scholarly journals $$ \mathcal{N} $$ = 1 QED in 2 + 1 dimensions: dualities and enhanced symmetries

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Benini ◽  
Sergio Benvenuti
Keyword(s):  
Fixed Points ◽  
Three Dimensional ◽  
Global Symmetry ◽  
Mass Terms

Abstract We consider three-dimensional sQED with 2 flavors and minimal supersymmetry. We discuss various models which are dual to Gross-Neveu-Yukawa theories. The U(2) ultraviolet global symmetry is often enhanced in the infrared, for instance to O(4) or SU(3). This is analogous to the conjectured behaviour of non-supersymmetric QED with 2 flavors. A perturbative analysis of the Gross-Neveu-Yukawa models in the D = 4 − ε expansion shows that the U(2) preserving superpotential deformations of the sQED (mod- ulo tuning mass terms to zero) are irrelevant, therefore the fixed points with enhanced symmetry are stable. We also construct an example of $$ \mathcal{N} $$ N = 2 sQED with 4 flavors that exhibits enhanced SO(6) symmetry.

scholarly journals Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
András L. Szabó ◽  
Bitan Roy
Keyword(s):  
Fixed Points ◽  
Chiral Symmetry ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Dirac Fermions ◽  
Electronic Interactions ◽  
Emergent Phenomena ◽  
Ordered Phases ◽  
The Stability

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

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.

LIMIT CYCLES OF A DOUBLE OSCILLATOR EXCITED BY DRY FRICTION

2011 ◽  
Vol 21 (10) ◽  
pp. 3043-3046 ◽  
Author(s):  
SERGEY STEPANOV
Keyword(s):  
Fixed Points ◽  
Numerical Method ◽  
Limit Cycles ◽  
Dry Friction ◽  
Coulomb Friction ◽  
Three Dimensional ◽  
Slip Mode ◽  
Two Dimensional ◽  
Parametric Investigation ◽  
Friction Laws

A two-mass oscillator with one mass lying on the driving belt with dry Coulomb friction is considered. A numerical method for finding all limit cycles and their parametric investigation, based on the analysis of fixed points of a two-dimensional map, is suggested. As successive points for the map we chose points of friction transferred from stick mode to slip mode. These transfers are defined by two equalities and yield a two-dimensional map, in contrast to three-dimensional maps that we can construct for regularized continuous dry friction laws.

scholarly journals Perturbative and nonperturbative studies of CFTs with MN global symmetry

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Johan Henriksson ◽  
Andreas Stergiou
Keyword(s):  
Fixed Points ◽  
Numerical Data ◽  
Three Dimensions ◽  
Global Symmetry ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
State Of Affairs ◽  
Perturbative Limit ◽  
Good Agreement

Fixed points in three dimensions described by conformal field theories with \ensuremath{M N}_{m,n} = O(m)^n\rtimes S_nMNm,n=O(m)n⋊Sn global symmetry have extensive applications in critical phenomena. Associated experimental data for m=n=2m=n=2 suggest the existence of two non-trivial fixed points, while the \varepsilonε expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters mm and nn, with critical exponents in good agreement with experimental determinations in the m=n=2m=n=2 case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters mm and nn. We find that one family of kinks approaches a perturbative limit as mm increases, and using large spin perturbation theory we construct a large mm expansion that fits well with the numerical data. This new expansion, akin to the large NN expansion of critical O(N)O(N) models, is compatible with the fixed point found in the \varepsilonε expansion. For the other family of kinks, we find that it persists only for n=2n=2, where for large mm it approaches a non-perturbative limit with \Delta_\phi\approx 0.75Δϕ≈0.75. We investigate the spectrum in the case \ensuremath{M N}_{100,2}MN100,2 and find consistency with expectations from the lightcone bootstrap.

A New Class of Three-Dimensional Maps with Hidden Chaotic Dynamics

2016 ◽  
Vol 26 (12) ◽  
pp. 1650206 ◽  
Author(s):  
Haibo Jiang ◽  
Yang Liu ◽  
Zhouchao Wei ◽  
Liping Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Chaotic Dynamics ◽  
Three Dimensional ◽  
Computational Procedure ◽  
Basins Of Attraction ◽  
Chaotic Attractors ◽  
Computer Search ◽  
New Class ◽  
Special Concern

This paper studies a new class of three-dimensional maps in a Jerk-like structure with a special concern of their hidden chaotic dynamics. Our investigation focuses on the hidden chaotic attractors in three typical scenarios of fixed points, namely no fixed point, single fixed point, and two fixed points. A systematic computer search is performed to explore possible hidden chaotic attractors, and a number of examples of the proposed maps are used for demonstration. Numerical results show that the routes to hidden chaotic attractors are complex, and the basins of attraction for the hidden chaotic attractors could be tiny, so that using the standard computational procedure for localization is impossible.

Lagrangian blocking in highly viscous shear flows past a sphere

2011 ◽  
Vol 669 ◽  
pp. 120-166 ◽  
Author(s):  
ROBERTO CAMASSA ◽  
RICHARD M. McLAUGHLIN ◽  
LONGHUA ZHAO
Keyword(s):  
Fixed Points ◽  
Closed Form ◽  
Three Dimensional ◽  
The Body ◽  
Fluid Particle ◽  
Background Flow ◽  
Particle Trajectories ◽  
Zero Velocity ◽  
Linear Shear ◽  
The Cross

An analytical and computational study of Lagrangian trajectories for linear shear flow past a sphere or spheroid at low Reynolds numbers is presented. Using the exact solutions available for the fluid flow in this geometry, we discover and analyse blocking phenomena, local bifurcation structures and their influence on dynamical effects arising in the fluid particle paths. In particular, building on the work by Chwang & Wu, who established an intriguing blocking phenomenon in two-dimensional flows, whereby a cylinder placed in a linear shear prevents an unbounded region of upstream fluid from passing the body, we show that a similar blocking exists in three-dimensional flows. For the special case when the sphere is centred on the zero-velocity plane of the background shear, the separatrix streamline surfaces which bound the blocked region are computable in closed form by quadrature. This allows estimation of the cross-sectional area of the blocked flow showing how the area transitions from finite to infinite values, depending on the cross-section location relative to the body. When the sphere is off-centre, the quadrature appears to be unavailable due to the broken up-down mirror symmetry. In this case, computations provide evidence for the persistence of the blocking region. Furthermore, we document a complex bifurcation structure in the particle trajectories as the sphere centre is moved from the zero-velocity plane of the background flow. We compute analytically the emergence of different fixed points in the flow and characterize the global streamline topology associated with these fixed points, which includes the emergence of a three-dimensional bounded eddy. Similar results for the case of spheroids are considered in Appendix B. Additionally, the broken symmetry offered by a tilted spheroid geometry induces new three-dimensional effects on streamline deflection, which can be viewed as effective positive or negative suction in the horizontal direction orthogonal to the background flow, depending on the tilt orientation. We conclude this study with results on the case of a sphere embedded at a generic position in a rotating background flow, with its own prescribed rotation including fixed and freely rotating. Exact closed-form solutions for fluid particle trajectories are derived.

scholarly journals Instantons, symmetries and anomalies in five dimensions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Pietro Benetti Genolini ◽  
Luigi Tizzano
Keyword(s):  
Fixed Points ◽  
Gauge Theories ◽  
Global Symmetry ◽  
Flavor Symmetry ◽  
Abelian Gauge ◽  
Five Dimensions ◽  
Fundamental Matter ◽  
Dynamical Properties ◽  
Supersymmetric Gauge ◽  
Classical Background

Abstract All five-dimensional non-abelian gauge theories have a U(1)I global symmetry associated with instantonic particles. We describe an obstruction to coupling U(1)I to a classical background gauge field that occurs whenever the theory has a one-form center symmetry. This is a finite-order mixed ’t Hooft anomaly between the two symmetries. We also show that a similar obstruction takes place in gauge theories with fundamental matter by studying twisted bundles for the ordinary flavor symmetry. We explore some general dynamical properties of the candidate phases implied by the anomaly. Finally, we apply our results to supersymmetric gauge theories in five dimensions and analyze the symmetry enhancement patterns occurring at their conjectured RG fixed points.

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