Wed·Aug 15, 2007Wednesday·August 15, 2007

1. 01*

   Simulation Results for U(1) Gauge Theory on Non-Commutative Spaces

   Wolfgang Bietenholz🇩🇪 · Antonio Bigarini🇮🇹 · Jun Nishimura🇯🇵 · Yoshiaki Susaki🇯🇵 · Alessandro Torrielli🇺🇸 · Jan Volkholz🇩🇪

   We present numerical results for U(1) gauge theory in 2d and 4d spaces involving a non-commutative plane. Simulations are feasible thanks to a mapping of the non-commutative plane onto a twisted matrix model. In d=2 it was a long-standing issue if Wilson loops are (partially) invariant under area-preserving diffeomorphisms. We show that non-perturbatively this invariance breaks, including the subgroup SL(2,R). In both cases, d=2 and d=4, we extrapolate our results to the continuum and infinite volume by means of a Double Scaling Limit. In d=4 this limit leads to a phase with broken translation symmetry, which is not affected by the perturbatively known IR instability. Therefore the photon may survive in a non-commutative world.

   hep-latastro-phhep-thPoS(2007)·4 citations
2. 02*

   Confining Effective Theories Based on Instantons and Merons

   F. Lenz🇩🇪 · J. W. Negele🇺🇸 · M. Thies🇩🇪

   An effective theory based on ensembles of either regular gauge instantons or merons is shown to produce confinement in SU(2) Yang-Mills theory. When the scale is set by the string tension, the action density, topological susceptibility and low-lying glueball spectrum are similar to those arising in lattice QCD. The physical mechanism producing confinement is explained, and a number of analytical insights into the effective theory are presented.

   ↳ hep-phhep-latnucl-thAnnals Phys.(2008)·13 citations
3. 03*

   Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)

   Mithat Unsal🇺🇸

   We analyze the vacuum structure of SU(2) QCD with multiple massless adjoint representation fermions formulated on a small spatial $S^1\times {\mathbb{R}}^3$. The absence of thermal fluctuations, and the fact that quantum fluctuations favoring the vacuum with unbroken center symmetry in a weakly coupled regime renders the interesting dynamics of these theories analytically calculable. Confinement, the area law behavior for large Wilson loops, and the generation of the mass gap in the gluonic sector are shown analytically. By abelian duality transformation, the long distance effective theory of QCD is mapped into an amalgamation of $d=3$ dimensional Sine-Gordon and NJL models. The duality necessitates going to IR first. In this regime, theory exhibits confinement without continuous chiral symmetry breaking. However, a flavor singlet chiral condensate (which breaks a discrete chiral symmetry) persists at arbitrarily small $S^1$. Under the reasonable assumption that the theory on ${\mathbb{R}}^4$ exhibits chiral symmetry breaking, there must exist a zero temperature chiral phase transition in the absence of any change in spatial center symmetry realizations.

   ↳ hep-thhep-lathep-phPRL(2008)·159 citations
4. 04*

   Two-particle scattering on the lattice: Phase shifts, spin-orbit coupling, and mixing angles

   Bugra Borasoy🇩🇪 · Evgeny Epelbaum🇩🇪 · Hermann Krebs🇩🇪 · Dean Lee🇺🇸 · Ulf-G. Meißner🇩🇪

   We determine two-particle scattering phase shifts and mixing angles for quantum theories defined with lattice regularization. The method is suitable for any nonrelativistic effective theory of point particles on the lattice. In the center-of-mass frame of the two-particle system we impose a hard spherical wall at some fixed large radius. For channels without partial-wave mixing the partial-wave phase shifts are determined from the energies of the nearly-spherical standing waves. For channels with partial-wave mixing further information is extracted by decomposing the standing wave at the wall boundary into spherical harmonics, and we solve coupled-channels equations to extract the phase shifts and mixing angles. The method is illustrated and tested by computing phase shifts and mixing angles on the lattice for spin-1/2 particles with an attractive Gaussian potential containing both central and tensor force parts.

   ↳ nucl-thhep-latphysics.atom-phEPJA(2007)·66 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.