scholarly journals Leading order anomalous dimensions at the Wilson-Fisher fixed point from CFT

2017 ◽  
Vol 2017 (7) ◽  
Author(s):  
Konstantinos Roumpedakis
Keyword(s):  
Fixed Point ◽  
Leading Order ◽  
Anomalous Dimensions

scholarly journals Anomalous dimensions of monopole operators in scalar QED3 with Chern-Simons term

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Shai M. Chester
Keyword(s):  
Fixed Point ◽  
Topological Charge ◽  
The State ◽  
Leading Order ◽  
State Operator ◽  
Anomalous Dimensions ◽  
Monopole Operators ◽  
Chern Simons ◽  
Scaling Dimension

Abstract We study monopole operators with the lowest possible topological charge q = 1/2 at the infrared fixed point of scalar electrodynamics in 2 + 1 dimension (scalar QED3) with N complex scalars and Chern-Simons coupling |k| = N. In the large N expansion, monopole operators in this theory with spins $$ \mathrm{\ell}<O\left(\sqrt{N}\right) $$ ℓ < O N and associated flavor representations are expected to have the same scaling dimension to sub-leading order in 1/N. We use the state-operator correspondence to calculate the scaling dimension to sub-leading order with the result N − 0.2743 + O(1/N), which improves on existing leading order results. We also compute the ℓ2/N term that breaks the degeneracy to sub-leading order for monopoles with spins $$ \mathrm{\ell}=O\left(\sqrt{N}\right) $$ ℓ = O N .

scholarly journals Bounds on multiscalar CFTs in the ε expansion

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Matthijs Hogervorst ◽  
Chiara Toldo
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Scalar Fields ◽  
Final Part ◽  
Leading Order ◽  
Quartic Coupling ◽  
Specific Domain ◽  
Bottom Up ◽  
Anomalous Dimensions ◽  
Do So

Abstract We study fixed points with N scalar fields in 4 − ε dimensions to leading order in ε using a bottom-up approach. We do so by analyzing O(N) invariants of the quartic coupling λijkl that describes such CFTs. In particular, we show that λiijj and $$ {\lambda}_{ijkl}^2 $$ λ ijkl 2 are restricted to a specific domain, refining a result by Rychkov and Stergiou. We also study averages of one-loop anomalous dimensions of composite operators without gradients. In many cases, we are able to show that the O(N) fixed point maximizes such averages. In the final part of this work, we generalize our results to theories with N complex scalars and to bosonic QED. In particular we show that to leading order in ε, there are no bosonic QED fixed points with N < 183 flavors.

scholarly journals CONFORMAL HOUSE

2010 ◽  
Vol 25 (24) ◽  
pp. 4603-4621 ◽  
Author(s):  
THOMAS A. RYTTOV ◽  
FRANCESCO SANNINO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Gauge Group ◽  
Gauge Theories ◽  
Simultaneous Presence ◽  
Consistency Check ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Mass Terms

We investigate the gauge dynamics of nonsupersymmetric SU (N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

scholarly journals RENORMALIZATION GROUP FLOW EQUATIONS FOR THE SCALAR O(N) THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2119-2124 ◽  
Author(s):  
B.-J. SCHAEFER ◽  
O. BOHR ◽  
J. WAMBACH
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Three Dimensions ◽  
Leading Order ◽  
Renormalization Group Flow ◽  
Derivative Expansion ◽  
Scalar Theory ◽  
Flow Equations ◽  
Self Consistent ◽  
Group Flow

Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and various critical exponents are calculated.

scholarly journals SUSY-like relation of the splitting functions in evolution of gluon and quark jet multiplicities

2018 ◽  
Vol 191 ◽  
pp. 04006
Author(s):  
Anatoly Kotikov
Keyword(s):  
Evolution Equations ◽  
Dglap Evolution ◽  
Leading Order ◽  
Logarithmic Order ◽  
World Data ◽  
Charged Hadrons ◽  
Anomalous Dimensions ◽  
The World ◽  
Fragmentation Functions ◽  
Gluon Fragmentation

We show the new relationship [1] between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the first Mellin moments Dq,g(μ2) of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. So far, such relationships have only been known from supersymmetric (SUSY) QCD. Exploiting available next-to-nextto- next-to-leading-order (NNNLO) information on the ratio D+g (μ2)=D+q (μ2) of the dominant plus components, the fit of the world data of Dq,g(μ2) for charged hadrons measured in e+e- annihilation leads to α(5)s (MZ) = 0:1205 +0:0016 -0:0020.

scholarly journals INFRARED FIXED POINT IN THE STRONG RUNNING COUPLING: UNRAVELING THE ΔI = 1/2 PUZZLE IN K-DECAYS

2013 ◽  
Vol 28 (25) ◽  
pp. 1360010 ◽  
Author(s):  
R. J. CREWTHER ◽  
LEWIS C. TUNSTALL
Keyword(s):  
Fixed Point ◽  
Perturbation Theory ◽  
Quantum Chromodynamics ◽  
Quark Condensate ◽  
Low Energy ◽  
Pole Term ◽  
Leading Order ◽  
Goldstone Bosons ◽  
Running Coupling ◽  
Scale Perturbation

In this paper, we present an explanation for the ΔI = 1/2 rule in K-decays based on the premise of an infrared fixed point α IR in the running coupling αs of quantum chromodynamics (QCD) for three light quarks u, d, s. At the fixed point, the quark condensate [Formula: see text] spontaneously breaks scale and chiral SU (3)L× SU (3)R symmetry. Consequently, the low-lying spectrum contains nine Nambu–Goldstone bosons: π, K, η and a QCD dilaton σ. We identify σ as the f0(500) resonance and construct a chiral-scale perturbation theory χPTσ for low-energy amplitudes expanded in αs about α IR . The ΔI = 1/2 rule emerges in the leading order of χPTσ through a σ-pole term KS→σ→ππ, with a gKSσ coupling fixed by data on γγ→π0π0 and KS→γγ. We also determine R IR ≈5 for the nonperturbative Drell–Yan ratio at α IR .

scholarly journals Random field Ising model and Parisi-Sourlas supersymmetry. Part II. Renormalization group

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Apratim Kaviraj ◽  
Slava Rychkov ◽  
Emilio Trevisani
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Random Field ◽  
Dimensional Reduction ◽  
Critical Dimension ◽  
Random Field Ising Model ◽  
Upper Critical Dimension ◽  
Anomalous Dimensions ◽  
Weakly Coupled

Abstract We revisit perturbative RG analysis in the replicated Landau-Ginzburg description of the Random Field Ising Model near the upper critical dimension 6. Working in a field basis with manifest vicinity to a weakly-coupled Parisi-Sourlas supersymmetric fixed point (Cardy, 1985), we look for interactions which may destabilize the SUSY RG flow and lead to the loss of dimensional reduction. This problem is reduced to studying the anomalous dimensions of “leaders” — lowest dimension parts of Sn-invariant perturbations in the Cardy basis. Leader operators are classified as non-susy-writable, susy-writable or susy-null depending on their symmetry. Susy-writable leaders are additionally classified as belonging to superprimary multiplets transforming in particular OSp(d|2) representations. We enumerate all leaders up to 6d dimension ∆ = 12, and compute their perturbative anomalous dimensions (up to two loops). We thus identify two perturbations (with susy- null and non-susy-writable leaders) becoming relevant below a critical dimension dc ≈ 4.2 - 4.7. This supports the scenario that the SUSY fixed point exists for all 3 < d ⩽ 6, but becomes unstable for d < dc.

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