Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP01(2018)109
Keywords
Chern-Simons Theories; Duality in Gauge Field Theories; Global Symmetries; Anomalies in Field and String Theories
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Funding
- Israel Science Foundation center for excellence grant
- I-CORE program of the Planning and Budgeting Committee
- Israel Science Foundation [1937/12]
- ERC STG grant [335182]
- Simons Foundation [488657]
- DOE [DE-SC0009988]
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We consider the dynamics of 2+1 dimensional SU(N) gauge theory with Chern-Simons level k and N-f fundamental fermions. By requiring consistency with previously suggested dualities for N-f <= 2k as well as the dynamics at k = 0 we propose that the theory with N-f > 2k breaks the U(N-f) global symmetry spontaneously to U(N-f /2 + k) x U(N-f /2 - k). In contrast to the 3+1 dimensional case, the symmetry breaking takes place in a range of quark masses and not just at one point. The target space never becomes parametrically large and the Nambu-Goldstone bosons are therefore not visible semi-classically. Such symmetry breaking is argued to take place in some intermediate range of the number of flavors, 2k < N-f < N-* (N, k), with the upper limit N-* obeying various constraints. The Lagrangian for the Nambu-Goldstone bosons has to be supplemented by nontrivial Wess-Zumino terms that are necessary for the consistency of the picture, even at k = 0. Furthermore, we suggest two scalar dual theories in this range of N-f. A similar picture is developed for SO(N) and Sp(N) gauge theories. It sheds new light on monopole condensation and confinement in the SO(N) & Spin(N) theories.
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