoint mass , follows immediately from the broken symmetry according to the usual coset construction [62].
- The monopole operators combine with non-monopole operators to form irreps of , and map to WF operators. For instance, the monopole combines with the adjoint mass to form the WF rank 2 traceless symmetric operator, which is relevant.
- For and , there is evidence of a second order phase transition both from lattice simulations [63, 64, 65] as well as from bootstrap [21, 22].
- T. Sulejmanpasic and C. Gattringer, Abelian gauge theories on the lattice: -Terms and compact gauge theory with(out) monopoles, Nucl. Phys. B 943, 114616 (2019).
- P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, A modified Villain formulation of fractons and other exotic theories, J. Math. Phys. 62, 102301 (2021).
- T. Jacobson and T. Sulejmanpasic, Modified Villain formulation of Abelian Chern-Simons theory, Phys. Rev. D 107, 125017 (2023).
- T. T. Dumitrescu, P. Niro, and R. Thorngren, Symmetry Breaking from Monopole Condensation in , arXiv:2410.05366v1.
- M. Barkeshli and J. McGreevy, Continuous transition between fractional quantum hall and superfluid states, Phys. Rev. B 89, 235116 (2014).
- W. Chen, M. P. A. Fisher, and Y.-S. Wu, Mott transition in an anyon gas, Phys. Rev. B 48, 13749 (1993).
- P. Sikivie, L. Susskind, M. B. Voloshin, and V. I. Zakharov, Isospin breaking in technicolor models, Nucl. Phys. B 173, 189 (1980).
- C. Córdova, P.-S. Hsin, and N. Seiberg, Time-reversal symmetry, anomalies, and dualities in , SciPost Phys. 5, 006 (2018).
- C. Cordova, P.-S. Hsin, and C. Zhang, Anomalies of non-invertible symmetries in , SciPost Phys. 17, 131 (2024).
- I. Hason, Z. Komargodski, and R. Thorngren, Anomaly matching in the symmetry broken phase: Domain walls, CPT, and the smith isomorphism, SciPost Phys. 8, 062 (2020).
- D. Gaiotto, A. Kapustin, Z. Komargodski, and N. Seiberg, Theta, time reversal, and temperature, J. High Energy Phys. 05 (2017) 91.
- T. Senthil and M. P. A. Fisher, Competing orders, non-linear sigma models, and topological terms in quantum magnets, Phys. Rev. B 74, 064405 (2006).
- C. Xu and A. W. W. Ludwig, Nonperturbative effects of topological -term on principal chiral nonlinear sigma models in (2+1) dimensions, Phys. Rev. Lett. 110, 200405 (2013).
- M. A. Metlitski and T. Grover, Entanglement entropy of systems with spontaneously broken continuous symmetry, arXiv:1112.5166v2.
- T. Grover, Entanglement monotonicity and the stability of gauge theories in three spacetime dimensions, Phys. Rev. Lett. 112, 151601 (2014).
- A. Sharon, dualities and the F-theorem, J. High Energy Phys. 08 (2018) 78.
- S. Hands, M. Mesiti, and J. Worthy, Critical behavior in the single flavor Thirring model in 2+1D, Phys. Rev. D 102, 094502 (2020).
- S. J. Hands, J. B. Kogut, and C. G. Strouthos, Noncompact QED(3) with N(f) greater than or equal to 2, Nucl. Phys. B 645, 321 (2002).
- C. Strouthos and J. B. Kogut, The phases of non-compact QED(3), PoS LATTICE2007, 278 (2007).
- E. Dyer, M. Mezei, S. S. Pufu, and S. Sachdev, Erratum to: Scaling dimensions of monopole operators in the theory in 2 + 1 dimensions, J. High Energ. Phys. 03 (2016) 111.
- S. M. Chester, É. Dupuis, and W. Witczak-Krempa, Evidence for web of dualities from monopole operators, Phys. Rev. D 108, L021701 (2023).
- S. M. Chester, L. V. Iliesiu, M. Mezei, and S. S. Pufu, Monopole Operators in Chern-Simons-Matter Theories, J. High Energy Phys. 05 (2018) 157.
- S. M. Chester, Anomalous dimensions of monopole operators in scalar with Chern-Simons term, J. High Energy Phys. 07 (2021) 34.
- S. Hellerman, D. Orlando, S. Reffert, and M. Watanabe, On the CFT operator spectrum at large global charge, J. High Energy Phys. 12 (2015) 1.
- C. G. Callan, S. Coleman, J. Wess, and B. Zumino, Structure of phenomenological lagrangians. II, Phys. Rev. 177, 2247 (1969).
- Y.-C. He, M. P. Zaletel, M. Oshikawa, and F. Pollmann, Signatures of dirac cones in a DMRG study of the Kagome Heisenberg model, Phys. Rev. X 7, 031020 (2017).
- S. Hu, W. Zhu, S. Eggert, and Y.-C. He, Dirac spin liquid on the spin-1 /2 triangular heisenberg antiferromagnet, Phys. Rev. Lett. 123, 207203 (2019).
- A. Wietek, S. Capponi, and A. M. Läuchli, Quantum electrodynamics in 2+1 dimensions as the organizing principle of a triangular lattice antiferromagnet, Phys. Rev. X 14, 021010 (2024).