ANEC in λϕ4 theory

Bautista, Teresa; Casarin, Lorenzo; Godazgar, Hadi

doi:10.1007/jhep01(2021)132

Cited by 4 publications

(2 citation statements)

References 39 publications

(69 reference statements)

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“…Light-ray operators built from the stress tensor have special algebraic properties [12,32,[62][63][64][65][66][67][68] and encode some universal features of higher-dimensional CFT [69][70][71][72]. They have been studied perturbatively in specific examples [73][74][75]. Higher spin generalizations were studied in [5,57,76,77].…”

Section: Jhep12(2023)139mentioning

confidence: 99%

Averaged null energy and the renormalization group

Hartman,

Mathys

2023

J. High Energ. Phys.

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We establish a connection between the averaged null energy condition (ANEC) and the monotonicity of the renormalization group, by studying the light-ray operator ∫ duTuu in quantum field theories that flow between two conformal fixed points. In four dimensions, we derive an exact sum rule relating this operator to the Euler coefficient in the trace anomaly, and show that the ANEC implies the a-theorem. The argument is based on matching anomalies in the stress tensor 3-point function, and relies on special properties of contact terms involving light-ray operators. We also illustrate the sum rule for the example of a free massive scalar field. Averaged null energy appears in a variety of other applications to quantum field theory, including causality constraints, Lorentzian inversion, and quantum information. The quantum information perspective provides a new derivation of the a-theorem from the monotonicity of relative entropy. The equation relating our sum rule to the dilaton scattering amplitude in the forward limit suggests an inversion formula for non-conformal theories.

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Section: Jhep12(2023)139mentioning

confidence: 99%

Averaged null energy and the renormalization group

Hartman,

Mathys

2023

J. High Energ. Phys.

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“…The systematic approach to study correlation functions of conserved currents was developed in [11, 12] and later extended to superconformal field theories in various dimensions. [ 14–28 ] Several novel approaches to the construction of correlation functions of conserved currents which carry out the calculations in momentum space, using methods such as spinor‐helicity variables were studied in [29–35]. The most studied examples of conserved currents in (super)conformal field theory are the energy‐momentum tensor and vector currents; their most general three‐point functions were determined in [11, 12].…”

Section: Introductionmentioning

confidence: 99%

Three‐Point Functions of Higher‐Spin Supercurrents in 4D N=1${{\cal N}}=1$ Superconformal Field Theory

Buchbinder

Hutomo

Tartaglino‐Mazzucchelli

2022

Fortschritte der Physik

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We develop a general formalism to study the three‐point correlation functions of conserved higher‐spin supercurrent multiplets Jαfalse(rfalse)α̇false(rfalse)$J_{\alpha (r) \dot{\alpha }(r)}$ in 4D scriptN=1${\cal N}=1$ superconformal theory. All the constraints imposed by scriptN=1${\cal N}=1$ superconformal symmetry on the three‐point function false⟨Jα(r1)trueα̇(r1)Jβ(r2)trueβ̇(r2)Jγ(r3)trueγ̇(r3)false⟩$\langle J_{\alpha (r_1) \dot{\alpha }(r_1)} J_{\beta (r_2) \dot{\beta }(r_2) }J_{\gamma (r_3) \dot{\gamma }(r_3)}\rangle$ are systematically derived for arbitrary r1,r2,r3$r_1, r_2, r_3$, thus reducing the problem mostly to computational and combinatorial. As an illustrative example, we explicitly work out the allowed tensor structures contained in false⟨Jα(r)trueα̇(r)Jβtrueβ̇Jγtrueγ̇false⟩$\langle J_{\alpha (r) \dot{\alpha }(r)} J_{\beta \dot{\beta } } J_{\gamma \dot{\gamma }}\rangle$, where Jαα̇$J_{\alpha \dot{\alpha }}$ is the supercurrent. We find that this three‐point function depends on two independent tensor structures, though the precise form of the correlator depends on whether r is even or odd. The case r=1$r=1$ reproduces the three‐point function of the ordinary supercurrent derived by Osborn. Additionally, we present the most general structure of mixed correlators of the form false⟨LLJα(r)trueα̇(r)false⟩$\langle L L J_{\alpha (r) \dot{\alpha }(r)}\rangle$ and false⟨Jα(r1)trueα̇(r1)Jβ(r2)trueβ̇(r2)Lfalse⟩$\langle J_{\alpha (r_1) \dot{\alpha }(r_1)} J_{\beta (r_2) \dot{\beta }(r_2)} L \rangle$, where L is the flavour current multiplet.

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ANEC on stress-tensor states in perturbative λ ϕ4 theory

Bautista

Casarin

2023

J. High Energ. Phys.

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We evaluate the Average Null Energy Condition (ANEC) on momentum eigenstates generated by the stress tensor in perturbative λ ϕ4 and general spacetime dimension. We first compute the norm of the stress-tensor state at second order in λ; as a by-product of the derivation we obtain the full expression for the stress tensor 2-point function at this order. We then compute the ANEC expectation value to first order in λ, which also depends on the coupling of the stress-tensor improvement term ξ. We study the bounds on these couplings that follow from the ANEC and unitarity at first order in perturbation theory. These bounds are stronger than unitarity in some regions of coupling space.

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ANEC in λϕ4 theory

Cited by 4 publications

References 39 publications

Averaged null energy and the renormalization group

Averaged null energy and the renormalization group

Three‐Point Functions of Higher‐Spin Supercurrents in 4D N=1${{\cal N}}=1$ Superconformal Field Theory

ANEC on stress-tensor states in perturbative λ ϕ4 theory

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