### Abstract

We study two dimensional U(N) and SU(N) gauge theories with a topological term on arbitrary surfaces. Starting from a lattice formulation we derive the continuum limit of the action which turns out to be a generalisation of the heat kernel in the presence of a topological term. In the continuum limit we can reconstruct the topological information encoded in the theta term. In the topologically trivial cases the theta term gives only a trivial shift to the ground state energy but in the topologically non-trivial ones it survives to be coupled to the dynamics in the continuum. In particular for the U(N) gauge group on orientable surfaces it gives rise to a phase transition at θ = π, similar to the ones observed in other models. Using the equivalence of 2d QCD and a 1d fermion gas on a circle we rewrite our result in the fermionic language and show that the theta term can be also interpreted as an external magnetic field imposed on the fermions.

Original language | English |
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Pages (from-to) | 45-58 |

Number of pages | 14 |

Journal | Nuclear Physics, Section B |

Volume | 454 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Nov 6 1995 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics, Section B*,

*454*(1-2), 45-58. https://doi.org/10.1016/0550-3213(95)00440-4