Heat kernel for Newton-Cartan trace anomalies

Auzzi, Roberto; Nardelli, Giuseppe

doi:10.1007/jhep07(2016)047

Cited by 16 publications

(46 citation statements)

References 65 publications

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“…The coefficients of the curvature squared terms are in addition identical to those derived using the heat kernel approach of [32].…”

Section: A the Trace Anomalymentioning

confidence: 75%

“…Motivated by the extension of these results to nonrelativistic systems on curved backgrounds, we will be concerned with the trace and diffeomorphism anomalies of the Schrödinger field on the Newton-Cartan (NC) background. Note that while the trace anomaly of the NC background has been considered in [29][30][31][32][33] following the discrete light-cone quantization (DLCQ) technique from higher dimensional relativistic backgrounds, our aim is to revisit the derivation starting from an action on the NC background. The interesting outcome of our derivation for the trace anomaly in 2+1 dimensions is that it takes the following general form 2 T 0 0 + T i i = 1 m(4π) 2 1 360 (R µν h µν ) 2 + 2m 4 ψ 2 + m 2 3 (ψR µν h µν + R µν v µ v ν ) (1.1) where ψ = τ µ A µ − 1 2 h µν A µ A ν and v µ = τ µ − h µν A ν .…”

Section: Introductionmentioning

confidence: 99%

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Gravitational anomalies on the Newton-Cartan background

Fernandes

Mitra

2017

Phys. Rev. D

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We derive the trace and diffeomorphism anomalies of the Schrödinger field minimally coupled to the Newton-Cartan background using Fujikawa's path integral approach. This approach in particular enables us to calculate the one-loop contributions due to all the fields of the NewtonCartan structure. We determine the coefficients and demonstrate that gravitational anomalies for this theory always arise in odd dimensions. Due to the gauge field contribution of the background we find that in 2 + 1 dimensions the trace anomaly contains terms which have a form similar to that of the 1 + 1 and 3 + 1 dimensional relativistic trace anomalies. This result reveals that the Newton-Cartan background which satisfies the Frobenius condition possesses a Type A trace anomaly in contrast with the result of Lishitz spacetimes. As an application we demonstrate that the coefficient of the term similar to the 1 + 1 dimensional relativistic trace anomaly satisfies a c-theorem condition.

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“…The coefficients of the curvature squared terms are in addition identical to those derived using the heat kernel approach of [32].…”

Section: A the Trace Anomalymentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Gravitational anomalies on the Newton-Cartan background

Fernandes

Mitra

2017

Phys. Rev. D

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“…Cohomological analysis and general properties were studied in [21,[24][25][26]. The first explicit calculation of anomalies for a physical system was performed in [27] with the Heat Kernel (HK) method, for the case of a free scalar. Later this result was confirmed in [28] using Fujikawa approach.…”

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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“…In particular, in the simplest sector N n = 0 the anomaly structure is identical to the trace anomaly of relativistic theories in 4 dimensions and a natural type A candidate for a monotonicity theorem is the coefficient of the E 4 term. The calculation of the N n = 0 anomaly in the case of a free scalar was recently done in [32].…”

Section: Jhep11(2016)163mentioning

confidence: 99%

“…The anomaly in eq. (2.19) was explicitly computed for a free scalar in [32]. The sectors with N n > 0 will be discussed in section 5.…”

Section: The Trace Anomaly Without Frobenius Conditionmentioning

confidence: 99%