scholarly journals Probing the Infrared Structure of Gauge Theories: A Padé-Approximant Approach

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 913-915 ◽  
Author(s):  
F. A. Chishtie ◽  
V. Elias ◽  
V. A. Miransky ◽  
T. G. Steele
Keyword(s):  
Fixed Point ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Padé Approximants ◽  
Padé Approximant ◽  
Pade Approximants ◽  
Pade Approximant ◽  
Specific Choice ◽  
Large N ◽  
Β Function

Padé-approximant treatments of the known terms of the QCD β-function are seen to develop possible infrared fixed point structure only if the number of fermion flavours is sufficiently large. This flavour threshold is seen to be between six and nine flavours, depending upon both the specific choice of approximant as well as on the presently-unknown five-loop β-function contribution. Below this flavour threshold, Padé approximants based upon the QCD β-function manifest the same infrared attractor structure as that which characterizes the exact NSVZ β-function of supersymmetric gluodynamics. Such infrared attractor structure is also seen to characterize Padé-approximant treatments of vector SU(N) gauge theory in the large N limit, suggesting common infrared dynamics for the strong and weak phases of this theory.

Padé Approximant Calculation of p-Wave π–π Scattering with a σ Model Lagrangian

1971 ◽  
Vol 49 (3) ◽  
pp. 360-366
Author(s):  
D. K. Elias
Keyword(s):  
Padé Approximants ◽  
Padé Approximant ◽  
P Wave ◽  
Pade Approximants ◽  
Pade Approximant ◽  
Wave Channel ◽  
Wave Resonance ◽  
Text Interaction ◽  
Range Of Values ◽  
D Wave

A π–π it interaction via a scalar I = 0, σ exchange is considered. The contribution of the t and u channel exchanges of the σ to the p-wave, I = 1 amplitude is calculated using Padé approximants. A p-wave resonance, interpreted as the p meson, the width of which depends on the mass of the input a meson, is found; for a certain range of values of the σ mass the ρ width compares not unfavorably with similar calculations using a [Formula: see text] interaction. However, for the range of masses considered the width is considerably smaller than the experimental value. The I = 0, d-wave channel is also considered and a resonance, interpreted as the ƒ0(1260), is found.

scholarly journals Weakly coupled conformal gauge theories on the lattice

2018 ◽  
Vol 175 ◽  
pp. 08028
Author(s):  
Zoltan Fodor ◽  
Kieran Holland ◽  
Julius Kuti ◽  
Daniel Nogradi ◽  
Chik Him Wong
Keyword(s):  
Fixed Point ◽  
Perturbation Theory ◽  
Gauge Theories ◽  
Conformal Window ◽  
Lattice Methods ◽  
Weakly Coupled ◽  
Conformal Gauge ◽  
Β Function

Results are reported for the β-function of weakly coupled conformal gauge theories on the lattice, SU(3) with Nf = 14 fundamental and Nf = 3 sextet fermions. The models are chosen to be close to the upper end of the conformal window where perturbation theory is reliable hence a fixed point is expected. The study serves as a test of how well lattice methods perform in the weakly coupled conformal cases. We also comment on the 5-loop β-function of two models close to the lower end of the conformal window, SU(3) with Nf = 12 fundamental and Nf = 2 sextet fermions.

LONG DISTANCE DYNAMICS AND CONFINEMENT VIA RG DECIMATIONS

2009 ◽  
Vol 24 (34) ◽  
pp. 2717-2730 ◽  
Author(s):  
E. T. TOMBOULIS
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Upper And Lower Bounds ◽  
Free Energies ◽  
Long Distance ◽  
Strongly Coupled ◽  
Four Dimensions ◽  
Lattice Regularization

We review a recently developed framework employing computable Renormalization Group (RG) decimations for gauge theories in the lattice regularization. They provide upper and lower bounds at every scale for free energies and some order parameters. By interpolating between these bounds representations of the exact quantities are obtained at progressively longer scales (coarser lattices). In the case of the SU(2) gauge theory in four dimensions RG flow to the confining strongly coupled regime is obtained for any initial coupling; whereas for the U(1) theory a fixed point is reached for small initial coupling.

scholarly journals Large N gauge theories with a dense spectrum and the weak gravity conjecture

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Prarit Agarwal ◽  
Jaewon Song
Keyword(s):  
Gauge Theory ◽  
General Theory ◽  
Quantum Gravity ◽  
Gauge Theories ◽  
Degree Of Freedom ◽  
Large N ◽  
The Matrix ◽  
Weak Gravity

Abstract We find large N gauge theories containing a large number of operators within a band of low conformal dimensions. One of such examples is the four-dimensional $$ \mathcal{N} $$ N = 1 supersymmetric SU(N) gauge theory with one adjoint and a pair of fundamental/anti-fundamental chiral multiplets. This theory flows to a superconformal theory in the infrared upon a superpotential coupling with gauge singlets. The gap in the low-lying spectrum scales as 1/N and the central charges scale as O(N1) contrary to the usual O(N2) scaling of ordinary gauge theory coming from the matrix degree of freedom. We find the AdS version of the Weak Gravity Conjecture (WGC) holds for this theory, although it cannot be holographically dual to supergravity. This supports the validity of WGC in a more general theory of quantum gravity.

scholarly journals ONE-LOOP RENORMALIZATION OF NON-ABELIAN GAUGE THEORY AND β FUNCTION BASED ON LOOP REGULARIZATION METHOD

2008 ◽  
Vol 23 (19) ◽  
pp. 2861-2913 ◽  
Author(s):  
JIAN-WEI CUI ◽  
YUE-LIANG WU
Keyword(s):  
Gauge Theory ◽  
Regularization Method ◽  
Gauge Theories ◽  
Field Theories ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Cutoff Energy ◽  
Original Field ◽  
Β Function ◽  
Renormalization Constants

All one-loop renormalization constants for non-Abelian gauge theory are computed in detail by using the symmetry-preserving loop regularization method proposed in Refs. 1 and 2. The resulting renormalization constants are manifestly shown to satisfy Ward–Takahaski–Slavnov–Taylor identities, and lead to the well-known one loop β function for non-Abelian gauge theory of QCD.3-5 The loop regularization method is realized in the dimension of original field theories, it maintains not only symmetries but also divergent behaviors of original field theories with the introduction of two energy scales. Such two scales play the roles of characterizing and sliding energy scales as well as ultraviolet and infrared cutoff energy scales. An explicit check of those identities provides a clear demonstration how the symmetry-preserving loop regularization method can consistently be applied to non-Abelian gauge theories.

Asymptotic Padé Approximants and the SQCD β-function

1997 ◽  
Vol 407 (2) ◽  
pp. 143-146 ◽  
Author(s):  
I. Jack ◽  
D.R.T. Jones ◽  
M.A. Samuel
Keyword(s):  
Padé Approximants ◽  
Pade Approximants ◽  
Β Function
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