Weyl consistency conditions in non-relativistic quantum field theory

Pal, Sridip; Grinstein, Benjamı́n

doi:10.1007/jhep12(2016)012

Cited by 26 publications

(30 citation statements)

References 72 publications

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“…The main missing ingredient to the proof is to control the positivity of some anomaly coefficients whose relativistic analog turn out to be proportional to the Zamolodchikov metric. Local renormalization group for Lifshitz theories was studied in [48].…”

Section: Jhep08(2017)042mentioning

confidence: 99%

Trace anomaly for non-relativistic fermions

Auzzi

Baiguera

Nardelli

2017

J. High Energ. Phys.

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Abstract:We study the coupling of a 2 + 1 dimensional non-relativistic spin 1/2 fermion to a curved Newton-Cartan geometry, using null reduction from an extra-dimensional relativistic Dirac action in curved spacetime. We analyze Weyl invariance in detail: we show that at the classical level it is preserved in an arbitrary curved background, whereas at the quantum level it is broken by anomalies. We compute the trace anomaly using the Heat Kernel method and we show that the anomaly coefficients a, c are proportional to the relativistic ones for a Dirac fermion in 3 + 1 dimensions. As for the previously studied scalar case, these coefficents are proportional to 1/m, where m is the non-relativistic mass of the particle.

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Section: Jhep08(2017)042mentioning

confidence: 99%

Trace anomaly for non-relativistic fermions

Auzzi

Baiguera

Nardelli

2017

J. High Energ. Phys.

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“…However it is still interesting to study the local RG equations; for example it might be possible to identify monotonic scheme-dependent quantities analog to the a of the relativistic four-dimensional case. A similar study, in the case without boost invariance, was done in [29].…”

Section: Jhep11(2016)163mentioning

confidence: 83%

“….Ã 4 whose evolution is described by an equation which is similar to the one for a in the relativistic case. An analogous study was performed in [29] in the case of non-relativistic theories without boost invariance.…”

Section: Discussionmentioning

confidence: 99%

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On Newton-Cartan local renormalization group and anomalies

Auzzi

Baiguera

Filippini

et al. 2016

J. High Energ. Phys.

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“…The methodology introduced here could be leveraged to also describe the operator content beyond the realm of heavy particle effective field theory with a single heavy field, for example, fermions at unitarity [19,20], two nucleon systems [21,22], and it could have potential application in writing an operator basis for anisotropic Weyl anomaly, i.e., the anomaly associated with nonrelativistic scaling upon coupling the theory with curved space-time [23][24][25].…”

Section: Discussionmentioning

confidence: 99%

Conformal structure of the heavy particle EFT operator basis

Kobach

Pal

2018

Physics Letters B

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An operator basis of an effective theory with a heavy particle, subject to external gauge fields, is spanned by a particular kind of neutral scalar primary of the non-relativistic conformal group. We calculate the characters that can be used for generating the operators in a non-relativistic effective field theory, which accounts for redundancies from the equations of motion and integration by parts. I. INTRODUCTIONIf one can say that a particle, and not its antiparticle, exists in the laboratory, then the length scale of its spatial wave function ∆x is parametrically larger than its Compton wavelength 1/M . This hierarchy of scales leads to heavy particle effective field theories (heavy particle EFTs), where one can systematically include higher powers of 1/(∆x M ). Such systems are, in fact, fairly common. For example, the b quark can be located anywhere within a B meson, which has a spatial size of ∼ 1/Λ QCD , and heavy quark effective field theory is an expansion in powers of Λ QCD /m b ∼ 0.3. A more dramatic example is the electron in a hydrogen atom, whose wave function has a size ∆x ∼ 10 −10 m, and 1/(∆x m e ) ∼ 10 −3 , which is why the Schrödinger equation for single-partial quantum mechanics works so well in describing this system, using only the first-order expansion in 1/M . Sometimes these theories are called non-relativistic effective field theories, insofar as there is a inertial frame in which there are non-relativistic particles.Even though heavy particle EFTs describe common physical scenarios, enumerating the independent operators that appear in the Lagrangian, i.e., defining the operator basis, takes considerable effort. The reason for this is that defining the operator basis is more than just requiring that the operators preserve certain symmetries -it also involves accounting for non-trivial redundancies between operators from the classical equations of motion and integration by parts [1,2]. There are popular EFTs with Lagrangians containing heavy fields, e.g., NRQED (external abelian gauge fields), and HQET and NRQCD (external color gauge fields). The operator basis for NRQED was written to order O(1/M 3 ) in Ref. [3] and to O(1/M 4 ) in Ref. [4]. The HQET/NRQCD operator basis was enumerated up to O(1/M 3 ) in Ref. [5], and to O(1/M 4 ) by Ref. [6], which was later confirmed in Ref. [7].A huge stride was taken recently by the authors of Refs. [8][9][10], where they noticed that the operator basis for a relativistic EFT can be organized according to the representations of the conformal group. In particular, accounting for the redundancies from the classical equations of motion can be mapped to the null conditions that saturate unitarity in the conformal group, and choosing the operator basis to be spanned only by primaries of the conformal algebra removes any redundancies associated with integration by parts. By embedding operators into representations of the conformal group, one can use characters as inputs into a Hilbert series, which then can generate the operator basis, counting the numbe...

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Weyl consistency conditions in non-relativistic quantum field theory

Cited by 26 publications

References 72 publications

Trace anomaly for non-relativistic fermions

Trace anomaly for non-relativistic fermions

On Newton-Cartan local renormalization group and anomalies

Conformal structure of the heavy particle EFT operator basis

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