Numerical determination of monopole scaling dimension in parity-invariant three-dimensional noncompact QED

Karthik, Nikhil; Narayanan, Rajamani

doi:10.1103/PhysRevD.100.054514

Title: Numerical determination of monopole scaling dimension in parity-invariant three-dimensional noncompact QED

Journal Article · Thu Sep 26 00:00:00 EDT 2019 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.100.054514· OSTI ID:1566894

Karthik, Nikhil;

We present a direct Monte Carlo determination of the scaling dimension of a topological defect operator in the infrared fixed point of a three-dimensional interacting quantum field theory. For this, we compute the free energy to introduce the background gauge field of the $$Q$$ = 1 monopole-antimonopole pair in threedimensional noncompact QED with $$N$$ = 2, 4 and 12 flavors of massless two-component fermions, and study its asymptotic logarithmic dependence on the monopole-antimonopole separation. We estimate the scaling dimension in the $$N$$ = 12 case to be consistent with the large-$$N$$ (free fermion) value. We find the deviations from this large-$$N$$ value for $$N$$ = 2 and 4 are positive but small, implying that the higher-order corrections in the large-$$N$$ expansion become mildly important for $$N$$ = 2, 4.

View Journal Article

Cite

Export

Save

Research Organization:: Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0012704

OSTI ID:: 1566894

Alternate ID(s):: OSTI ID: 1570680

Report Number(s):: BNL-212180-2019-JAAM; PRVDAQ; 054514

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 100 Journal Issue: 5; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 15 works

Citation information provided by
Web of Science

References (34)

Magnetic monopole plasma phase in $(2 + 1) d$ compact quantum electrodynamics with fermionic matter Armour, Wesley; Hands, Simon; Kogut, John B. Physical Review D, Vol. 84, Issue 1 https://doi.org/10.1103/PhysRevD.84.014502	journal	July 2011
Topological excitations and Monte Carlo simulation of Abelian gauge theory DeGrand, T. A.; Toussaint, Doug Physical Review D, Vol. 22, Issue 10 https://doi.org/10.1103/PhysRevD.22.2478	journal	November 1980
Compact gauge fields and the infrared catastrophe Polyakov, A. M. Physics Letters B, Vol. 59, Issue 1 https://doi.org/10.1016/0370-2693(75)90162-8	journal	October 1975
Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases Xu, Xiao Yan; Qi, Yang; Zhang, Long Physical Review X, Vol. 9, Issue 2 https://doi.org/10.1103/PhysRevX.9.021022	journal	May 2019
Monopole scaling dimension using Monte-Carlo simulation Karthik, Nikhil Physical Review D, Vol. 98, Issue 7 https://doi.org/10.1103/PhysRevD.98.074513	journal	October 2018
Dynamics of compact quantum electrodynamics at large fermion flavor Wang, Wei; Lu, Da-Chuan; Xu, Xiao Yan Physical Review B, Vol. 100, Issue 8 https://doi.org/10.1103/PhysRevB.100.085123	journal	August 2019
Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet Villain, J. Journal de Physique, Vol. 36, Issue 6 https://doi.org/10.1051/jphys:01975003606058100	journal	January 1975
Quantum Electrodynamics in $d = 3$ from the $ε$ Expansion Di Pietro, Lorenzo; Komargodski, Zohar; Shamir, Itamar Physical Review Letters, Vol. 116, Issue 13 https://doi.org/10.1103/PhysRevLett.116.131601	journal	April 2016
Quark confinement and topology of gauge theories Polyakov, A. M. Nuclear Physics B, Vol. 120, Issue 3 https://doi.org/10.1016/0550-3213(77)90086-4	journal	March 1977
Monopoles in ${CP}^{N - 1}$ model via the state-operator correspondence Metlitski, Max A.; Hermele, Michael; Senthil, T. Physical Review B, Vol. 78, Issue 21 https://doi.org/10.1103/PhysRevB.78.214418	journal	December 2008
Vortex tension as an order parameter in three-dimensional U(1) + Higgs theory Kajantie, K.; Laine, M.; Neuhaus, T. Nuclear Physics B, Vol. 546, Issue 1-2 https://doi.org/10.1016/S0550-3213(99)00033-4	journal	April 1999
Deconfined Quantum Critical Points: Symmetries and Dualities Wang, Chong; Nahum, Adam; Metlitski, Max A. Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/PhysRevX.7.031051	journal	September 2017
Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation Herbut, Igor F. Physical Review D, Vol. 94, Issue 2 https://doi.org/10.1103/PhysRevD.94.025036	journal	July 2016
Critical behavior of ( $2 + 1$ )-dimensional QED: $1 / N_{f}$ corrections in the Landau gauge Kotikov, A. V.; Shilin, V. I.; Teber, S. Physical Review D, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRevD.94.056009	journal	September 2016
Monopole operators from the 4 − ϵ expansion Chester, Shai M.; Mezei, Márk; Pufu, Silviu S. Journal of High Energy Physics, Vol. 2016, Issue 12 https://doi.org/10.1007/JHEP12(2016)015	journal	December 2016
No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions Karthik, Nikhil; Narayanan, Rajamani Physical Review D, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevD.93.045020	journal	February 2016
Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics Pufu, Silviu S. Physical Review D, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevD.89.065016	journal	March 2014
Critical number of fermions in three-dimensional QED Gusynin, V. P.; Pyatkovskiy, P. K. Physical Review D, Vol. 94, Issue 12 https://doi.org/10.1103/PhysRevD.94.125009	journal	December 2016
Action of hedgehog instantons in the disordered phase of the (2 + 1)-dimensional CPN−1 model Murthy, Ganpathy; Sachdev, Subir Nuclear Physics B, Vol. 344, Issue 3 https://doi.org/10.1016/0550-3213(90)90670-9	journal	November 1990
Topological Disorder Operators in Three-Dimensional Conformal Field Theory Borokhov, Vadim; Kapustin, Anton; Wu, Xinkai Journal of High Energy Physics, Vol. 2002, Issue 11 https://doi.org/10.1088/1126-6708/2002/11/049	journal	November 2002
Nonperturbative beta function in three-dimensional electrodynamics Raviv, Ohad; Shamir, Yigal; Svetitsky, Benjamin Physical Review D, Vol. 90, Issue 1 https://doi.org/10.1103/PhysRevD.90.014512	journal	July 2014
Conformal QED _d , F -theorem and the ϵ expansion Giombi, Simone; Klebanov, Igor R.; Tarnopolsky, Grigory Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 13 https://doi.org/10.1088/1751-8113/49/13/135403	journal	February 2016
Abelian gauge theories on the lattice: θ-Terms and compact gauge theory with(out) monopoles Sulejmanpasic, Tin; Gattringer, Christof Nuclear Physics B, Vol. 943 https://doi.org/10.1016/j.nuclphysb.2019.114616	journal	June 2019
Scaling dimensions in QED3 from the ϵ-expansion Di Pietro, Lorenzo; Stamou, Emmanuel Journal of High Energy Physics, Vol. 2017, Issue 12 https://doi.org/10.1007/JHEP12(2017)054	journal	December 2017
Large Nf quantum field theory Gracey, J. A. International Journal of Modern Physics A, Vol. 33, Issue 35 https://doi.org/10.1142/S0217751X18300326	journal	December 2018
Towards bootstrapping QED3 Chester, Shai M.; Pufu, Silviu S. Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)019	journal	August 2016
Anomalous dimensions of scalar operators in QED3 Chester, Shai M.; Pufu, Silviu S. Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)069	journal	August 2016
Monopoles in 2 + 1-dimensional conformal field theories with global U(1) symmetry Pufu, Silviu S.; Sachdev, Subir Journal of High Energy Physics, Vol. 2013, Issue 9 https://doi.org/10.1007/JHEP09(2013)127	journal	September 2013
Phase of the fermion determinant in ${QED}_{3}$ using a gauge invariant lattice regularization Karthik, Nikhil; Narayanan, Rajamani Physical Review D, Vol. 92, Issue 2 https://doi.org/10.1103/PhysRevD.92.025003	journal	July 2015
Noncompact three-dimensional quantum electrodynamics with Nf=1 and Nf=4 Hands, S.; Kogut, J.; Scorzato, L. Physical Review B, Vol. 70, Issue 10 https://doi.org/10.1103/PhysRevB.70.104501	journal	September 2004
Scale invariance of parity-invariant three-dimensional QED Karthik, Nikhil; Narayanan, Rajamani Physical Review D, Vol. 94, Issue 6 https://doi.org/10.1103/PhysRevD.94.065026	journal	September 2016
Strong coupling and mean field methods in lattice gauge theories Drouffe, J. Physics Reports, Vol. 102, Issue 1-2 https://doi.org/10.1016/0370-1573(83)90034-0	journal	December 1983
Mandelstam-'t Hooft duality in abelian lattice models Peskin, Michael E. Annals of Physics, Vol. 113, Issue 1 https://doi.org/10.1016/0003-4916(78)90252-X	journal	July 1978
Non-compact QED3 with Nf⩾2 Hands, S. J.; Kogut, J. B.; Strouthos, C. G. Nuclear Physics B, Vol. 645, Issue 1-2 https://doi.org/10.1016/S0550-3213(02)00869-6	journal	November 2002