Gauge theories induced by bosons in the fundamental representation

Abstract

A lattice theory of scalar bosons in the fundamental representation of the gauge group SU (N c ) and of the global symmetry group SU (N f ) is shown to induce a standard gauge theory only at large N f . The system is in a deconfined phase at strong scalar self-coupling and any finite N f . The requirement of convergence of the effective gauge action imposes a lower limit on the scalar mass.

Solution of gauge theories induced by fundamental representation scalars

“…At this point one can introduce the bilinear combinations just as in (6) to get the quenched theory for the positive adjoint matrix Φ, The action, in terms of the eigenvalues of Φ, φ α takes the form…”

“…The gauge theory induced by such a scalar field is not asymptotically free in four dimensions and as such is not likely to be confining either. In fact, the induced theory will only be asymptotically free if the number of complex scalars, N f , satisfies the inequality N f > 11N c [5], [6]. This is the primary reason why we previously considered a scalar field theory with U (N c ) gauge × U (N f ) global symmetry.…”

“…This is the primary reason why we previously considered a scalar field theory with U (N c ) gauge × U (N f ) global symmetry. [6] The prevalent argument against theories with fundamental representation scalars, rather then adjoint representation ones has been the lack of existence of a master field, precluding chances for finding exact solutions. While in gauge theories induced by adjoint representation scalars the master field is composed of the eigenvalues of the scalar field matrix, for fundamental representation scalars no such quantity seems to exist.…”