2019/12/31 by Adam Nahum
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Computer science #Conjecture #Fixed point #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Parameter space #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Space (punctuation) #Statistics #Symmetry (geometry) #cond-mat.stat-mech #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.102.201116
3 pages, 2 figures
arxiv created 2019/12/31 · openalex publication_date 2020/11/30 · openalex created_date 2020/12/07 · arxiv updated 2020/12/30 · openalex updated_date 2026/08/05
We suggest the possibility that the two-dimensional SU(2)k Wess-Zumino-Witten (WZW) theory, which has global SO(4) symmetry, can be continued to 2+\ensuremathε dimensions by enlarging the symmetry to SO(4+\ensuremathε). This is motivated by the three-dimensional sigma model with SO(5) symmetry and a WZW term, which is relevant to deconfined criticality. If such a continuation exists, the structure of the renormalization group flows at small \ensuremathε may be fixed by assuming analyticity in \ensuremathε. This leads to the conjecture that the WZW fixed point annihilates with a new, unstable fixed point at a critical dimensionality dc>2. We suggest that dc<3 for all k, and we compute dc in the limit of large k. The flows support the conjecture that the deconfined phase transition in SU(2) magnets is a ``pseudocritical'' point with approximate SO(5), controlled by a fixed point slightly outside the physical parameter space.