Published for SISSA by Springer Received: September 24, 2015 Revised: November 26, 2015 Accepted: December 5, 2015 Published: January 13, 2016 Geometry and dynamics of a coupled 4D-2D quantum field theory JHEP01(2016)075 Stefano Bolognesi,a;b Chandrasekhar Chatterjee,b;a Jarah Evslin,c;b Kenichi Konishi,a;b Keisuke Ohashia;b;d and Luigi Sevesoa aDepartment of Physics \E. Fermi", University of Pisa, Largo Pontecorvo, 3, Ed. C, 56127 Pisa, Italy bINFN, Sezione di Pisa, Largo Pontecorvo, 3, Ed. C, 56127 Pisa, Italy cInstitute of Modern Physics, Chinese Academy of Sciences, NanChangLu 509, 730000 Lanzhou, China dOsaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan E-mail:
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[email protected] Abstract: Geometric and dynamical aspects of a coupled 4D-2D interacting quantum field theory | the gauged nonAbelian vortex | are investigated. The fluctuations of the internal 2D nonAbelian vortex zeromodes excite the massless 4D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2D CPN−1 zeromodes associated with a nonAbelian vortex become nonnormalizable. Moreover, all sorts of global, topological 4D effects such as the nonAbelian Aharonov- Bohm effect come into play. These topological global features and the dynamical properties associated with the fluctuation of the 2D vortex moduli modes are intimately correlated, as shown concretely here in a U0(1) × SUl(N) × SUr(N) model with scalar fields in a bifundamental representation of the two SU(N) factor gauge groups.