TY - JOUR
T1 - Fractional instantons and bions in the principal chiral model on (Formula presented.) with twisted boundary conditions
AU - Nitta, Muneto
N1 - Funding Information:
The author thanks Tatsuhiro Misumi and Norisuke Sakai for a discussion on bions. This work is supported in part by Grant-in-Aid for Scientific Research No. 25400268 and by the ?Topological Quantum Phenomena? Grant-in-Aid for Scientific Research on Innovative Areas (No. 25103720) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.
Publisher Copyright:
© 2015, The Author(s).
PY - 2015/8/1
Y1 - 2015/8/1
N2 - Abstract: Bions are multiple fractional instanton configurations with zero instanton charge playing important roles in quantum field theories on a compactified space with a twisted boundary condition. We classify fractional instantons and bions in the SU(N) principal chiral model on (Formula presented.) with twisted boundary conditions. We find that fractional instantons are global vortices wrapping around S1 with their U(1) moduli twisted along S1, that carry 1/N instanton (baryon) numbers for the (Formula presented.) symmetric twisted boundary condition and irrational instanton numbers for generic boundary condition. We work out neutral and charged bions for the SU(3) case with the (Formula presented.) symmetric twisted boundary condition. We also find for generic boundary conditions that only the simplest neutral bions have zero instanton charges but instanton charges are not canceled out for charged bions. A correspondence between fractional instantons and bions in the SU(N) principal chiral model and those in Yang-Mills theory is given through a non-Abelian Josephson junction.
AB - Abstract: Bions are multiple fractional instanton configurations with zero instanton charge playing important roles in quantum field theories on a compactified space with a twisted boundary condition. We classify fractional instantons and bions in the SU(N) principal chiral model on (Formula presented.) with twisted boundary conditions. We find that fractional instantons are global vortices wrapping around S1 with their U(1) moduli twisted along S1, that carry 1/N instanton (baryon) numbers for the (Formula presented.) symmetric twisted boundary condition and irrational instanton numbers for generic boundary condition. We work out neutral and charged bions for the SU(3) case with the (Formula presented.) symmetric twisted boundary condition. We also find for generic boundary conditions that only the simplest neutral bions have zero instanton charges but instanton charges are not canceled out for charged bions. A correspondence between fractional instantons and bions in the SU(N) principal chiral model and those in Yang-Mills theory is given through a non-Abelian Josephson junction.
KW - Field Theories in Lower Dimensions
KW - Sigma Models
KW - Solitons Monopoles and Instantons
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U2 - 10.1007/JHEP08(2015)063
DO - 10.1007/JHEP08(2015)063
M3 - Article
AN - SCOPUS:84958238916
SN - 1126-6708
VL - 2015
SP - 1
EP - 25
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 8
M1 - 63
ER -