is no longer commutative, and is in addition non-local. New phases and soliton solutions appear making the dynamics richer[@gubser; @stripe; @trg1; @trg2].

Writing quantum field theories on such spaces requires some care, if one wishes to discuss questions related to Poincaré invariance. To give up this spacetime symmetry almost entirely (which is what conventional quantization does) seems too heavy a price, as it affects the notion of identity of particles (“of two identical particles in one frame should describe two identical particles in [*all*]{} reference frames”), and leads to unacceptable coupling between UV- and IR- degrees of freedom as well[@minwalla]. The program of twisted quantization initiated in [@bmpv; @replyto] on the the other hand, avoids these pitfalls: Poincaré invariance can be maintained, a generalized notion of identical particles can be defined, and UV and IR degrees of freedom decouple nicely [@bpq], thus rekindling the hope that phenomenologically interesting models can be constructed. Indeed one can construct quantum gauge theories with arbitrary gauge groups consistently [@bpqv1].

In this paper, we address the issue of SSB and Higgs phenomenon in twisted quantum theories, and demonstrate signatures of noncommutativity. Our general formulation applies to an arbitrary group $G$ breaking to a subgroup $H$. 