scholarly journals Two dimensional renormalization group flows in next to leading order

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Rubik Poghossian
Keyword(s):  
Renormalization Group ◽  
Two Dimensional ◽  
Leading Order ◽  
Renormalization Group Flows

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

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 Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clifford V. Johnson ◽  
Felipe Rosso
Keyword(s):  
Phase Structure ◽  
Scalar Potential ◽  
String Equation ◽  
Two Dimensional ◽  
Leading Order ◽  
Classical Analysis ◽  
First Order ◽  
First Order Phase Transition ◽  
Definition Of ◽  
First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

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