Holographic Ward identities for symmetry breaking in two dimensions

Argurio, Riccardo; Giribet, Gastón; Marzolla, Andrea; Naegels, Daniel; Sierra-Garcıa, J. Anıbal

doi:10.1007/jhep04(2017)007

Cited by 13 publications

(21 citation statements)

References 161 publications

(346 reference statements)

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“…We extend the analysis of [16] to the above mentioned case of d ď z`1. As in the relativistic case [7], we find that alternative quantization for the vector is needed, albeit in the present case of Lifshitz scaling, only the temporal component of the vector is involved. This quantization which treats differently space and time is actually needed to enforce the proper gauge invariance of the generating functional.…”

Section: Introductionmentioning

confidence: 47%

“…It is important for the following to note thatã 0 is a gauge invariant quantity and therefore cannot be the source for the temporal part of a conserved current. Note that in the limiting, relativistic, case where d " 2 and z " 1, i.e.d " 2, all leading and subleading terms of the vector modes have the same order in r respectively : This case was already discussed in [7] (see also [21,22]) so we will keepd ą 2 from now on.…”

Section: Quantum Corrections To the Symmetry Breaking Vevmentioning

confidence: 98%

“…We see that the only divergence is logarithmic and takes place for the temporal component of the vector. As in [7], we explore now two ways of renormalizing this sector. Adding a mass-like countertermS…”

Section: It Leads Tomentioning

confidence: 99%

“…Hence, it cannot reproduce a source for J t on the QFT side of the correspondence if J µ is a conserved current. Inspired again by [7], we propose the following counterterm 6…”

Section: It Leads Tomentioning

confidence: 99%

“…It was shown in [7] that indeed AdS 3 holography allows for spontaneous symmetry breaking in its dual two-dimensional QFT. It was realized there that, however, the holographic set-up keeps a score of the peculiarity related to being in two dimensions: the bulk vector dual to the current of the symmetry which was to be broken, has to undergo alternative quantization to properly account for the conserved current Ward identities.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Are there Goldstone bosons in d≤z+1 ?

2019

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We study the viability of spontaneous breaking of continuous symmetries in theories with Lifshitz scaling, according to the number of space-time dimensions d and the dynamical scaling z. Then, the answer to the question in the title is no (quantum field theoretically) and yes (holographically). With field theory tools, we show that symmetry breaking is indeed prevented by large quantum fluctuations when d ď z`1, as expected from scaling arguments. With holographic tools, on the other hand, we find nothing that prevents the existence of a vacuum expectation value. This difference is made possible by the large N limit of holography. An important subtlety in this last framework is that in order to get a proper description of a conserved current, renormalization of the temporal mode of the bulk vector requires an alternative quantization. We also comment on the implications of turning on temperature.

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Section: Introductionmentioning

confidence: 47%

Section: Quantum Corrections To the Symmetry Breaking Vevmentioning

confidence: 98%

Section: It Leads Tomentioning

confidence: 99%

“…Hence, it cannot reproduce a source for J t on the QFT side of the correspondence if J µ is a conserved current. Inspired again by [7], we propose the following counterterm 6…”

Section: It Leads Tomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Are there Goldstone bosons in d≤z+1 ?

2019

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Black hole elasticity and gapped transverse phonons in holography

Alberte

Ammon

Baggioli

et al. 2018

J. High Energ. Phys.

135

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Abstract:We study the elastic response of planar black hole (BH) solutions in a simple class of holographic models with broken translational invariance. We compute the transverse quasi-normal mode spectrum and the propagation speed of the lowest energy mode. We find that the speed of the lowest mode relates to the BH rigidity modulus as dictated by elasticity theory. This allows to identify these modes as transverse phonons -the pseudo Goldstone bosons of spontaneously broken translational invariance. In addition, we show that these modes have a mass gap controlled by an explicit source of the translational symmetry breaking. These results provide a new confirmation that the BHs in these models do exhibit solid properties that become more manifest at low temperatures. Also, by the AdS/CFT correspondence, this allows to extend the standard results from the effective field theory for solids to quantum-critical materials.

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Symmetry breaking in holographic theories with Lifshitz scaling

Argurio

Hartong

Marzolla

et al. 2018

J. High Energ. Phys.

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Abstract:We study holographically Lifshitz-scaling theories with broken symmetries. In order to do this, we set up a bulk action with a complex scalar and a massless vector on a background which consists in a Lifshitz metric and a massive vector. We first study separately the complex scalar and the massless vector, finding a similar pattern in the twopoint functions that we can compute analytically. By coupling the probe complex scalar to the background massive vector we can construct probe actions that are more general than the usual Klein-Gordon action. Some of these actions have Galilean boost symmetry. Finally, in the presence of a symmetry breaking scalar profile in the bulk, we reproduce the expected Ward identities of a Lifshitz-scaling theory with a broken global continuous symmetry. In the spontaneous case, the latter imply the presence of a gapless mode, the Goldstone boson, which will have dispersion relations dictated by the Lifshitz scaling.

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Holographic Ward identities for symmetry breaking in two dimensions

Cited by 13 publications

References 161 publications

Are there Goldstone bosons in d≤z+1 ?

Are there Goldstone bosons in d≤z+1 ?

Black hole elasticity and gapped transverse phonons in holography

Symmetry breaking in holographic theories with Lifshitz scaling

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