2017/11/30 by Mohamed M. Anber, Erich Poppitz
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #hep-lat #hep-ph #hep-th
paper · pdf · doi:10.1007/jhep03(2018)052
30 pages, 10 figures; typos corrected, references added, matches the published version in JHEP
openalex created_date 2017/11/10 · openalex publication_date 2018/03/01 · arxiv created 2018/03/13 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/06
A bstract We show that new nonperturbative scales exist in four-dimensional N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> = 1 super-Yang-Mills theory compactified on a circle, with an iterated-exponential dependence on the inverse gauge coupling. The lightest states with the quantum numbers of four-dimensional glueballs are nonrelativistic bound states of dual Cartan gluons and superpartners, with binding energy equal to e^-e^1/g2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msup><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:msup></mml:mrow></mml:msup></mml:math> in units of the confining mass gap. Focusing on SU(2) gauge group, we construct the nonrelativistic effective theory, show that the lightest glueball/glueballino states fill a chiral supermultiplet, and determine their “doubly-nonperturbative” binding energy. The iterated-exponential dependence on the gauge coupling is due to nonperturbative couplings in the long distance theory, \uplambda ∼ e-(1)/(g2) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>λ</mml:mi><mml:mo>∼</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msup><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mfrac></mml:mrow></mml:msup></mml:math> , which are responsible for attractive interactions, in turn producing exponentially small, ∼ e-(1)/(λ ) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>∼</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mi>λ</mml:mi></mml:mfrac></mml:mrow></mml:msup></mml:math> , effects.