TY - JOUR

T1 - Subtleties in QCD theory in two dimensions

AU - Frishman, Y.

AU - Hanany, A.

AU - Sonnenschein, J.

N1 - Funding Information:
* Supported in part by the Israel Academy of Sciences. ** Work supported in part by the US-Israel Binational Science Foundation and the Israel Academy of Sciences.

PY - 1994/10/24

Y1 - 1994/10/24

N2 - It is shown that in a formulation of Yang-Mills theory in two dimensions in terms of A = i f- 1 ∂ f, over(A, -) = i over(f, -) over(∂, -) over(f, -)- 1 with f (z, over(z, -)), over(f, -) (z, over(z, -)) ∈ [S U (NC)]c the complexification of SU(NC), reveals certain subtleties. "Physical" massive color singlet states seem to exist. When coupled to NF quarks the coupling constant is renormalized in such a way that it vanishes for the pure Yang-Mills case. This renders the above states massless and unphysical. In the abelian case, on the other hand, the known results of the Schwinger model are reproduced with no need of such a renormalization. The massless QCD2 theory is analyzed in similar terms and peculiar massive states appear, with a mass of ec sqrt(NF / 2 π) .

AB - It is shown that in a formulation of Yang-Mills theory in two dimensions in terms of A = i f- 1 ∂ f, over(A, -) = i over(f, -) over(∂, -) over(f, -)- 1 with f (z, over(z, -)), over(f, -) (z, over(z, -)) ∈ [S U (NC)]c the complexification of SU(NC), reveals certain subtleties. "Physical" massive color singlet states seem to exist. When coupled to NF quarks the coupling constant is renormalized in such a way that it vanishes for the pure Yang-Mills case. This renders the above states massless and unphysical. In the abelian case, on the other hand, the known results of the Schwinger model are reproduced with no need of such a renormalization. The massless QCD2 theory is analyzed in similar terms and peculiar massive states appear, with a mass of ec sqrt(NF / 2 π) .

UR - http://www.scopus.com/inward/record.url?scp=0001996286&partnerID=8YFLogxK

U2 - 10.1016/S0550-3213(94)80042-1

DO - 10.1016/S0550-3213(94)80042-1

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AN - SCOPUS:0001996286

SN - 0550-3213

VL - 429

SP - 75

EP - 89

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 1

ER -