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 GAUGED NAMBU-JONA-LASINIO MODEL AT O(1/N) WITH AND WITHOUT A CHERN-SIMONS TERM

1993 ◽  
Vol 08 (23) ◽  
pp. 2205-2212 ◽  
Author(s):  
J.A. GRACEY
Keyword(s):  
Critical Exponents ◽  
Three Dimensional ◽  
Dyson Equation ◽  
Scaling Behavior ◽  
Leading Order ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Anomalous Dimensions ◽  
Large N ◽  
Chern Simons

We solve the gauged Nambu-Jona-Lasinio model at leading order in the large-N expansion by computing the anomalous dimensions of all the fields of the model and other gauge independent critical exponents by examining the scaling behavior of the Schwinger Dyson equation. We then restrict to the three-dimensional model and include a Chern-Simons term to discover the θ-dependence of the same exponents where θ is the Chern-Simons coupling.

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 M2-BRANES AND AdS/CFT

2010 ◽  
Vol 25 (02n03) ◽  
pp. 332-350 ◽  
Author(s):  
IGOR R. KLEBANOV
Keyword(s):  
Abjm Theory ◽  
Dual Formulation ◽  
Matter Theory ◽  
Monopole Operators ◽  
M Theory ◽  
Chern Simons

We provide a brief introduction to the ABJM theory, the level kU(N) × U(N) superconformal Chern-Simons matter theory which has been conjectured to describe N coincident M2 -branes. We discuss its dual formulation in terms of M -theory on AdS4 × S7/ℤk and review some of the evidence in favor of the conjecture. We end with a brief discussion of the important role played by the monopole operators.

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 The scaling dimension of low lying Dirac eigenmodes and of the topological charge density

2005 ◽  
Vol 140 ◽  
pp. 626-628 ◽  
Author(s):  
C. Aubin ◽  
C. Bernard ◽  
Steven Gottlieb ◽  
E.B. Gregory ◽  
Urs M. Heller ◽  
...  
Keyword(s):  
Charge Density ◽  
Topological Charge ◽  
Scaling Dimension

scholarly journals Near-BPS baby Skyrmions

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Sven Bjarke Gudnason ◽  
Marco Barsanti ◽  
Stefano Bolognesi
Keyword(s):  
Binding Energy ◽  
Topological Charge ◽  
Harmonic Maps ◽  
Single Point ◽  
Pion Mass ◽  
Mass Term ◽  
Skyrme Model ◽  
Classical Solutions ◽  
Leading Order ◽  
Area Preserving

Abstract We consider the baby-Skyrme model in the regime close to the so-called restricted baby-Skyrme model, which is a BPS model with area-preserving diffeomorphism invariance. The perturbation takes the form of the standard kinetic Dirichlet term with a small coefficient ϵ. Classical solutions of this model, to leading order in ϵ, are called restricted harmonic maps. In the BPS limit (ϵ → 0) of the model with the potential being the standard pion-mass term, the solution with unit topological charge is a compacton. Using analytical and numerical arguments we obtain solutions to the problem for topological sectors greater than one. We develop a perturbative scheme in ϵ with which we can calculate the corrections to the BPS mass. The leading order ($$ \mathcal{O}\left({\upepsilon}^1\right) $$ O ϵ 1 ) corrections show that the baby Skyrmion with topological charge two is energetically preferred. The binding energy requires us to go to the third order in ϵ to capture the relevant terms in perturbation theory, however, the binding energy contributes to the total energy at order ϵ2. We find that the baby Skyrmions — in the near-BPS regime — are compactons of topological charge two, that touch each other on their periphery at a single point and with orientations in the attractive channel.

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