Nonrelativistic trace and diffeomorphism anomalies in particle number background

Auzzi, Roberto; Baiguera, Stefano; Nardelli, Giuseppe

doi:10.1103/physrevd.97.085010

Cited by 7 publications

(6 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is simple to check that they satisfy the Newton Cartan algebra ( 13) and also the additional relations (14). Furthermore, the various metrics satisfy the proper transformations, as expected for tensors.…”

Section: Galilean Gauge Theory and Newton Cartan Geometrymentioning

confidence: 77%

“…A number of different approaches to pursue this problem have appeared in the recent past [9,10], the most popular among these is based on the gauging of (extended) Galilean group algebra [11,12]. Just as variants of the approach have been followed in the applications to condensed matter systems, especially fractional quantum Hall effect [9], [13], [14], new results of fundamental implications have also been mooted in giving an action principle for Newtonian gravity [15]. However, in some cases the approach is confronted with various inconsistencies like non canonical transformations of the metric, wrong flat limit etc., as discussed in [16].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A new action for nonrelativistic particle in curved background

Banerjee

Mukherjee²

2019

Physics Letters B

View full text Add to dashboard Cite

We obtain a new form for the action of a nonrelativistic particle coupled to Newtonian gravity. The result is different from that existing in the literature which, as shown here, is riddled with problems and inconsistencies. The present derivation is based on the formalism of galilean gauge theory, introduced by us as an alternative method of analysing nonrelativistic symmetries in gravitational background.

show abstract

Section: Galilean Gauge Theory and Newton Cartan Geometrymentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

A new action for nonrelativistic particle in curved background

Banerjee

Mukherjee²

2019

Physics Letters B

View full text Add to dashboard Cite

show abstract

“…We plan to make contact with both of these directions by performing the systematic classification of the trace anomaly for Carroll-invariant theories, using a cohomological approach. Furthermore, the conformal scalar actions presented in this work open the possibility for the computation of the trace anomaly in specific models, for example using heat kernel techniques [68,69] (see [70][71][72][73][74][75] for applications in the non-relativistic case) or perturbative methods [76] (see [77] for the Lifshitz case). The computation of the conformal anomaly in explicit examples is not only a consistency check of the cohomology result, but will also determine the central charges of the models under consideration.…”

Section: Discussionmentioning

confidence: 99%

Conformal Carroll Scalars with Boosts

Baiguera¹,

Oling²,

Sybesma³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

We construct two distinct actions for scalar fields that are invariant under local Carroll boosts and Weyl transformations. Conformal Carroll field theories were recently argued to be related to the celestial holography description of asymptotically flat spacetimes. However, only few explicit examples of such theories are known, and they lack local Carroll boost symmetry on a generic curved background. We derive two types of conformal Carroll scalar actions with boost symmetry on a curved background in any dimension and compute their energy-momentum tensors, which are traceless. In the first type of theories, time derivatives dominate and spatial derivatives are suppressed. In the second type, spatial derivatives dominate, and constraints are present to ensure local boost invariance. By integrating out these constraints, we show that the spatial conformal Carroll theories can be reduced to lower-dimensional Euclidean CFTs, which is reminiscent of the embedding space construction.

show abstract

“…For example, Minkowski spacetime can be seen as the (left) coset space G/H, in which G is the Poincaré group and H the subgroup corresponding to Lorentz transformations. Recently, non-Lorentzian geometry, with Newton-Cartan (NC) geometry as an important case, has gained interest due to its applications in non-AdS holography [1][2][3][4][5][6], field theory [7][8][9][10][11][12][13][14][15][16][17][18][19], gravity [20][21][22][23][24][25][26][27][28] and string theory [29,30]. The present paper has two aims: first, to address the natural question whether the notion of coset spacetime can be extended to these more general geometries; second, to present a formulation that can be of use when considering nonrelativistic spaces as possible gravitational backgrounds dual to nonrelativistic field theories.…”

Section: Introductionmentioning

confidence: 99%

Homogeneous nonrelativistic geometries as coset spaces

Hartong

Keeler

Obers

2018

Class. Quantum Grav.

View full text Add to dashboard Cite

We generalize the coset procedure of homogeneous spacetimes in (pseudo-)Riemannian geometry to non-Lorentzian geometries. These are manifolds endowed with nowhere vanishing invertible vielbeins that transform under local non-Lorentzian tangent space transformations. In particular we focus on nonrelativistic symmetry algebras that give rise to (torsional) Newton-Cartan geometries, for which we demonstrate how the Newton-Cartan metric complex is determined by degenerate co-and contravariant symmetric bilinear forms on the coset. In specific cases we also show the connection of the resulting nonrelativistic coset spacetimes to pseudo-Riemannian cosets via Inönü-Wigner contraction of relativistic algebras as well as null reduction. Our construction is of use for example when considering limits of the AdS/CFT correspondence in which nonrelativistic spacetimes appear as gravitational backgrounds for nonrelativistic string or gravity theories.In view of their importance in nonrelativistic holography 2 , Lifshitz and Schrödinger spacetimes were already studied via coset constructions in [44] (and applied in e.g. [45-47]). Since nonrelativistic algebras are not semi-simple and have a degenerate Cartan-Killing metric, the standard (Riemannian) coset method of contracting the (inverse) vielbeins with the (inverse) Cartan-Killing metric, obtaining the metric and its inverse, does not apply. Instead of the Cartan-Killing metric, [44] uses the most general non-degenerate group invariant symmetric bilinear form, as [48] did for the Nappi-Witten WZW model on the non-semi simple group E c 2 , which is the centrally extended 2-dimensional Euclidean group. Thus [44] recovers the so-called Lifshitz and Schrödinger spacetimes, first proposed in [49, 50] and [51, 52], from a pseudo-Riemannian coset construction by performing cosets on the Lifshitz and Schrödinger groups respectively.However, aside from the somewhat counterintuitive concept of proposing locally relativistic spacetimes as duals to nonrelativistic field theories [34], difficulties with field profile reconstruction [53][54][55] as well as spacetime reconstruction [56] motivate the consideration of alternatives. As advocated in e.g. [25], such nonrelativistic spacetimes are more naturally viewed as Newton-Cartan spacetimes, described by a clock 1-form, degenerate spatial metric and an extra U (1) connection that contains the Newtonian potential. As we will see in this paper, the key observation is first of all that for certain choices of subgroup H ⊂ G the invariant bilinear form on the coset is necessarily degenerate. Consequently there are two (degenerate) distinct group-invariant bilinear forms on the coset: a covariant bilinear form (Ω ab ) and a corresponding dual bilinear form (Ω ab ). These objects are obviously not inverses of each other as they are both degenerate. With these two objects, we can construct the Newton-Cartan geometric data 3 for several interesting cases.Since some nonrelativistic algebras can be obtained using Inönü-Wigner contractions of relativi...

show abstract

Nonrelativistic trace and diffeomorphism anomalies in particle number background

Cited by 7 publications

References 62 publications

A new action for nonrelativistic particle in curved background

A new action for nonrelativistic particle in curved background

Conformal Carroll Scalars with Boosts

Homogeneous nonrelativistic geometries as coset spaces

Contact Info

Product

Resources

About