TY - JOUR
T1 - QCD-like theories on R3×S1
T2 - A smooth journey from small to large r(S1) with double-trace deformations
AU - Shifman, M.
AU - Ünsal, Mithat
PY - 2008/9/3
Y1 - 2008/9/3
N2 - We consider QCD-like theories with one massless fermion in various representations of the gauge group SU(N). The theories are formulated on R3×S1. In the decompactification limit of large r(S1) all these theories are characterized by confinement, mass gap, and spontaneous breaking of a (discrete) chiral symmetry (χSB). At small r(S1), in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double-trace deformation. With this deformation, the theories at hand are at weak coupling at small r(S1) and yet exhibit basic features of the large r(S1) limit: confinement and χSB. We calculate the string tension, mass gap, bifermion condensates, and θ dependence. The double-trace deformation becomes dynamically irrelevant at large r(S1). Despite the fact that at small r(S1) confinement is Abelian, while it is expected to be non-Abelian at large r(S1), we argue that small and large r(S1) physics are continuously connected. If so, one can use small r(S1) laboratory to extract lessons about QCD and QCD-like theories on R4.
AB - We consider QCD-like theories with one massless fermion in various representations of the gauge group SU(N). The theories are formulated on R3×S1. In the decompactification limit of large r(S1) all these theories are characterized by confinement, mass gap, and spontaneous breaking of a (discrete) chiral symmetry (χSB). At small r(S1), in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double-trace deformation. With this deformation, the theories at hand are at weak coupling at small r(S1) and yet exhibit basic features of the large r(S1) limit: confinement and χSB. We calculate the string tension, mass gap, bifermion condensates, and θ dependence. The double-trace deformation becomes dynamically irrelevant at large r(S1). Despite the fact that at small r(S1) confinement is Abelian, while it is expected to be non-Abelian at large r(S1), we argue that small and large r(S1) physics are continuously connected. If so, one can use small r(S1) laboratory to extract lessons about QCD and QCD-like theories on R4.
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U2 - 10.1103/PhysRevD.78.065004
DO - 10.1103/PhysRevD.78.065004
M3 - Article
AN - SCOPUS:51649106143
SN - 1550-7998
VL - 78
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
IS - 6
M1 - 065004
ER -