scholarly journals Probing renormalization group flows using entanglement entropy

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Hong Liu ◽  
Márk Mezei
Keyword(s):  
Renormalization Group ◽  
Entanglement Entropy ◽  
Renormalization Group Flows

scholarly journals Holographic and localization calculations of boundary F for $$ \mathcal{N} $$ = 4 SUSY Yang-Mills theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Mark Van Raamsdonk ◽  
Chris Waddell
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Partition Function ◽  
Boundary Conditions ◽  
Half Space ◽  
Scale Invariance ◽  
Entanglement Entropy ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Renormalization Group Flows

Abstract $$ \mathcal{N} $$ N = 4 Supersymmetric Yang-Mills (SYM) theory can be defined on a half-space with a variety of boundary conditions preserving scale invariance and half of the original supersymmetry; more general theories with the same symmetry can be obtained by coupling to a 3D SCFT at the boundary. Each of these theories is characterized by a quantity called “boundary F”, conjectured to decrease under boundary renormalization group flows. In this paper, we calculate boundary F for U(N) $$ \mathcal{N} $$ N = 4 SYM theory with the most general half-supersymmetric boundary conditions arising from string theory constructions with D3-branes ending on collections of D5-branes and/or NS5-branes. We first perform the calculation holographically by evaluating the entanglement entropy for a half-ball centered on the boundary using the Ryu-Takayanagi formula in the dual type IIB supergravity solutions. For boundary conditions associated with D3-branes ending on D5 branes only or NS5-branes only, we also calculate boundary F exactly by evaluating the hemisphere partition function using supersymmetric localization. The leading terms at large N in the supergravity and localization results agree exactly as a function of the t’ Hooft coupling λ.

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.

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