TY - JOUR
T1 - Can fermions save large N dimensional reduction?
AU - Bedaque, Paulo F.
AU - Buchoff, Michael I.
AU - Cherman, Aleksey
AU - Springer, Roxanne P.
PY - 2009
Y1 - 2009
N2 - This paper explores whether Eguchi-Kawai reduction for gauge theories with adjoint fermions is valid. The Eguchi-Kawai reduction relates gauge theories in different numbers of dimensions in the large N limit provided that certain conditions are met. In principle, this relation opens up the possibility of learning about the dynamics of 4D gauge theories through techniques only available in lower dimensions. Dimensional reduction can be understood as a special case of large N equivalence between theories related by an orbifold projection. In this work, we focus on the simplest case of dimensional reduction, relating a 4D gauge theory to a 3D gauge theory via an orbifold projection. A necessary condition for the large N equivalence between the 4D and 3D theories to hold is that certain discrete symmetries in the two theories must not be broken spontaneously. In pure 4D Yang-Mills theory, these symmetries break spontaneously as the size of one of the spacetime dimensions shrinks. An analysis of the effect of adjoint fermions on the relevant symmetries of the 4D theory shows that the fermions help stabilize the symmetries. We consider the same problem from the point of view of the lower dimensional 3D theory and find that, surprisingly, adjoint fermions are not generally enough to stabilize the necessary symmetries of the 3D theory. In fact, a rich phase diagram arises, with a complicated pattern of symmetry breaking. We discuss the possible causes and consequences of this finding.
AB - This paper explores whether Eguchi-Kawai reduction for gauge theories with adjoint fermions is valid. The Eguchi-Kawai reduction relates gauge theories in different numbers of dimensions in the large N limit provided that certain conditions are met. In principle, this relation opens up the possibility of learning about the dynamics of 4D gauge theories through techniques only available in lower dimensions. Dimensional reduction can be understood as a special case of large N equivalence between theories related by an orbifold projection. In this work, we focus on the simplest case of dimensional reduction, relating a 4D gauge theory to a 3D gauge theory via an orbifold projection. A necessary condition for the large N equivalence between the 4D and 3D theories to hold is that certain discrete symmetries in the two theories must not be broken spontaneously. In pure 4D Yang-Mills theory, these symmetries break spontaneously as the size of one of the spacetime dimensions shrinks. An analysis of the effect of adjoint fermions on the relevant symmetries of the 4D theory shows that the fermions help stabilize the symmetries. We consider the same problem from the point of view of the lower dimensional 3D theory and find that, surprisingly, adjoint fermions are not generally enough to stabilize the necessary symmetries of the 3D theory. In fact, a rich phase diagram arises, with a complicated pattern of symmetry breaking. We discuss the possible causes and consequences of this finding.
KW - 1/N Expansion
KW - Field Theories in Lower Dimensions
KW - Lattice Gauge Field Theories
KW - Spontaneous Symmetry Breaking
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U2 - 10.1088/1126-6708/2009/10/070
DO - 10.1088/1126-6708/2009/10/070
M3 - Article
AN - SCOPUS:70350787088
SN - 1126-6708
VL - 2009
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 10
M1 - 070
ER -