Built on

A. Grassi, Z. Komargodski and L. Tizzano, Extremal Correlators and Random Matrix Theory , 1908.10306
Original
1908
Earlier work this paper cites.
G. Arias-Tamargo, D. Rodriguez-Gomez and J. G. Russo, The large charge limit of scalar field theories and the Wilson-Fisher fixed point at ϵ = 0 \epsilon=0 , 1908.11347
Original
1908
Earlier work this paper cites.
L. S. Brown and J. C. Collins, Dimensional Renormalization of Scalar Field Theory in Curved Space-time , Annals Phys. 130
1980
Earlier work this paper cites.
V. A. Rubakov, Nonperturbative aspects of multiparticle production , in 2nd Rencontres du Vietnam: Consisting of 2 parallel conferences: Astrophysics Meeting: From the Sun and Beyond / Particle Physics Meeting: Physics at the Frontiers of the Standard Model, Ho Chi Minh City, Vietnam, October 21-28, 1995 , 1995, hep-ph/9511236
1995
Earlier work this paper cites.
M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory . Westview Press, 1995
1995
Earlier work this paper cites.
D. T. Son, Semiclassical approach for multiparticle production in scalar theories , Nucl. Phys. B477
1996
Earlier work this paper cites.

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2019

The Epsilon Expansion Meets Semiclassics

Badel, Gil, Cuomo, Gabriel, Monin, Alexander et al.

Understand

We study the scaling dimension $\Delta_{\phi^n}$ of the operator $\phi^n$ where $\phi$ is the fundamental complex field of the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-\varepsilon$.

Even for a perturbatively small fixed point coupling $\lambda_*$, standard perturbation theory breaks down for sufficiently large $\lambda_*n$.
Treating $\lambda_* n$ as fixed for small $\lambda_*$ we show that $\Delta_{\phi^n}$ can be successfully computed through a semiclassical expansion around a non-trivial trajectory, resulting in $$ \Delta_{\phi^n}=\frac{1}{\lambda_*}\Delta_{-1}(\lambda_* n)+\Delta_{0}(\lambda_* n)+\lambda_* \Delta_{1}(\lambda_* n)+\ldots $$ We explicitly compute the first two orders in the expansion, $\Delta_{-1}(\lambda_* n)$ and $\Delta_{0}(\lambda_* n)$.
The result, when expanded at small $\lambda_* n$, perfectly agrees with all available diagrammatic computations.

Built on

A. Grassi, Z. Komargodski and L. Tizzano, Extremal Correlators and Random Matrix Theory , 1908.10306
Original
1908
Earlier work this paper cites.
G. Arias-Tamargo, D. Rodriguez-Gomez and J. G. Russo, The large charge limit of scalar field theories and the Wilson-Fisher fixed point at ϵ = 0 \epsilon=0 , 1908.11347
Original
1908
Earlier work this paper cites.
L. S. Brown and J. C. Collins, Dimensional Renormalization of Scalar Field Theory in Curved Space-time , Annals Phys. 130
1980
Earlier work this paper cites.
V. A. Rubakov, Nonperturbative aspects of multiparticle production , in 2nd Rencontres du Vietnam: Consisting of 2 parallel conferences: Astrophysics Meeting: From the Sun and Beyond / Particle Physics Meeting: Physics at the Frontiers of the Standard Model, Ho Chi Minh City, Vietnam, October 21-28, 1995 , 1995, hep-ph/9511236
1995
Earlier work this paper cites.
M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory . Westview Press, 1995
1995
Earlier work this paper cites.
D. T. Son, Semiclassical approach for multiparticle production in scalar theories , Nucl. Phys. B477
1996
Earlier work this paper cites.

Similar

H. Kleinert and V. Schulte-Frohlinde, Critical properties of phi**4-theories . 2001
2001
Cited alongside, same era.
P. Calabrese, A. Pelissetto and E. Vicari, Multicritical phenomena in O(n(1)) + O(n(2)) symmetric theories , Phys. Rev. B67
2003
Cited alongside, same era.
M. De Prato, A. Pelissetto and E. Vicari, Third harmonic exponent in three-dimensional N vector models , Phys. Rev. B68
2003
Cited alongside, same era.
S. Hellerman, D. Orlando, S. Reffert and M. Watanabe, On the CFT Operator Spectrum at Large Global Charge , JHEP 12
Original
2015
Cited alongside, same era.
S. Rychkov, EPFL Lectures on Conformal Field Theory in D ≥ 3 D\geq 3 Dimensions , SpringerBriefs in Physics. 2016, 10.1007/978-3-319-43626-5 , [ 1601.05000 ]
Original
2016
Cited alongside, same era.