Lessons from QCD on a circle Aleksey Cherman INT, University of Washington SEWM 2018, Barcelona
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Lessons from QCD-like theories on a circle Aleksey Cherman INT, University of Washington SEWM 2018, Barcelona
QCD still has mysteries! Lots of formal and not so formal issues. Don’t understand mechanisms of mass gap, confinement, chiral symmetry breaking in detail. Don’t fully understand phase diagram. Don’t understand why nuclear physics exists. Basic issue: strong coupling seems essential, but that’s exactly where our QFT tools fail. So what is to be done? Old idea: look at related QFTs, try to make progress.
Analytic approaches to QCD Very few classes of 4d QFTs which are both solvable, and resemble QCD. Worth taking each one seriously! (1) AdS/CFT models — powerful, but large N, no asymptotic freedom. (2) SUSY models — nice, but have light scalars. Hope for no phase transitions on way back to QCD. This talk: new analytic approach using “adiabatic compactification” Works for finite N asymptotically free QFTs without scalars; gives insights into confinement, chiral symmetry breaking, etc. Absence of phase transitions between strong and weak coupling has very interesting implications.
Unsal 2007; Adiabatic continuity Kovtun, Unsal, Yaffe 2008; AC, Shifman, Unsal, 2018? Claim: there exist 4d SU(N) gauge theories without fundamental scalar fields with a controllable coupling parameter, with (a) confinement already at weak coupling (b) no phase transitions on way to strong coupling Simplest example: adjoint QCD Adjoint QCD = SU(N) gauge theory + N F Weyl adjoint fermions Who cares? First, statement is theoretically surprising. Second, QCD(Adj) is much closer to QCD than it looks. Third, related constructions for normal YM and QCD using Unsal-Yaffe double-trace deformations. Unsal, Yaffe 2008
<latexit sha1_base64="rhi5/y5FzTaRGA7Zn8rVFv3nG4=">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</latexit> Adjoint QCD Adjoint QCD — QCD(Adj) — is a close cousin to normal QCD. Has continuous SU(N F ) chiral symmetry and a Z N center symmetry. Expect confinement and spontaneous chiral symmetry breaking on R 4 In fact, at large N, QCD(Adj) becomes equivalent to QCD(AS), in a common subsector. Armoni, Shifman, Veneziano, 2003 QCD(AS) = SU(N) + N F Dirac two-index anti-symmetric fermions. For N = 3, QCD(AS) = QCD, due to So studying QCD(Adj) is no worse than studying the large N limit of normal QCD
Unsal, Yaffe, Idea: put QCD(Adj) on a circle Shifman, … 2008-onward Break 4D Lorentz, but as little as possible! S 1 R 3 If circle size L is small, might get weak coupling by asymptotic freedom Would happen if relevant coupling for deep IR is λ (1/L) This is not obvious. Small S 1 can cause phase transitions. If they appear, small circle physics completely different from large circle. Can phase transitions in L be prevented?
<latexit sha1_base64="FSC9jP8V1v8H3hZdt6cLbl3oY=">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</latexit> <latexit sha1_base64="ETZxfWFyspTgkyXKAiLcOh7RfE=">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</latexit> Self-Higgsing? When YM compactified on S 1 , Polyakov loops become important A 3 can act as a (compact) adjoint Higgs field Non-coincident eigenvalues for Ω ⇒ “broken” gauge group SU(N) → U(1) N-1 in long-distance 3D EFT Resulting m W ~ 1/L - would guarantee weak coupling in IR But we don’t get to choose eigenvalues: theory picks own vacuum
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