Spontaneous Breaking Of Local Symmetry Research Articles

SUPERGRAVITY DUAL OF THE SUPERCONFORMAL ANOMALY

The supergravity dual of the superconformal anomaly multiplet in a four-dimensional supersymmetric gauge theory is investigated. We consider a well-established dual correspondence between an [Formula: see text]SU(N+M) × SU(N) supersymmetric gauge theory and type IIB superstring in a space–time background described by the Klebanov–Strassler solution. Based on the fact that fractional D3-branes lead to superconformal anomaly on the field theory side and in the meantime deform AdS 5 × T1, 1 space–time background on the gravity side, we observe the five-dimensional gauged supergravity yielded from the spontaneous compactification on the deformed T1, 1, and find that the spontaneous breaking of local symmetries and the consequent super-Higgs effect in the gauged AdS5 supergravity should be the dual of the superconformal anomaly of the four-dimensional supersymmetric gauge theory.

Impossibility of spontaneously breaking local symmetries and the sign problem

Elitzur's theorem stating the impossibility of spontaneous breaking of local symmetries in a gauge theory is reexamined. The existing proofs of this theorem rely on gauge invariance as well as positivity of the weight in the Euclidean partition function. We examine the validity of Elitzur's theorem in gauge theories for which the Euclidean measure of the partition function is not positive definite. We find that Elitzur's theorem does not follow from gauge invariance alone. We formulate a general criterion under which spontaneous breaking of local symmetries in a gauge theory is excluded. Finally we illustrate the results in an exactly solvable two dimensional Abelian gauge theory.

Generalized symmetry breaking on orbifolds.

We reconsider the phenomenon of mass generation via coordinate-dependent compactifications of higher-dimensional theories on orbifolds. For definiteness, we study a generic five-dimensional theory compactified on S(1)/Z(2). We show that the presence of fixed points, where the fields or their derivatives may be discontinuous, permits new realizations of the Scherk-Schwarz mechanism where, for example, the mass terms are localized at the orbifold fixed points. Our technique can be used to describe the explicit breaking of global flavor symmetries and supersymmetries by brane-localized mass terms. It can also be applied to the spontaneous breaking of local symmetries, such as gauge symmetries or supergravities.

Impossibility of spontaneously breaking local symmetries

It is argued that a spontaneous breaking of local symmetry for a symmetrical gauge theory without gauge fixing is impossible. The argument is demonstrated in a simple system of Abelian gauge fields on a lattice.