https://doi.org/10.1140/epjc/s10052-026-15437-1
Review
The Carrollian kaleidoscope
1
Indian Institute of Technology Kanpur, 208016, Kanpur, India
2
Birla Institute of Technology and Science, Pilani Campus, 333031, Pilani, Rajasthan, India
3
Asia Pacific Center for Theoretical Physics, Postech, 37673, Pohang, Korea
4
Department of Physics and Astronomy, University of Victoria, V8W 2Y2, Victoria, BC, Canada
5
Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, 700064, Kolkata, India
6
Homi Bhabha National Institute, Anushakti Nagar, 400094, Mumbai, India
a
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Received:
22
July
2025
Accepted:
10
February
2026
Published online:
29
April
2026
Abstract
The Carroll group arises in the vanishing speed of light limit of the Poincaré group and was initially discarded as just a mathematical curiosity. However, recent developments have proved otherwise. Carroll and conformal Carroll symmetries are now ubiquitous, appearing in diverse physical phenomena starting from condensed matter physics to quantum gravity. This review aims to provide the reader a gateway into this fast-developing field. After an introduction and setting the stage with basics of the symmetry in question, we detail the construction of Carrollian and Carrollian Conformal field theories (CCFT). We then focus on applications. By far the most popular of these applications is in the context of the construction of holography in asymptotically flat spacetimes (AFS) in terms of a co-dimension one dual CCFT. We review the early work on AFS
/CCFT
before delving into an in-depth analysis for the construction of the dual to 4D AFS. Two other important sets of applications are in hydrodynamics and in condensed matter physics, which we discuss in detail. Carroll hydrodynamics is introduced as the 
limit of relativistic hydrodynamics first and then reconstructed from a symmetry based approach. Relations to ultrarelativistic flows and connections to the quark-gluon plasma are discussed with concrete examples of the Bjorken and Gubser flow models. In condensed matter applications, we cover connections to fractons, flat bands, and phase separation in Luttinger liquid models. To conclude, we give very brief outlines of other topics of interest including string theory and black hole horizons.
© The Author(s) 2026
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Funded by SCOAP3.
