Vacuum structure of charge k two-dimensional QED and dynamics of an anti D-string near an O1-plane

  • Adi ArmoniEmail author
  • Shigeki Sugimoto
Open Access
Regular Article - Theoretical Physics


We study the vacuum structure of Nf flavour two-dimensional QED with an arbitrary integer charge k. We find that the axial symmetry is spontaneously broken from \( {\mathbb{Z}}_{k{N}_f} \) to \( {\mathbb{Z}}_{N_f} \) due to the non-vanishing condensate of a flavour singlet operator, resulting in k degenerate vacua. An explicit construction of the k vacua is given by using a

non-commutative algebra obtained as a central extension of the \( {\mathbb{Z}}_{k{N}_f} \) discrete axial symmetry and ℤk 1-form (center) symmetry, which represents the mixed ’t Hooft anomaly between them.

We then give a string theory realization of such a system with k = 2 and Nf = 8 by putting an anti D-string in the vicinity of an orientifold O1-plane and study its dynamics using the two-dimensional gauge theory realized on it. We calculate the potential between the anti D-string and the O1-plane and find repulsion in both weak and strong coupling regimes of the two-dimensional gauge theory, corresponding to long and short distances, respectively. We also calculate the potential for the (Q, −1)-string (the bound state of an anti D-string and Q fundamental strings) located close to the O1-plane. The result is non-perturbative in the string coupling.


Anomalies in Field and String Theories Brane Dynamics in Gauge Theories Confinement Field Theories in Lower Dimensions 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics, College of ScienceSwansea UniversitySwanseaU.K.
  2. 2.Center for Gravitational Physics, Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  3. 3.Kavli Institute for the Physics and Mathematics of the Universe (WPI)The University of TokyoKashiwaJapan

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