c -theorem and spectral representation

Cappelli, Andrea; Friedan, Daniel; Latorre, José I.

doi:10.1016/0550-3213(91)90102-4

Cited by 218 publications

(362 citation statements)

References 32 publications

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“…As we discussed earlier in this section, by choosing 23) and combining equation (B.13)and (B.21) we can conclude that the on-shell action with the boundary data A (0) and π (0) must take the following form: 24) with the understanding that A (0) and π (0) are completely free parameters in the above expression.…”

Section: A1 Conformal Radial Coordinatementioning

confidence: 99%

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An effective theory for holographic RG flows

Kaplan

Wang

2015

J. High Energ. Phys.

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We study the dilaton action induced by RG flows between holographic CFT fixed points. For this purpose we introduce a general bulk effective theory for the goldstone boson of the broken spacetime symmetry, providing an AdS analog of the EFT of Inflation. In two dimensions, we use the effective theory to compute the dilaton action, as well as the UV and IR conformal anomalies, without further assumptions. In higher dimensions we take a 'slow-flow' limit analogous to the assumption of slow-roll in Inflation, and in this context we obtain the dilaton action, focusing on terms proportional to the difference of the A-type anomalies. We include Gauss-Bonnet terms in the gravitational action in order to verify that our method correctly differentiates between A-type and other anomalies.

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Section: A1 Conformal Radial Coordinatementioning

confidence: 99%

“…In fact we can construct a cfunction along the RG flow, which is defined for all energy scales and is equal to c UV and c IR , respectively, at the UV and IR fixed point. To state this in a bit more detail, note that we can write [23] …”

Section: Jhep02(2015)056mentioning

confidence: 99%

An effective theory for holographic RG flows

Kaplan

Wang

2015

J. High Energ. Phys.

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“…We now plug (3.4) and (3.8) into (2.24) and expand to quadratic order in δA. Notice that, to this order, N µ P µ = 0, and N H = H (2) . After integration by parts, the terms S grav + S matter of the action expanded to quadratic order can be brought to the form…”

Section: Jhep03(2016)033mentioning

confidence: 99%

“…Here unitarity of Θ(x) implies Zamolodchikov's c-theorem, and its two-point function yields the sum rule [1,2] C UV − C IR = 3π d 2 x x 2 0|Θ(x)Θ(0)|0 , (1.2) where C UV and C IR are the central charges of the UV and IR fixed points. The situation in higher dimensions is more complicated and interesting.…”

Section: Jhep03(2016)033mentioning

confidence: 99%

“…The situation in higher dimensions is more complicated and interesting. Early efforts were oriented at studying the stress-tensor two point function in d > 2 [2][3][4][5][6]; however, in general there is no clear connection of this quantity to global aspects of the RG. Instead, the generalization of (1.2) to d = 4 involves the 4-point function of Θ(x), and it has been shown that unitarity implies the a-theorem a UV > a IR [7].…”

Section: Jhep03(2016)033mentioning

confidence: 99%

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Holographic RG flows, entanglement entropy and the sum rule

Casini

Testé

Torroba

2016

J. High Energ. Phys.

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Abstract:We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d = 2 and in d > 2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.

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Conformal Invariance in Quantum Field Theory and Statistical Mechanics

Asorey

1992

Fortschr. Phys.

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c -theorem and spectral representation

Cited by 218 publications

References 32 publications

An effective theory for holographic RG flows

An effective theory for holographic RG flows

Holographic RG flows, entanglement entropy and the sum rule

Conformal Invariance in Quantum Field Theory and Statistical Mechanics

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