Abstract
We study the viability of spontaneous breaking of continuous symmetries in theories with Lifshitz scaling, according to the number of space-time dimensions $d$ and the dynamical scaling $z$. Then, the answer to the question in the title is no (quantum field theoretically) and yes (holographically). With field theory tools, we show that symmetry breaking is indeed prevented by large quantum fluctuations when $d\leq z+1$, as expected from scaling arguments. With holographic tools, on the other hand, we find nothing that prevents the existence of a vacuum expectation value. This difference is made possible by the large $N$ limit of holography. An important subtlety in this last framework is that in order to get a proper description of a conserved current, renormalization of the temporal mode of the bulk vector requires an alternative quantization. We also comment on the implications of turning on temperature.
Highlights
Spontaneous symmetry breaking is known to be fragile in situations where fluctuations are large
We explore what happens to spontaneous symmetry breaking in Lifshitz scaling theories which are described holographically, i.e., in a large N limit
As in the relativistic case [7], we find that alternative quantization for the vector is needed, albeit in the present case of Lifshitz scaling, only the temporal component of the vector is involved
Summary
Spontaneous symmetry breaking is known to be fragile in situations where fluctuations are large This is true for thermal fluctuations in two spatial dimensions [1,2] and for quantum fluctuations in two relativistic space-time dimensions [3]. It can be seen that the large quantum fluctuations are suppressed by a 1=N power [6] This is precisely the case for theories which have a holographic dual. As in the relativistic case [7], we find that alternative quantization for the vector is needed, albeit in the present case of Lifshitz scaling, only the temporal component of the vector is involved This quantization which treats space and time differently is needed to enforce the proper gauge invariance of the generating functional.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
