QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1)with Double-Trace Deformations

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We consider QCD-like theories with one massless fermion in various representations of the gauge group SU(N). The theories are formulated on R{sub 3} x S{sub 1}. In the decompactification limit of large r(S{sub 1}) all these theories are characterized by confinement, mass gap and spontaneous breaking of a (discrete) chiral symmetry ({chi}SB). At small r(S{sub 1}), in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double trace deformation. With these deformation, the theories at hand are at weak coupling at small r(S{sub 1}) and yet exhibit basic features of the large-r(S{sub ... continued below

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50 pages

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Shifman, Mikhail; U., /Minnesota; Unsal, Mithat & /SLAC /Stanford U., Phys. Dept. February 22, 2008.

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We consider QCD-like theories with one massless fermion in various representations of the gauge group SU(N). The theories are formulated on R{sub 3} x S{sub 1}. In the decompactification limit of large r(S{sub 1}) all these theories are characterized by confinement, mass gap and spontaneous breaking of a (discrete) chiral symmetry ({chi}SB). At small r(S{sub 1}), in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double trace deformation. With these deformation, the theories at hand are at weak coupling at small r(S{sub 1}) and yet exhibit basic features of the large-r(S{sub 1}) limit: confinement and {chi}SB. We calculate the string tension, mass gap, bifermion condensates and {theta} dependence. The double-trace deformation becomes dynamically irrelevant at large r(S{sub 1}). Despite the fact that at small r(S{sub 1}) confinement is Abelian, while it is expected to be non-Abelian at large r(S{sub 1}), we argue that small and large-r(S{sub 1}) physics are continuously connected. If so, one can use small-r(S{sub 1}) laboratory to extract lessons about QCD and QCD-like theories on R{sub 4}.

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50 pages

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  • Journal Name: Physical Review D

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  • Report No.: SLAC-PUB-13120
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 924100
  • Archival Resource Key: ark:/67531/metadc900283

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  • February 22, 2008

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  • Sept. 27, 2016, 1:39 a.m.

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  • Dec. 7, 2016, 7:15 p.m.

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Shifman, Mikhail; U., /Minnesota; Unsal, Mithat & /SLAC /Stanford U., Phys. Dept. QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1)with Double-Trace Deformations, article, February 22, 2008; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc900283/: accessed July 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.