Thermal CFTs in momentum space

Manenti, Andrea

doi:10.1007/jhep01(2020)009

Cited by 10 publications

(9 citation statements)

References 43 publications

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“…The general framework for CFTs at finite temperature has been recently studied in [53][54][55]. Ultimately, symmetry breaking at finite temperature in CFTs should be understood in this language.…”

Section: ð1:7þmentioning

confidence: 99%

Thermal order in conformal theories

et al. 2020

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It is widely expected that at sufficiently high temperatures order is always lost, e.g., magnets lose their ferromagnetic properties. We pose the question of whether this is always the case in the context of quantum field theory in d space dimensions. More concretely, one can ask whether there exist critical points (CFTs) which break some global symmetry at arbitrary finite temperature. The most familiar CFTs do not exhibit symmetry breaking at finite temperature, and moreover, in the context of the AdS=CFT correspondence, critical points at finite temperature are described by an uncharged black brane which obeys a no-hair theorem. Yet, we show that there exist CFTs which have some of their internal symmetries broken at arbitrary finite temperature. Our main example is a vector model which we study both in the epsilon expansion and arbitrary rank as well as the large rank limit (and arbitrary dimension). The large rank limit of the vector model displays a conformal manifold, a moduli space of vacua, and a deformed moduli space of vacua at finite temperature. The appropriate Nambu-Goldstone bosons including the dilatonlike particle are identified. Using these tools we establish symmetry breaking at finite temperature for finite small ϵ. We also prove that a large class of other fixed points, which describe some of the most common quantum magnets, indeed behave as expected and do not break any global symmetry at finite temperature. We discuss some of the consequences of finite temperature symmetry breaking for the spectrum of local operators. Finally, we propose a class of fixed points which appear to be possible candidates for finite temperature symmetry breaking in d ¼ 2.

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Section: ð1:7þmentioning

confidence: 99%

Thermal order in conformal theories

et al. 2020

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“…The general framework for CFTs at finite temperature has been recently studied in [49][50][51]. Ultimately, symmetry breaking at finite temperature in CFTs should be understood in this language.…”

Section: Consequences For the Spectrum Of Operators And The Phase Dia...mentioning

confidence: 99%

Thermal Order in Conformal Theories

Chai,

Chaudhuri,

Choi

et al. 2020

Preprint

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It is widely expected that at sufficiently high temperatures order is always lost, e.g. magnets loose their ferromagnetic properties. We pose the question of whether this is always the case in the context of quantum field theory in d space dimensions. More concretely, one can ask whether there exist critical points (CFTs) which break some global symmetry at arbitrary finite temperature. The most familiar CFTs do not exhibit symmetry breaking at finite temperature, and moreover, in the context of the AdS/CFT correspondence, critical points at finite temperature are described by an uncharged black brane which obeys a no-hair theorem. Yet, we show that there exist CFTs which have some of their internal symmetries broken at arbitrary finite temperature. Our main example is a vector model which we study both in the epsilon expansion and arbitrary rank as well as the large rank limit (and arbitrary dimension). The large rank limit of the vector model displays a conformal manifold, a moduli space of vacua, and a deformed moduli space of vacua at finite temperature. The appropriate Nambu-Goldstone bosons including the dilaton-like particle are identified. Using these tools we establish symmetry breaking at finite temperature for finite small . We also prove that a large class of other fixed points, which describe some of the most common quantum magnets, indeed behave as expected and do not break any global symmetry at finite temperature. We discuss some of the consequences of finite temperature symmetry breaking for the spectrum of local operators.Finally, we propose a class of fixed points which appear to be possible candidates for finite temperature symmetry breaking in d = 2.

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“…It would be nice to use the analytic bootstrap at finite temperature [39][40][41] to compute the values of Υ and H xx and compare them with the predictions given in this work.…”

Section: Conductivity At Finite Temperaturementioning

confidence: 86%

Mixed scalar-current bootstrap in three dimensions

Reehorst

Trevisani

Vichi

2020

J. High Energ. Phys.

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We study the mixed system of correlation functions involving a scalar field charged under a global U(1) symmetry and the associated conserved spin-1 current Jμ. Using numerical bootstrap techniques we obtain bounds on new observables not accessible in the usual scalar bootstrap. We then specialize to the O(2) model and extract rigorous bounds on the three-point function coefficient of two currents and the unique relevant scalar singlet, as well as those of two currents and the stress tensor. Using these results, and comparing with a quantum Monte Carlo simulation of the O(2) model conductivity, we give estimates of the thermal one-point function of the relevant singlet and the stress tensor. We also obtain new bounds on operators in various sectors.

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Thermal CFTs in momentum space

Cited by 10 publications

References 43 publications

Thermal order in conformal theories

Thermal order in conformal theories

Thermal Order in Conformal Theories

Mixed scalar-current bootstrap in three dimensions

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