TY - JOUR

T1 - Dualities in 3D large N vector models

AU - Muteeb, Nouman

AU - Zayas, Leopoldo A.Pando

AU - Quevedo, Fernando

N1 - Publisher Copyright:
© 2016, The Author(s).

PY - 2016/5/1

Y1 - 2016/5/1

N2 - Using an explicit path integral approach we derive non-abelian bosonization and duality of 3D systems in the large N limit. We first consider a fermionic U(N) vector model coupled to level k Chern-Simons theory, following standard techniques we gauge the original global symmetry and impose the corresponding field strength Fμν to vanish introducing a Lagrange multiplier Λ. Exchanging the order of integrations we obtain the bosonized theory with Λ as the propagating field using the large N rather than the previously used large mass limit. Next we follow the same procedure to dualize the scalar U (N) vector model coupled to Chern-Simons and find its corresponding dual theory. Finally, we compare the partition functions of the two resulting theories and find that they agree in the large N limit including a level/rank duality. This provides a constructive evidence for previous proposals on level/rank duality of 3D vector models in the large N limit. We also present a partial analysis at subleading order in large N and find that the duality does not generically hold at this level.

AB - Using an explicit path integral approach we derive non-abelian bosonization and duality of 3D systems in the large N limit. We first consider a fermionic U(N) vector model coupled to level k Chern-Simons theory, following standard techniques we gauge the original global symmetry and impose the corresponding field strength Fμν to vanish introducing a Lagrange multiplier Λ. Exchanging the order of integrations we obtain the bosonized theory with Λ as the propagating field using the large N rather than the previously used large mass limit. Next we follow the same procedure to dualize the scalar U (N) vector model coupled to Chern-Simons and find its corresponding dual theory. Finally, we compare the partition functions of the two resulting theories and find that they agree in the large N limit including a level/rank duality. This provides a constructive evidence for previous proposals on level/rank duality of 3D vector models in the large N limit. We also present a partial analysis at subleading order in large N and find that the duality does not generically hold at this level.

KW - 1/N Expansion

KW - Chern-Simons Theories

KW - Duality in Gauge Field Theories

KW - Field Theories in Lower Dimensions

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U2 - 10.1007/JHEP05(2016)045

DO - 10.1007/JHEP05(2016)045

M3 - Article

AN - SCOPUS:84984839764

SN - 1126-6708

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

M1 - 45

ER -