TY - JOUR

T1 - Chiral symmetry, the 1/N expansion and the SU(N) thirring model

AU - Witten, Edward

N1 - Funding Information:
* Research supported in part by the National Science Foundation under Grant No. PHY77-22864 and by the Harvard Society of Fellows.

PY - 1978/11/27

Y1 - 1978/11/27

N2 - In the two-dimensional SU(N) Thirring model, the 1/N expansion seems to predict spontaneous breaking of the continuous chiral symmetry. This is impossible in two-dimensions. Reasoning along the lines of Berezinski, Kosterlitz and Thouless for the two-dimensional XY model, we argue that, in fact, rather than showing long-range order, 〈ψψ(x) ψψ(0)〉 vanishes in this model as |x|-1/N at large |x|. The 1/N expansion is, in fact, a rather good guide to the properties of this model.

AB - In the two-dimensional SU(N) Thirring model, the 1/N expansion seems to predict spontaneous breaking of the continuous chiral symmetry. This is impossible in two-dimensions. Reasoning along the lines of Berezinski, Kosterlitz and Thouless for the two-dimensional XY model, we argue that, in fact, rather than showing long-range order, 〈ψψ(x) ψψ(0)〉 vanishes in this model as |x|-1/N at large |x|. The 1/N expansion is, in fact, a rather good guide to the properties of this model.

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U2 - 10.1016/0550-3213(78)90416-9

DO - 10.1016/0550-3213(78)90416-9

M3 - Article

AN - SCOPUS:0001189908

VL - 145

SP - 110

EP - 118

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1

ER -