336 research outputs found
Field Theories on Null Manifolds
We argue that generic field theories defined on null manifolds should have an emergent BMS or conformal Carrollian structure. We then focus on a simple interacting conformal Carrollian theory, viz. Carrollian scalar electrodynamics. We look at weak (on-shell) and strong invariance (off-shell) of its equations of motion under conformal Carrollian symmetries. Helmholtz conditions are necessary and sufficient conditions for a set of equations to arise from a Lagrangian. We investigate whether the equations of motion of Carrollian scalar electrodynamics satisfy these conditions. Then we proposed an action for the electric sector of the theory. This action is the first example for an interacting conformal Carrollian Field Theory. The proposed action respects the finite and infinite conformal Carrollian symmetries in d = 4. We calculate conserved charges corresponding to these finite and infinite symmetries and then rewrite the conserved charges in terms of the canonical variables. We finally compute the Poisson brackets for these charges and confirm that infinite Carrollian conformal algebra is satisfied at the level of charges
Torsion and anomalies in the warped limit of Lifschitz theories
We describe the physics of fermionic Lifschitz theories once the anisotropic scaling exponent is made arbitrarily small. In this limit the system acquires an enhanced (Carrollian) boost symmetry. We show, both through the explicit computation of the path integral Jacobian and through the solution of the Wess-Zumino consistency conditions, that the translation symmetry in the anisotropic direction becomes anomalous. This turns out to be a mixed anomaly between boosts and translations. In a Newton-Cartan formulation of the space-time geometry such anomaly is sourced by torsion. We use these results to give an effective field theory description of the anomalous transport coefficients, which were originally computed through Kubo formulas in [1]. Along the way we provide a link with warped CFTsThis work is supported by FPA2015-65480-P and by the Spanish Research Agency (Agencia
Estatal de Investigación) through the grant IFT Centro de Excelencia Severo Ochoa SEV2016-0597. The work of C.C. is funded by Fundación La Caixa under “La Caixa-Severo
Ochoa” international predoctoral grant. the author would like to thank Karl Landsteiner
and Eric Bergshoeff for discussions and comments on the draft. He also would like to
thank the organizers of the “Effective Theories of Quantum Phases of Matter” workshop
at NORDITA, where part of this work was presente
AdS-Carroll Branes
Coset methods are used to determine the action of a co-dimension one brane
(domain wall) embedded in (d+1)-dimensional AdS space in the Carroll limit in
which the speed of light goes to zero. The action is invariant under the
non-linearly realized symmetries of the AdS-Carroll spacetime. The
Nambu-Goldstone field exhibits a static spatial distribution for the brane with
a time varying momentum density related to the brane's spatial shape as well as
the AdS-C geometry. The AdS-C vector field dual theory is obtained.Comment: 47 page
Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension
We extend a recent classification of three-dimensional spatially isotropic
homogeneous spacetimes to Chern--Simons theories as three-dimensional gravity
theories on these spacetimes. By this we find gravitational theories for all
carrollian, galilean, and aristotelian counterparts of the lorentzian theories.
In order to define a nondegenerate bilinear form for each of the theories, we
introduce (not necessarily central) extensions of the original kinematical
algebras. Using the structure of so-called double extensions, this can be done
systematically. For homogeneous spaces that arise as a limit of (anti-)de
Sitter spacetime, we show that it is possible to take the limit on the level of
the action, after an appropriate extension. We extend our systematic
construction of nondegenerate bilinear forms also to all higher-dimensional
kinematical algebras.Comment: 52 pages, 2 figures, 11 tables; v2: matches published version,
additional references added and incorporated referee suggestion
Conformal Carroll groups
Conformal extensions of Levy-Leblond's Carroll group, based on geometric
properties analogous to those of Newton-Cartan space-time are proposed. The
extensions are labelled by an integer . This framework includes and extends
our recent study of the Bondi-Metzner-Sachs (BMS) and Newman-Unti (NU) groups.
The relation to Conformal Galilei groups is clarified. Conformal Carroll
symmetry is illustrated by "Carrollian photons". Motion both in the
Newton-Cartan and Carroll spaces may be related to that of strings in the
Bargmann space.Comment: 31 pages, no figures. Minor misprints corrected and clarifications
added. To be published in J. Phys.
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