Convexity, large charge and the large-N phase diagram of the φ4 theory

Moser, Rafael; Orlando, Domenico; Reffert, Susanne

doi:10.1007/jhep02(2022)152

Cited by 18 publications

(22 citation statements)

References 62 publications

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“…Feynman diagrams thereby helping shed light on higher order computations in different regimes [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. The approach can be extended to non-conformal QFTs as illustrated in [73][74][75][76][77], with possible physical applications such as the study of multi-boson production processes in the Standard Model.…”

Section: Jhep06(2022)041mentioning

confidence: 99%

The analytic structure of the fixed charge expansion

Antipin

Bersini

Sannino

et al. 2022

J. High Energ. Phys.

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We investigate the analytic properties of the fixed charge expansion for a number of conformal field theories in different space-time dimensions. The models investigated here are O(N) and QED3. We show that in d = 3 − ϵ dimensions the contribution to the O(N) fixed charge Q conformal dimensions obtained in the double scaling limit of large charge and vanishing ϵ is non-Borel summable, doubly factorial divergent, and with order $$ \sqrt{Q} $$ Q optimal truncation order. By using resurgence techniques we show that the singularities in the Borel plane are related to worldline instantons that were discovered in the other double scaling limit of large Q and N of ref. [1]. In d = 4 − ϵ dimensions the story changes since in the same large Q and small E regime the next order corrections to the scaling dimensions lead to a convergent series. The resummed series displays a new branch cut singularity which is relevant for the stability of the O(N) large charge sector for negative ϵ. Although the QED3 model shares the same large charge behaviour of the O(N) model, we discover that at leading order in the large number of matter field expansion the large charge scaling dimensions are Borel summable, single factorial divergent, and with order Q optimal truncation order.

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Section: Jhep06(2022)041mentioning

confidence: 99%

The analytic structure of the fixed charge expansion

Antipin

Bersini

Sannino

et al. 2022

J. High Energ. Phys.

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show abstract

“…Such a concavity is conjectured to indicate some sickness of the theory (e.g., non-unitarity) in relation to the weak gravity conjecture [87,88] (For a review of weak gravity conjecture in general see [89].) As discussed in [37,38], this inevitably leads to complex operator dimensions at large Q. However, the theory of resurgence might tell us how the sickness (in this the imaginary part in the operator dimension) comes about already at small Q.…”

Section: Discussionmentioning

confidence: 99%

“…This reduces the computation of (2.7) to the "Legendre transformation" of the the grand canonical partition function with imaginary chemical potential. One caveat, which is why we put "Legendre transformation" into the quotation mark, is that the grand canonical partition function is not really a convex function for 4 < D < 6 where the theory is not unitary [37,38]. 6 Indeed, this is related to the fact that the value of the chemical potential, ω ≡ iθ/β, at the saddle-point develops an imaginary part, as we explain later.…”

Section: Partition Function In the Sector Of Fixed Chargementioning

confidence: 99%

Stability Analysis of a Non-Unitary CFT

Watanabe¹

2022

Preprint

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We study instability of the lowest dimension operator (i.e., the imaginary part of its operator dimension) in the rank-Q traceless symmetric representation of the O(N ) Wilson-Fisher fixed point in D = 4 + . We find a new semi-classical bounce solution, which gives an imaginary part to the operator dimension of orderis fixed. The form of F ( Q), normalised as F (0) = 1, is also computed. This non-perturbative correction continues to give the leading effect even when Q is finite, indicating the instability of operators for any values of Q. We also observe a phase transition at Q = N +8 6 √ 3 associated with the condensation of bounces, similar to the Gross-Witten-Wadia transition.

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“…The EFT description allows us to make several predictions about the behavior the theory in sectors of large global charge. This was also extended to non-Abelian symmetries such as O(2n) in many recent studies [14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 91%

Large-charge conformal dimensions at the $O(N)$ Wilson-Fisher fixed point

Singh¹

2022

Preprint

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Recent work using a large-charge expansion for the O(N ) Wilson-Fisher conformal field theory has shown that the anomalous dimensions of large-charge operators can be expressed in terms of a few low-energy constants (LECs) of a large-charge effective field theory (EFT). By performing lattice Monte Carlo computations at the O(N ) Wilson-Fisher fixed point, we compute the anomalous dimensions of large-charge operators up to N = 8 and charge Q = 10, and extract the leading and subleading LECs of the O(N ) large-charge EFT. To alleviate the signal-to-noise ratio problem present in the large-charge sector of conventional lattice formulations of the O(N ) theory, we employ a recently developed qubit formulation of the O(N ) nonlinear sigma models with a worm algorithm. This enables us to test the validity of the large-charge expansion and the recent large-N predictions for the coefficients of the large-charge EFT.

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Convexity, large charge and the large-N phase diagram of the φ4 theory

Cited by 18 publications

References 62 publications

The analytic structure of the fixed charge expansion

The analytic structure of the fixed charge expansion

Stability Analysis of a Non-Unitary CFT

Large-charge conformal dimensions at the $O(N)$ Wilson-Fisher fixed point

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