scholarly journals Evidence for a 5d F-theorem

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Martin Fluder ◽  
Christoph F. Uhlemann
Keyword(s):  
Free Energy ◽  
Renormalization Group ◽  
General Expression ◽  
Geometric Parameters ◽  
Regularity Conditions ◽  
Large Sample ◽  
Large Numbers ◽  
Renormalization Group Flows

Abstract Renormalization group flows are studied between 5d SCFTs engineered by (p, q) 5-brane webs with large numbers of external 5-branes. A general expression for the free energy on S5 in terms of single-valued trilogarithm functions is derived from their supergravity duals, which are characterized by the 5-brane charges and additional geometric parameters. The additional geometric parameters are fixed by regularity conditions, and we show that the solutions to the regularity conditions extremize a trial free energy. These results are used to survey a large sample of $$ \mathcal{O} $$ O (105) renormalization group flows between different 5d SCFTs, including Higgs branch flows and flows that preserve the SU(2) R- symmetry. In all cases the free energy changes monotonically towards the infrared, in line with a 5d F -theorem.

scholarly journals HETEROTIC T-DUALITY AND THE RENORMALIZATION GROUP

1999 ◽  
Vol 14 (14) ◽  
pp. 2257-2271 ◽  
Author(s):  
KASPER OLSEN ◽  
RICARDO SCHIAPPA
Keyword(s):  
Renormalization Group ◽  
Sigma Models ◽  
Sigma Model ◽  
Beta Function ◽  
Target Space ◽  
Loop Order ◽  
Duality Transformations ◽  
Duality Symmetry ◽  
The One ◽  
Renormalization Group Flows

We consider target space duality transformations for heterotic sigma models and strings away from renormalization group fixed points. By imposing certain consistency requirements between the T-duality symmetry and renormalization group flows, the one-loop gauge beta function is uniquely determined, without any diagram calculations. Classical T-duality symmetry is a valid quantum symmetry of the heterotic sigma model, severely constraining its renormalization flows at this one-loop order. The issue of heterotic anomalies and their cancellation is addressed from this duality constraining viewpoint.

PERTURBED W3 CONFORMAL THEORIES AND SPIN-4/3 PARAFERMIONIC COSET MODELS

1991 ◽  
Vol 06 (25) ◽  
pp. 2281-2287 ◽  
Author(s):  
R. B. MANN ◽  
H. B. ZHENG
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Renormalization Group Flows ◽  
Coset Models

Renormalization group flows in W3, conformal theories are analyzed in relation to the ones in spin-4/3 parafermionic coset models and some of the operator content for new fixed points is identified.

Consistency of Sample Estimates of Risk Averse Stochastic Programs

2013 ◽  
Vol 50 (02) ◽  
pp. 533-541 ◽  
Author(s):  
Alexander Shapiro
Keyword(s):  
Stochastic Programming ◽  
Law Of Large Numbers ◽  
Risk Measures ◽  
Regularity Conditions ◽  
Distributed Data ◽  
Risk Averse ◽  
Asymptotic Consistency ◽  
Stochastic Programs ◽  
Large Numbers ◽  
Independent Identically Distributed

In this paper we study asymptotic consistency of law invariant convex risk measures and the corresponding risk averse stochastic programming problems for independent, identically distributed data. Under mild regularity conditions, we prove a law of large numbers and epiconvergence of the corresponding statistical estimators. This can be applied in a straightforward way to establish convergence with probability 1 of sample-based estimators of risk averse stochastic programming problems.

scholarly journals FREE ENERGY DECREASES ALONG WILSON RENORMALIZATION GROUP TRAJECTORIES

1995 ◽  
Vol 10 (21) ◽  
pp. 1543-1548 ◽  
Author(s):  
VIPUL PERIWAL
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Spectral Representation ◽  
Point Function ◽  
Cutoff Function ◽  
Wilson Renormalization Group

The free energy is shown to decrease along Wilson renormalization group trajectories, in a dimension-independent fashion, for d>2. The argument assumes the monotonicity of the cutoff function, and positivity of a spectral representation of the two-point function. The argument is valid for all orders in perturbation theory.

Estimates on Renormalization Group Transformations

1998 ◽  
Vol 50 (4) ◽  
pp. 756-793 ◽  
Author(s):  
D. Brydges ◽  
J. Dimock ◽  
T. R. Hurd
Keyword(s):  
Renormalization Group ◽  
Gaussian Measure ◽  
Ultra Violet ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
Scalar Quantum ◽  
Polymer Expansion ◽  
Renormalization Group Flows

AbstractWe consider a specific realization of the renormalization group (RG) transformation acting on functional measures for scalar quantum fields which are expressible as a polymer expansion times an ultra-violet cutoff Gaussian measure. The new and improved definitions and estimates we present are sufficiently general and powerful to allow iteration of the transformation, hence the analysis of complete renormalization group flows, and hence the construction of a variety of scalar quantum field theories.

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