scholarly journals ${\mathcal N}=8$ GAUGED SUPERGRAVITY THEORY AND ${\mathcal N}=6$ SUPERCONFORMAL CHERN–SIMONS MATTER THEORY

2010 ◽  
Vol 25 (17) ◽  
pp. 3407-3444 ◽  
Author(s):  
CHANGHYUN AHN ◽  
KYUNGSUNG WOO
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Flow ◽  
Supergravity Theory ◽  
Four Dimensions ◽  
Probe Analysis ◽  
Matter Theory ◽  
Mass Terms ◽  
Group Flow ◽  
Chern Simons

By studying the previously known holographic [Formula: see text] supersymmetric renormalization group flow (Gowdigere–Warner) in four dimensions, we find the mass deformed Chern–Simons matter theory which has [Formula: see text] supersymmetry by adding the four mass terms among eight adjoint fields. The geometric superpotential from the 11 dimensions is found and provides the M2-brane probe analysis. As second example, we consider known holographic [Formula: see text] supersymmetric renormalization group flow (Pope–Warner) in four dimensions. The eight mass terms are added and similar geometric superpotential is obtained.

scholarly journals Generalized global symmetries of T[M] theories. Part I

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Sergei Gukov ◽  
Po-Shen Hsin ◽  
Du Pei
Keyword(s):  
Renormalization Group ◽  
Symmetry Breaking ◽  
General Framework ◽  
Dimensional Manifold ◽  
Renormalization Group Flow ◽  
Dimensional Theory ◽  
Group Flow ◽  
Group Symmetries ◽  
Chern Simons ◽  
Special Case

Abstract We study reductions of 6d theories on a d-dimensional manifold Md, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting (6 −d)-dimensional theory T[Md]. We refine and generalize the notion of “polarization” to polarization on Md, which serves to fix the spectrum of local and extended operators in T[Md]. Another important feature of theories T[Md] is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries. We study the origin of such symmetries as well as physical implications including symmetry breaking and symmetry enhancement in the renormalization group flow. To better probe the IR physics, we also investigate the ’t Hooft anomaly of 5d Chern-Simons matter theories. The present paper focuses on developing the general framework as well as the special case of d = 0 and 1, while an upcoming paper will discuss the case of d = 2, 3 and 4.

scholarly journals Renormalization group flow of Chern-Simons boundary conditions and generalized Ricci tensor

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Ján Pulmann ◽  
Pavol Ševera ◽  
Donald R. Youmans
Keyword(s):  
Boundary Condition ◽  
Renormalization Group ◽  
Boundary Conditions ◽  
Ricci Tensor ◽  
Simons Theory ◽  
Renormalization Group Flow ◽  
Group Flow ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We find a Chern-Simons propagator on the ball with the chiral boundary condition. We use it to study perturbatively Chern-Simons boundary conditions related to 2-dim σ-models and to Poisson-Lie T-duality. In particular, we find their renormalization group flow, given by the generalized Ricci tensor. Finally we briefly discuss what happens when the Chern-Simons theory is replaced by a Courant σ-model or possibly by a more general AKSZ model.

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.

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