scholarly journals Multiple mass hierarchies from complex fixed point collisions

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Antón F. Faedo ◽  
Carlos Hoyos ◽  
David Mateos ◽  
Javier G. Subils
Keyword(s):  
Fixed Points ◽  
Real Axis ◽  
Weak Coupling ◽  
Large Mass ◽  
Complex Conjugate ◽  
Mass Hierarchy ◽  
Renormalization Group Flow ◽  
Complex Flows ◽  
The Real ◽  
Group Flow

Abstract A pair of complex-conjugate fixed points that lie close to the real axis generates a large mass hierarchy in the real renormalization group flow that passes in between them. We show that pairs of complex fixed points that are close to the real axis and to one another generate multiple hierarchies, some of which can be parametrically enhanced. We illustrate this effect at weak coupling with field-theory examples, and at strong coupling using holography. We also construct complex flows between complex fixed points, including flows that violate the c-theorem.

scholarly journals Pseudo-hermitian random matrix theory: a review

2021 ◽  
Vol 2038 (1) ◽  
pp. 012009
Author(s):  
Joshua Feinberg ◽  
Roman Riser
Keyword(s):  
Real Axis ◽  
Complex Plane ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Complex Conjugate ◽  
Indefinite Metric ◽  
The Real ◽  
New Type ◽  
Diagrammatic Method

Abstract We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of this new type of random matrices, we focus on two specific models of matrices which are pseudo-hermitian with respect to a given indefinite metric B. Eigenvalues of pseudo-hermitian matrices are either real, or come in complex-conjugate pairs. The diagrammatic method is applied to deriving explicit analytical expressions for the density of eigenvalues in the complex plane and on the real axis, in the large-N, planar limit. In one of the models we discuss, the metric B depends on a certain real parameter t. As t varies, the model exhibits various ‘phase transitions’ associated with eigenvalues flowing from the complex plane onto the real axis, causing disjoint eigenvalue support intervals to merge. Our analytical results agree well with presented numerical simulations.

GENERALIZED COULOMB GAS MODELS WITH EXPONENTIAL INTERACTIONS AND A SERIES OF CENTRAL CHARGES

1991 ◽  
Vol 06 (12) ◽  
pp. 2189-2211
Author(s):  
MYUNG-HOON CHUNG
Keyword(s):  
Renormalization Group ◽  
Vector Field ◽  
Fixed Points ◽  
Root Systems ◽  
Coulomb Gas ◽  
Renormalization Group Flow ◽  
Geometrical Figure ◽  
Fermionic Fields ◽  
Background Charge ◽  
Group Flow

The renormalization of the generalized Coulomb gas model with exponential interactions is studied. This model contains a bosonic vector field and several fermionic fields in the presence of a background charge vector. It is shown that the vectors associated with the exponential interactions should satisfy certain conditions for the action to be renormalizable. The conditions require the vectors to form a geometrical figure. In particular, models are considered where the vectors are root systems which form equilateral geometrical figures. Explicit β-functions are obtained for these models. They show several nontrivial fixed points at which the central charges of the system are evaluated. It is found that a renormalization group flow connects the extremal nontrivial fixed points. Some possible applications are indicated.

ON THE RENORMALIZATION GROUP FLOW IN N = 2 SUPERCONFORMAL MODELS

1990 ◽  
Vol 05 (27) ◽  
pp. 2261-2265 ◽  
Author(s):  
E. GAVA ◽  
M. STANISHKOV
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Renormalization Group Flow ◽  
Β Function ◽  
Group Flow ◽  
Chiral Superfield

We show that the β-function of N = 2 superconformal models perturbed by a slightly relevant chiral superfield does not have non-trivial IR fixed points to all orders in perturbation theory.

scholarly journals INTERACTING WESS–ZUMINO–NOVIKOV–WITTEN MODELS

1996 ◽  
Vol 11 (14) ◽  
pp. 2591-2611
Author(s):  
OLEG A. SOLOVIEV
Keyword(s):  
Renormalization Group ◽  
Strong Coupling ◽  
Weak Coupling ◽  
Chiral Model ◽  
Renormalization Group Flow ◽  
Coupling Phase ◽  
Duality Symmetry ◽  
Current Interaction ◽  
Principal Chiral Model ◽  
Group Flow

We study the system of two WZNW models coupled to each other via the current–current interaction. The system is proven to possess the strong/weak coupling duality symmetry. The strong coupling phase of this theory is discussed in detail. It is shown that in this phase the interacting WZNW models approach nontrivial conformal points along the renormalization group flow. The relation between the principal chiral model and interacting WZNW models is investigated.

scholarly journals 3d large $N$ vector models at the boundary

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Lorenzo Di Pietro ◽  
Edoardo Lauria ◽  
Pierluigi Niro
Keyword(s):  
Fixed Point ◽  
Weak Coupling ◽  
Vector Model ◽  
Boundary Theory ◽  
Weak Duality ◽  
Renormalization Group Flow ◽  
Boundary Interaction ◽  
Large N ◽  
Group Flow ◽  
N Vector

We consider a 4d scalar field coupled to large NN free or critical O(N)O(N) vector models, either bosonic or fermionic, on a 3d boundary. We compute the \betaβ function of the classically marginal bulk/boundary interaction at the first non-trivial order in the large NN expansion and exactly in the coupling. Starting with the free (critical) vector model at weak coupling, we find a fixed point at infinite coupling in which the boundary theory is the critical (free) vector model and the bulk decouples. We show that a strong/weak duality relates one description of the renormalization group flow to another one in which the free and the critical vector models are exchanged. We then consider the theory with an additional Maxwell field in the bulk, which also gives decoupling limits with gauged vector models on the boundary.

scholarly journals Ruppeiner curvature along a renormalization group flow

2021 ◽  
pp. 136450
Author(s):  
Pavan Kumar Yerra ◽  
Chandrasekhar Bhamidipati
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Flow ◽  
Group Flow

scholarly journals RG flows of integrable σ-models and the twist function

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
François Delduc ◽  
Sylvain Lacroix ◽  
Konstantinos Sfetsos ◽  
Konstantinos Siampos
Keyword(s):  
Renormalization Group ◽  
Large Class ◽  
Rational Function ◽  
Integrable Model ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Non Linear ◽  
Group Flow

Abstract In the study of integrable non-linear σ-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central rôle. For a large class of such models, we show that they are one-loop renormalizable, and that the renormalization group flow equations can be written directly in terms of the twist function in a remarkably simple way. The resulting equation appears to have a universal character when the integrable model is characterized by a twist function.

On Graeffe's Method for Complex Roots of Algebraic Equations

1924 ◽  
Vol 22 (2) ◽  
pp. 83-87 ◽  
Author(s):  
S. Brodetsky ◽  
G. Smeal
Keyword(s):  
Nineteenth Century ◽  
Real Axis ◽  
Practical Method ◽  
Algebraic Equations ◽  
Argand Diagram ◽  
Considerable Difficulty ◽  
The Real ◽  
Real Roots ◽  
Bipolar Coordinates ◽  
Complex Roots

The only really useful practical method for solving numerical algebraic equations of higher orders, possessing complex roots, is that devised by C. H. Graeffe early in the nineteenth century. When an equation with real coefficients has only one or two pairs of complex roots, the Graeffe process leads to the evaluation of these roots without great labour. If, however, the equation has a number of pairs of complex roots there is considerable difficulty in completing the solution: the moduli of the roots are found easily, but the evaluation of the arguments often leads to long and wearisome calculations. The best method that has yet been suggested for overcoming this difficulty is that by C. Runge (Praxis der Gleichungen, Sammlung Schubert). It consists in making a change in the origin of the Argand diagram by shifting it to some other point on the real axis of the original Argand plane. The new moduli and the old moduli of the complex roots can then be used as bipolar coordinates for deducing the complex roots completely: this also checks the real roots.

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