Carrollian conservation laws and Ricci-flat gravity

We describe how fermionic Lifschitz theories naturally develop non-dissipative response to torsion 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].

Section: Further Remarksmentioning

confidence: 99%

Torsion and anomalies in the warped limit of Lifschitz theories

Copetti

2020

“…Finally, all these ultra-relativistic theories constructedà la CS could have some applications in the context of Carrollian fluids (and their relations with flat holography, see Refs. [31][32][33][34]).…”

Section: Discussionmentioning

confidence: 99%

“…Afterwards, in [15], the AdS Carroll CS gravity theory was discussed for the first time. 1 Non-relativistic symmetry groups play a remarkable role also in holography [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. More specifically, in the work [24], connections among Carrollian physics, holography of flat space, and the Bondi-Metzner-Sachs (BMS) algebra were discovered and followed up in [25] (see also Refs.…”

mentioning

confidence: 99%

“…[26,27] and [28]). Besides, conformal extensions of the Carroll group were explored and related to the BMS group in [29,30], while in [31][32][33][34] it was shewed the way in which Carrollian structures and geometry emerge in the flat holography and fluid/gravity correspondence framework.Recently, in [35] the construction of the three-dimensional N = 1 CS supergravity theory invariant under the so-called AdS Carroll superalgebra (ultra-relativistic contraction of the N = 1 AdS superalgebra, see [14]), together with the study of its flat limit, has been presented for the first time. In the study done in [35], the method introduced in [36] was adopted.…”

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confidence: 99%

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confidence: 99%

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$$ \mathcal{N} $$-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions

Ali

Ravera

2020

In this work we present the ultra-relativistic N -extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under N -extended AdS Carroll superalgebras. We first consider the (2, 0) and (1, 1) cases; subsequently, we generalize our analysis to N = (N , 0), with N even, and to N = (p, q), with p, q > 0. The N -extended AdS Carroll superalgebras are obtained through the Carrollian (i.e., ultra-relativistic) contraction applied to an so(2) extension of osp(2|2) ⊗ sp(2), to osp(2|1) ⊗ osp(2, 1), to an so(N ) extension of osp(2|N ) ⊗ sp(2), and to the direct sum of an so(p) ⊕ so(q) algebra and osp(2|p) ⊗ osp(2, q), respectively. We also analyze the flat limit (ℓ → ∞, being ℓ the length parameter) of the aforementioned N -extended Chern-Simons AdS Carroll supergravities, in which we recover the ultrarelativistic N -extended (flat) Chern-Simons supergravity theories invariant under N -extended super-Carroll algebras. The flat limit is applied at the level of the superalgebras, Chern-Simons actions, supersymmetry transformation laws, and field equations.The study of spacetime symmetries has proved to be fundamental for analyzing and understanding various physical models. For instance, think of Newtonian gravity, Maxwell's electromagnetism, special and general relativity, string and supergravity theory. Most of these theories are based on relativistic symmetries. On the other hand, during the years models with non-relativistic symmetries have also been developed and analyzed, and and are still the subject of in-depth studies.In this context, Carroll symmetries [1,2], arising when the velocity of light is sent to zero (i.e., in the ultra-relativistic limit, c → 0), have attracted some interest over recent years. In fact, models with Carroll symmetries occurred in the literature in the study of tachyon condensation [3], warped conformal field theories [4], and tensionless strings [5][6][7][8][9]. Moreover, a study exploring the Carroll limit corresponding to M2-as well as M3-branes propagating over D = 11 supergravity backgrounds in M-theory has been recently presented in [10].Concerning gravity theories, models of Carrollian (i.e., ultra-relativistic) gravity have been developed and analyzed in [11][12][13]. In particular, non-and ultra-relativistic Chern-Simons (CS) type actions in 2 + 1 dimensions were constructed in [12], where the authors included a spin-3 field coupled to gravity. The geometry of flat and Anti-de Sitter (AdS) Carroll spaces were investigated, both in the bosonic as well as in the supersymmetric case, in [14], were the authors focused on the symmetries of a particle moving in such spaces. Afterwards, in [15], the AdS Carroll CS gravity theory was discussed for the first time. 1 Non-relativistic symmetry groups play a remarkable role also in holography [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. More specifically, in the work [24], connections among Carrollian physics, holography of flat space, and the Bondi-Metzner-Sachs (BMS) algebra were discove...

Brown-York charges at null boundaries

Chandrasekaran

Flanagan

Shehzad

et al. 2022

The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface. We consider the generalization of this stress tensor to null hypersurfaces. Such a stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle, which fixes an induced Carroll structure on the null boundary. The formula for the mixed-index tensor Tij takes a remarkably simple form that is manifestly independent of the choice of auxiliary null vector at the null surface, and we compare this expression to previous proposals for null Brown-York stress tensors. The stress tensor we obtain satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the hypersurface, as a result of the null constraint equations. For transformations that act covariantly on the boundary structures, the Brown-York charges coincide with canonical charges constructed from a version of the Wald-Zoupas procedure. For anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry, which we explicity verify for a set of symmetries associated with finite null hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.