RENORMALIZATION GROUP AND STRING LOOPS

1990 ◽  
Vol 05 (04) ◽  
pp. 589-658 ◽  
Author(s):  
A.A. TSEYTLIN
Keyword(s):  
Renormalization Group ◽  
Moduli Spaces ◽  
Tree Level ◽  
Generating Functional ◽  
String Loop ◽  
Schottky Type ◽  
String Amplitudes ◽  
Group Flow ◽  
Model Approach

The fixed points of the 2-d renormalization group flow are known to correspond to the tree level string vacua. We analyze how the “renormalization group” (or “sigma model”) approach can be extended to the string loop level. The central role of the condition of renormalizability of the generating functional for string amplitudes with respect to both “local” and “modular” infinities is emphasized. Several one- and two-loop examples of renormalization are discussed. It is found that in order to ensure the renormalizability of the generating functional one is to use “extended” (e.g. Schottky-type) parametrizations of moduli spaces. An approach to a resummation of the string perturbative expansion based on operators of insertion of topological fixtures is suggested.

RENORMALIZATION GROUP FLOW AND OPEN STRING DYNAMICS

1988 ◽  
Vol 03 (18) ◽  
pp. 1797-1805 ◽  
Author(s):  
NAOHITO NAKAZAWA ◽  
KENJI SAKAI ◽  
JIRO SODA
Keyword(s):  
Renormalization Group ◽  
Sigma Model ◽  
Open String ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Renormalization Group Flow ◽  
Point Solution ◽  
Β Function ◽  
Group Flow ◽  
Model Approach

The renormalization group flow in the nonlinear sigma model approach is explicitly solved to the fourth order in the case of an open string propagating in the tachyon background. Using a regularization different from the original one used by Klebanov and Susskind (K-S), we show that its fixed point solution produces the tree-level 5-point tachyon amplitude. Furthermore we prove K-S’s conjecture, i.e., the equivalence between the vanishing β-function defined by our regularization and the equation of motion arising from the effective action, up to all orders.

RENORMALIZATION GROUP FLOW IN COLD AND DENSE YUKAWA THEORY

2007 ◽  
Vol 16 (09) ◽  
pp. 2806-2809 ◽  
Author(s):  
LETÍCIA F. PALHARES ◽  
EDUARDO S. FRAGA
Keyword(s):  
Renormalization Group ◽  
Fermion Mass ◽  
Zero Temperature ◽  
Renormalization Group Flow ◽  
Finite Density ◽  
Mass Effects ◽  
Fermion Masses ◽  
Group Flow ◽  
Yukawa Theory

We analyze the role of renormalization group (RG) running of the coupling and fermion masses in perturbative Yukawa theory at finite density. The dependence of the RG flow on the number of fermion flavors is discussed. Results for the fermionic contribution to the two-loop pressure at zero temperature and finite density are presented for NF = 4, and finite fermion mass effects are shown to be an important correction.

EXTENDED CHAMSEDDINE–FRÖHLICH APPROACH TO NONCOMMUTATIVE GEOMETRY AND THE TWO-DOUBLETS HIGGS MODEL

2007 ◽  
Vol 22 (32) ◽  
pp. 6279-6305 ◽  
Author(s):  
N. MEBARKI ◽  
M. HARRAT ◽  
M. BOUSSAHEL
Keyword(s):  
Renormalization Group ◽  
Noncommutative Geometry ◽  
Scalar Product ◽  
Higgs Model ◽  
Tree Level ◽  
Quantization Method ◽  
Renormalization Group Flow ◽  
New Approach ◽  
Mixing Angles ◽  
Group Flow

The Chamseddine–Fröhlich approach to noncommutative geometry is extended by the introduction of the strong interaction sector in the mathematical formalism, and generalization of the Dirac operator and scalar product. This new approach is applied to the reformulation of the two-doublets Higgs model where the fuzzy mass, coupling and unitarity relations as well as mixing angles are derived. These tree level relations are no more preserved under the renormalization group flow in the context of the standard quantization method.

scholarly journals Stochastic Inflation at NNLO

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Timothy Cohen ◽  
Daniel Green ◽  
Akhil Premkumar ◽  
Alexander Ridgway
Keyword(s):  
Renormalization Group ◽  
Initial Conditions ◽  
Planck Equation ◽  
Effective Theory ◽  
Tree Level ◽  
Order Effects ◽  
De Sitter ◽  
Light Scalar ◽  
Non Gaussian ◽  
Group Flow

Abstract Stochastic Inflation is an important framework for understanding the physics of de Sitter space and the phenomenology of inflation. In the leading approximation, this approach results in a Fokker-Planck equation that calculates the probability distribution for a light scalar field as a function of time. Despite its successes, the quantum field theoretic origins and the range of validity for this equation have remained elusive, and establishing a formalism to systematically incorporate higher order effects has been an area of active study. In this paper, we calculate the next-to-next-to-leading order (NNLO) corrections to Stochastic Inflation using Soft de Sitter Effective Theory (SdSET). In this effective description, Stochastic Inflation manifests as the renormalization group evolution of composite operators. The leading impact of non-Gaussian quantum fluctuations appears at NNLO, which is presented here for the first time; we derive the coefficient of this term from a two-loop anomalous dimension calculation within SdSET. We solve the resulting equation to determine the NNLO equilibrium distribution and the low-lying relaxation eigenvalues. In the process, we must match the UV theory onto SdSET at one-loop order, which provides a non-trivial confirmation that the separation into Wilson-coefficient corrections and contributions to initial conditions persists beyond tree level. Furthermore, these results illustrate how the naive factorization of time and momentum integrals in SdSET no longer holds in the presence of logarithmic divergences. It is these effects that ultimately give rise to the renormalization group flow that yields Stochastic Inflation.

The Non-Causal Character of Renormalization Group Explanations

2018 ◽  
Author(s):  
Margaret Morrison
Keyword(s):  
Probability Theory ◽  
Renormalization Group ◽  
Dynamical Systems ◽  
Recent Literature ◽  
Mathematical Explanation ◽  
Causal Status ◽  
Physical Information ◽  
The Relationship ◽  
Structural Aspects

After reviewing some of the recent literature on non-causal and mathematical explanation, this chapter develops an argument as to why renormalization group (RG) methods should be seen as providing non-causal, yet physical, information about certain kinds of systems/phenomena. The argument centres on the structural character of RG explanations and the relationship between RG and probability theory. These features are crucial for the claim that the non-causal status of RG explanations involves something different from simply ignoring or “averaging over” microphysical details—the kind of explanations common to statistical mechanics. The chapter concludes with a discussion of the role of RG in treating dynamical systems and how that role exemplifies the structural aspects of RG explanations which in turn exemplifies the non-causal features.

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 Impact of tumor-parenchyma biomechanics on liver metastatic progression: a multi-model approach

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yafei Wang ◽  
Erik Brodin ◽  
Kenichiro Nishii ◽  
Hermann B. Frieboes ◽  
Shannon M. Mumenthaler ◽  
...  
Keyword(s):  
Time Scales ◽  
Constitutive Relations ◽  
Elastic Tissue ◽  
Metastatic Progression ◽  
Patient Death ◽  
Metastatic Growth ◽  
Tumor Parenchyma ◽  
Short Time ◽  
Model Approach

AbstractColorectal cancer and other cancers often metastasize to the liver in later stages of the disease, contributing significantly to patient death. While the biomechanical properties of the liver parenchyma (normal liver tissue) are known to affect tumor cell behavior in primary and metastatic tumors, the role of these properties in driving or inhibiting metastatic inception remains poorly understood, as are the longer-term multicellular dynamics. This study adopts a multi-model approach to study the dynamics of tumor-parenchyma biomechanical interactions during metastatic seeding and growth. We employ a detailed poroviscoelastic model of a liver lobule to study how micrometastases disrupt flow and pressure on short time scales. Results from short-time simulations in detailed single hepatic lobules motivate constitutive relations and biological hypotheses for a minimal agent-based model of metastatic growth in centimeter-scale tissue over months-long time scales. After a parameter space investigation, we find that the balance of basic tumor-parenchyma biomechanical interactions on shorter time scales (adhesion, repulsion, and elastic tissue deformation over minutes) and longer time scales (plastic tissue relaxation over hours) can explain a broad range of behaviors of micrometastases, without the need for complex molecular-scale signaling. These interactions may arrest the growth of micrometastases in a dormant state and prevent newly arriving cancer cells from establishing successful metastatic foci. Moreover, the simulations indicate ways in which dormant tumors could “reawaken” after changes in parenchymal tissue mechanical properties, as may arise during aging or following acute liver illness or injury. We conclude that the proposed modeling approach yields insight into the role of tumor-parenchyma biomechanics in promoting liver metastatic growth, and advances the longer term goal of identifying conditions to clinically arrest and reverse the course of late-stage cancer.

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